17 December 2004 | Draft
using geometry to embody developmental integrity
- / -
Case for multi-dimensional accounting
"Three sets of books": shadow of the "bottom line"
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.
Case for multi-dimensional accounting
Chris Lucas (Multidimensional
Economics, 1999) outlines a complexity-based economics in the light
of the following assessment.
Current economic theory reduces all things to one dimension, that of monetary
value, in fact that seems to be the whole basis of the science. Yet value
is not in itself a one dimensional concept, we value many things that are
impossible to classify in such linear monetary terms, air or sunlight for
example. Complex notions of value require a type of economics that is itself
complex and multi-dimensional, a value system that goes beyond the trade based
concept of material exchange and takes into account the wider needs of people
Vahe Poladian, et al (Time
is Not Money: The case for multi-dimensional accounting in value-based software
engineering, 2003) argue that:
Indeed, in theoretical economics all costs can, in principle, be expressed
in dollars. Software engineering problems, however, often present situations
in which converting all costs to a common currency is problematical. In this
paper we pinpoint some of these situations and the underlying causes of the
problems, and we argue that it is often better to treat costs as a multidimensional
value, with dimensions corresponding to distinct types of resources. We go
on to highlight the differences among cost dimensions that need to be considered
when developing cost-benefit analyses, and we suggest mechanisms for mediating
among heterogeneous cost dimensions.
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
The results of this study indicate that the form of the representation of
data affects the accuracy of the predictions novices make based on that data.
Additionally, one can conclude that multidimensional visual representation
of complex multidimensional data results in greater decision making accuracy
because it facilitates the direct examination of the complex relationships
in the data. This conclusion has implications within the realm of accounting
with respect to decision-making when multiple variables are involved. As variables
increase in complexity (defined as dimensionality), there should be representations
that show the interaction among the variables to help enhance decision-making
accuracy. Furthermore, with the trend towards supporting decision-making with
multidimensional data using on-line analytical processing (OLAP), knowledge
discovery, and data mining tools, this conclusion implies that in the future,
designers of advanced accounting information systems should be cognizant of
the need to "fit" the dimensionality of the data to the dimensionality of
the visual representation. Otherwise, the effectiveness of the decision maker
may be compromised.
Bookkeeping: The Mathematical Formulation and Generalization, 1986)
explores the lack of any mathematical exploration of standard double entry bookkeeping
which might enable its generalization:
With [one] exception, the author has not been able to find a single mathematics
book, elementary or advanced, popular or esoteric, which notes that the ordered
pairs of the group of differences construction are the T-accounts used in
the business world for about five centuries. And this mathematical basis for
DEB is totally unknown in the "parallel universe" of accounting. This almost
complete lack of cross-fertilization between mathematics and accounting is
a topic of some interest for intellectual history and the sociology of knowledge.
The story is probably rather simple from the mathematics side. Double-entry
bookkeeping is apparently too mundane to hold the sustained attention of mathematicians.
The real question lies on the accounting side. Over the last century, how
could professional accountants and accounting professors have failed to find
the mathematical basis for DEB even though it was part of undergraduate algebra?
[see also below]
In arguing for "a more flexible approach to logic chains", Réal Lavergne
Management and Accountability for Enhanced Aid Effectiveness, 2002)
One of the dangers of the textbook logical framework analysis (LFA) is that
it seems to imply a degree of orderliness and certainty about managing for
development that often belies reality. At least superficially, the logic model
assumes that there is consensus about the goals and objectives of the project
and about the choice of strategies to achieve those goals and objectives.
It also implies a linear chain of causality from inputs and activities to
outputs and successive levels of outcomes, of the sort that one can observe
in the HIV/AIDS example cited above. It suggests a degree of predictability
that makes it possible to plan in advance and a capacity to measure outcomes
that may be unrealistic in many cases.
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
As a process which aggregates information and subjective opinions, the financial
evaluation of the company raises very many problems relating to issues such
as measurement, imprecision and uncertainty. The methods used in the process
of financial evaluation are classically based on additivity. By construction,
these methods abandon the idea of expressing phenomena of synergy (or redundancy,
nay mutual inhibition) linked to over-additivity (or under-additivity) that
may be observed between the elements of an organised set such as a firm's
assets. This synergy (respectively redundancy) effect may lead to a value
of the set of assets greater (resp. lower) than the sum of the values of all
assets. This is particularly the case in the presence of intangible assets
as good will.
"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
As a result, double-entry bookkeeping can only be called an "absolutely perfect
system" in a world where there are no time intervals worth mentioning between
the expectation, the agreement, and the claim. This may have been the case
in our world 500 years ago, where merchants brought their commodities to the
market and transactions were completed within a single day. Unlike then, in
our modern society there is often a considerable span of time between the
measurement points expected and agreed, and also between agreed and realized.
These time intervals can be seen in both income and expense accounts.
He concluded that:
... despite its overwhelming formal strength, double-entry bookkeeping still
has extreme serious weaknesses as far as its description range is concerned.
The very method once considered to be a step forward and the stroke of genius,
must now be seen as a logical straitjacket preventing complete and timely
descriptions of the financial position.
Therefore, I am of the opinion that the epistemological problem of accounting
could be on the brink of a solution, if the reader accepts the following two
conclusions involving a rejection of the teleological explanation and basing
it on the causal explanation:
1. In its original form, the double-entry bookkeeping system is a model for
describing, explaining, and predicting the financial consequences of the operations
of an organization.
2. The double-entry bookkeeping system is a logically incomplete model since
the time intervals of expected/agreed and agreed/realized are absent in a
model that only describes the time interval of realized/paid.
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:
A distinction is made between vertical and horizontal double-entry bookkeeping,
which, if applied simultaneously, result in quadruple-entry bookkeeping. Vertical
bookkeeping refers to the double-entry bookkeeping used in business practice.
Horizontal bookkeeping requires that the transactions and other economic relationships
between agents answer strict consistency rules regarding valuation, timing,
and classification. At the micro level, this consistency is not guaranteed.
The article reviews three options to reinforce the micro-macro link... and
concludes with a few suggestions that could be used in the upcoming revisions
of the international statistical manuals.
Harry Postner (Winter
of Our Discontents: A Personal View of the National Economic Accounts,
2001) discusses the relationship between economic accounting and commercial
First, it should be noted that national accounts are an aggregation of the
economy's sectoral accounts. Each sectoral group of economic transactors,
for example, households or corporate enterprises, practises double-entry bookkeeping
for its transactions over the sector's own sequence of accounts... The accounting
entries are also inter-related through cross-sectoral transaction articulation,
for example, employee compensation received by households equals employee
compensation paid by (corporate) enterprises. This implies the system as a
whole practises quadruple-entry bookkeeping that is a unique feature of a
complete set of national economic accounts. The idea of sectoral interdependence
is the centre of attention.
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
- the work of Ijiri [1966, 1975] on multidimensional accounting,
- the work by McCarthy [1978, 1979, 1982] on the REA model and his suggestion
that conventional accounting reports should be defined as views of an underlying
set of facts about the enterprise, and his willingness to abandon double-entry
accounting that shaped the Resource and Exchange Events (REE) model
- the work of Weber [1977, 1986] on packaged software as a source of evidence
about how computer-based accounting is currently practiced. [more]
Examples of multidimensional accounting include:
- Multicurrency General Ledger: Its operation and control are fully automated.
All trades forming part of the accounting process are identified by their
monetary origin and, through a given exchange rate, the value of the transaction
is calculated at its monetary equivalency.
- Multiple Structures: The accounting of an institution is organized from
a basic structure so as to be able to draw out information by specific criteria
in a way that is both automatic and on line, without having to manipulate
it outside the books or incur costly manual processes.
- Parameter model: The double-entry accounting system is supplemented by matrix
accounting, so that each account (according to the needs or criteria of each
user) stores through parameters, balances and movements, without having to
establish additional accounts. In the based on a matrix, lines represent accounts
and columns represent parameters (criteria) associated with each of them.
So, with just one record, each account stores the required criteria that can
then be consulted according to need.
Vector accounting: David Ellerman (Double Entry
Multidimensional Accounting, 1986) proposes a model of double entry multidimensional
accounting using vectors of property rights. He notes that:
There is, in modern algebra, a standard construction called the group
of differences [or 'Pacioli
group' named after the "Father of Accounting", Luca Pacioli (Summa
de arithmetica, geometrica, proportioni et proportionalita, 1494)]...
the intuitive algebra of T-accounts used in double entry bookkeeping is precisely
equivalent to that group of differences construction.... The T-accounts of
double entry bookeeping are the ordered pairs of the group of differences
construction... Double entry bookkeeping lives in group theory, not in matrix
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").
...vector accounting shows that an accounting equation can still be used
in the presence of incomparability between dimensions by using vector equations.
This is a mathematical fact independent of the content. the content of the
vector accounting formalism could be property accounting, social accounting,
accounting for physical inventories at different locations, and so forth.
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
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.
|Table 1: Accounting bottom lines
|Single bottom line
||Accounting isolated from non-local,
non-economic, financial factors
||Accounting isolated from non-economic,
financial factors -- although subject to legal constraints (health and safety
|Double bottom line
||Accounting partially conditioned
by legal constraints (health and safety legislation) on the enterprise
||Accounting partially conditioned
by social constraints beyond those envisaged by legislation. Structural
adjustment "with a human face"
|Triple bottom line
||Accounting conditioned by impact
on the immediate natural and social environment (localized
corporate social responsibility)
||Accounting conditioned by impact
on the wider natural environment and social environment (global
corporate social responsibility)
|Quadruple bottom line
||Accounting recognizing a relationship
with the transcendent, providing for that relation in decision-making (as
in faith-based governance) and exhibiting a degree of openness to wider
||Accounting reflecting involvement
of stakeholders (including employees) in ethics of strategic decision-making,
management practices and governance
|Quintuple bottom line
||Accounting recognizing a relationship
with the transcendent, providing for that relation in decision-making and
exhibiting a degree of openness to wider community
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):
Almost inevitably, sustainability accounting currently deals with economic,
environmental and social issues in relative isolation from each other. Attempts
are being made to explore the inter-relationships between these three central
pillars of sustainability...but, with the possibility of some experimentation
with integrated performance indicators (socio/economic or eco-financial),
corporate progress towards sustainability is mainly measured in discrete chunks
rather than as an integrated whole.
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
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
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.
- A relationship with the transcendent, generally seen as both immanent and
transcendental. This relationship is focused on trust, surrender and for Sufis,
- A practice, either regular meditation or some type of prayer (but not prayer
where the goal is to ask for particular products or for the train to come
- A physical practice to transform or harmonize the body - yoga, tai chi,
chi kung, and other similar practices.
- Social - a relationship with the community, global, or local, a caring
for others. This differs from a debate on whose God, or who is true and who
is false, to an epistemology of depth and shallow with openness and inclusion
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.
"Three sets of books": shadow of the "bottom
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:
- A decade ago, the Italian government revised the gross domestic product
upward by about 17% to account for the black market, although it is generally
acknowledged that this percentage is still too low. Italians like to joke
about taxes: "We have three sets of books: one for the government, one for
the bank, and one for ourselves." [more]
- "Organized crime controls retail... Hotel managers know how much they have
to provide for the mob cut. Most Russians keep three sets of books: the books
for the mob, the ones for the tax collector and the real books." [more]
- How much money does the business really make? I have heard it said that
some shopkeepers keep three sets of books - one for the tax man showing they
made no money; one for the buyer showing they made lots of money; and one
for themselves telling the truth. [more]
- And because factories in developing countries often supply a variety of
buyers, they are faced with many different, and sometimes conflicting, codes
of conduct. Some factories "have two or three sets of books" to deceive tax
collectors and multinational purchasers about working conditions and the real
costs of production. [more]
- Another ... company told us how they keep three sets of books: one for the
overseas investor, one for tax man and another showing what was actually happening.
This kind of sometimes necessary "triple-think" encourages those involved
to be deceptive and makes others think that all business is simply a racket.
- In Indonesia, before the revival of the capital market and the introduction
of accounting reforms in the 1980s and early 1990s, it had been common for
private companies to maintain three sets of books -- one which showed the
"true" state of the business and was used for management decision-making;
one which showed a positive result and which was used for raising loans from
foreign and local banks; and one which showed a loss or small profit and was
used for taxation purposes.
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:
By entering a 2-digit code in a hidden location, a second set of votes is
created. This set of votes can be changed, so that it no longer matches the
correct votes. The voting system will then read the totals from the bogus
vote set. It takes only seconds to change the votes, and to date not a single
location in the U.S. has implemented security measures to fully mitigate the
risks....The GEMS program ... typically receives incoming votes by modem,
though some counties follow better security by disconnecting modems and bringing
votes in physically. GEMS stores the votes in a vote ledger...Any properly
designed accounting program will allow only one set of books.... But in the
files we examined, we found that the GEMS system contained three sets of "books."
(Bev Harris, Diebold
GEMS central tabulator contains a stunning security hole 30 August
2004) [more |
more | more
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):
2: Accounting sets of books
(regulatory authority, fiscal authorities)
(bank, lawyers, etc)
|declared profit/loss in standard financial
tax avoidance; use of tax havens; stock options (as a means of tax avoidance);
bribes and kickbacks; "commissions"; overbilling; overselling
|social audit; compliance with labour conventions;
worker representation; gender equality
||outsourcing to less constrained
regimes, externalizing losses; non-compliance with labour legislation
||concealed exploitation of
employees and suppliers
|environmental audit (energy, water); minimize
adverse environmental impacts; compliance with standards
||lobbying for favourable
legislation and loopholes; undue influence on regulatory bodies and inspectors;
exporting toxic waste; non-compliance
||concealed discharge of wastes
|ethical decision-making &
practices; gerrymandering; croneyism; nepotism; price-fixing cartels
the table" deals with employees
|faith-based decision-making, appeals for divine
blessing by decision-makers
manipulation of gullible believers; reporting on sins
in confession only
This table benefitted from the insights of
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:
- the kind of thinking that is articulated in detailed project analysis, replete
with systems diagrams respectful of the complexity held to lie within the
boundaries of the system with which the project is concerned -- but totally
lacking in any coherent overview comprehensible to wider audiences called
upon to assess the merits of the initiative
- the kind of imaginative presentation, using the best aesthetic input, to
convey a "concept" to a wider audience -- but totally lacking the
pattern of connectedness on which the viability of the initiative depends.
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
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
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:
Clearly the most favored representations of a total set of human needs are
the list and the table-matrix. However, both conceal the question of completeness,
as noted below.
A list does not order the relationships between its elements except in relation
to nested sublists or in the case of a list in series form. This does not
imply that such relationships are lacking, merely that they cannot be reflected
in the list form. Note that a list is in fact a series of "points," but it
is not necessary to conceive of it as such. The points could be represented
as areas on a surface. It is only in the matrix that the manner in which the
total area is cut up becomes explicit.
The cells of a matrix may be thought of as subareas of the area representing
the totality that the matrix attempts to reflect. The subareas are, of course,
positioned with respect to column and row commonalities. It is now interesting
to ask why the area is bounded in such a limiting manner, for the rectangular
or square form is one of the simplest. It provides a (paned) "window" through
which the totality may be perceived. But it raises questions about the "wall"
in which the window is set and the position of the observer in relation to
the observed on the other side of the window.
Now to the extent that the matrix is complete in its coverage, there really
should not be any "wall." The matrix should in such cases in effect "wrap
around" the observer; all is window and nothing is implicit, unexplicated,
or excluded. If this is not so, then the wall should be conceived as wrapping
around the observer, possibly with other windows corresponding to other partial
views of the external totality to which the observer may turn his attention.
From this point of view the conventional two-dimensional matrix raises the
question of the conceptual significance of crossing the encompassing boundary.
It seems irrational and unmeaningful because the wall is unrecognized. There
is almost a flavor of danger of "falling over the edge," as sailors feared
with the early "flat earth" models.
If it is assumed that the matrix is complete, then it should be possible
to represent it without such an arbitrary external boundary. If the external
boundary is eliminated, then the matrix takes the form of a closed surface
(wrapped around the observer). By what procedure can a two-dimensional matrix
be so modified, and to what does it give rise?
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
Spreadsheet to torus
A simple exercise in geometry can be used to transform the spreadsheet -- as
a sheet -- into a torus (namely a doughnut shape):
- the top and bottom of the spreadsheet are joined to create a tube, with
the spreadsheet columns constituting circular bands at different points on
its length -- along which the columns run
- the ends of the tube are connected -- linking the left and right ends of
the rows of the spreadsheet
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
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,
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:
- Each "bottom line" should be understood as the carrier of a distinct
kind of "value" or "currency". This would be consistent
with some of the arguments for multidimensional accounting.
- Different "bottom lines" could, for example, be represented by
straight geometric lines.
- Lines might be variously oriented to one another as an indication of such
difference in value type. In this sense the "currency", whether
monetary or otherwise, would be distinguished from other value types by orientation.
- Rather than being lines over a flat surface, the lines could be on the surface
of a sphere, curving to follow the curvature of that sphere (for a justification
for curvature in this context see Jonathan Tennenbaum. Incommensurability
and Analysis Situs, 1997).
- Lines could even be understood as circling around the sphere, so that each
line was in effect a circle. "Budget lines" are reframed as "budget
- As a circle, the lines might then hold insights into systemic feedback loops,
given that lines do not then have a starting place and an ending place. Each
circle is understood (and experienced) as a complete (sub) system, possibly
with some degree of interdependence, if not integrity.
- In a sustainable undertaking, such circles are then necessarily conduits
for value flows, whether monetary or otherwise.
- Circles might not all circle the sphere they together define. Some might
indeed do so (as the "great circles" of geometry and navigation),
to be understood as in some way reflecting "global" flows. Others
might circle regions of the sphere -- reflecting "regional" flows
(perhaps parallel to a "global" flow as indicative of similar value
orientation). The smallest might reflect "local" flows.
- Lines might intersect. Three such lines might, for example, intersect to
form a triangle.
- Intersection points of lines would then be understood as nodes at which
value was transformed between different "currencies".
- When three distinct "great circle" lines intersect, they effectively
interlock and give form to a larger system with a degree of integrity and
sustainability. This might be understood as the minimum criteria for the emergence
of a distinct and sustainable psycho-social system.
- More lines, carrying a greater variety of values, might circle the sphere
- In the simplest case, the intersection of three such lines generates triangles.
But in more complex cases, four circular lines generate squares, five would
generate pentagons, etc.
- Such zones reflect the intersection of an extensive selection of explicit
values -- relating disparate value factors. In practice they correspond to
the functioning of a "multi-stakeholder" panel where different values
have to be held and adjusted in relation to one another (eg economic issues,
social issues, environmental issues, cultural issues, political issues, security
- There are constraints on the variety of flows that can characterize such
zones -- as with the variety of stakeholders in a panel. Zones defined by
more than six flows would tend to be rare or less stable. This suggests that
an "octuple bottom line" may, for example, be less likely to be
called for or recognized.
- As value conduits, the "flow" in the lines may increase or decrease.
It might be understood to reverse. In financial terms this clearly reflects
positive (income) or negative (costs) flows.
- At intersection points, the relative level and direction of flows give rise
to tensions and pressures that affect the degree of transformation between
flows lines of different types.
- The spherical system of circular flows is then in a dynamic condition adjusting
flows in relation to one another -- between values of different types. This
process may be understood as a dynamic set of checks and balances vital to
the integrity of the system.
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
Synergetics and tensegrity
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:
Synergetics promulgates a system of mensuration employing 60-degree vectorial
coordination comprehensive to both physics and chemistry, and to both arithmetic
and geometry, in rational whole numbers. Synergetics originates in the assumption
that dimension must be physical; that conceptuality is metaphysical and independent
of size; and that a triangle is a triangle independent of size. Since physical
Universe is entirely energetic, all dimension must be energetic. Synergetics
is energetic geometry since it identifies energy with number. Energetic geometry
employs 60-degree coordination because that is nature's way to closest-pack
spheres. Synergetics provides geometrical conceptuality in respect to energy
quanta. In synergetics, the energy as mass is constant, and nonlimit frequency
is variable. Vectors and tensors constitute all elementary definition. Synergetics
shows how we may measure our experiences geometrically and topologically and
how we may employ geometry and topology to coordinate all information regarding
our experiences, both metaphysical and physical. [more]
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:
"graphical, functional and mathematical orderings and simplifications
of the omni-complicated and inter-related processes of the World. The conceptual
simplifications of "reality" into the vectors of an interacting process which
can be dealt with on a scientific basis. [more]
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].
"Sustainability" through "golden mean accounting"?
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
Divina Proportione, 1509, illustrated by Leonardo da Vinci). A glass
rhombicuboctahedron half-filled with water is the focus of a widely analyzed
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
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:
Hyperbolic descriptions of indifference tradeoffs are inseparable from the
SFEcon initiative. So far as we know, these descriptors are unique in providing
the references by which capitalistic systems might navigate among their chaotic
states toward stasis governed by a unified expression of value....
In searching for a meta-pattern behind the natural dynamism of economic order,
we might well consult ancient wisdom in beginning with a generator of elementary
forms that can grow in time and space by replication of their simple rules.
Perhaps the economist's notion of a general optimum might then be discovered
as a pattern around which economic dynamics are stabilized. [more]
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:
Aristotle also understood that there was not an absolute mean. The "golden
mean" will be relative to individual character and circumstances. The "golden
mean" is not a bad reminder for thinking about the challenges of developing
and implementing a decentralized budget model at the university. There is
no single best model. Our challenge has been finding the model that makes
sense for our circumstances. And finding that model has been governed by the
need for hitting the mean between too little and too much control, or the
same thing from the other side, between excesses and deficiencies of decentralization.
Similar metaphoric recognition is given in the case of the well-known alternative
commuity, The Farm:
The Second Foundation is an attempt to explore more harmonious and equitable
social and economic systems. It starts by establishing a golden mean between
those things which are best handled collectively - through group agreement
or social contract - and those things which are best handled individually
- at a family level. [more]
Severyn T. Bruyn (Civil
Republic: Beyond Capitalism and Nationalism) also focuses on the metaphorical
insight, arguing optimistically:
Aristotle might ask: Could extreme principles (e.g. freedom vs. order) be
resolved in a Golden Mean? Could great philosophical differences join in some
higher order of thought and practice? Could there be a middle-path, perhaps
a synthesis? Could the market develop a civil order of freedom with a civil
order of justice?
The answer is yes, but there are a lot of details. It is a fact that
the corporation operates in a culture of contradictions in which the principles
of freedom and order are at play. It follows that good citizenship in "justice-oriented
free markets" can be a goal. The goal can be set forth through civil associations.
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.
Towards a "semantic dome"
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".
This semantic dimension is already evident, coincidentally and ironically,
in the "DOME"
approach articulated by Zhan Cui and Paul O'Brien (Domain
Ontology Management Environment, 2000):
Business-to-business e-commerce requires dynamic and open-interoperable information
systems. Although, XML/DTD allow large organisational databases to publish
information over the Internet, the automatic sharing of information among
these systems has been prevented by semantic heterogeneity. True electronic
commerce will not come until the semantics of the terms used to model these
information systems could be captured and processed by computers. To develop
a machine process-able ontology (vocabulary) is intrinsically hard. The semantics
of a term varies from one context to another. We believe ontology engineering
will be a major effort of any future application development process. In this
paper we describe our work on building a Domain Ontology Management Environment
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
- DOME [of Honeywell] is an extensible system for graphically developing,
analyzing and transforming models of systems and software...DOME is used to
build models and to build notations. For quickly building models, DOME comes
with a set of notations, which can also easily be extended. But DOME is designed
for developing new notations, and then modeling systems based on them. For
instance, if a project needs a special interface description, a DOME notation
could be developed for it, complete with custom visual elements, required
interface properties and analysis reports. [more]
- Dome [Document Object Model Editor] is an visual programming language for
manipulation of XML documents. It is being used in the AKT
project to trawl through large websites, extracting information from them
by transforming the source HTML into RDF. [more]
- The DOME (Distributed Object-based Modeling Environment) environment developed
at CAD Lab of MIT that may provide basic support for web-based collaborative
problem solving, especially through integrated modeling. [more]
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
a Semantic- Web- Services- enabled Knowledge Ecosystem Some Research Issues,
2003). Such work is seen as the underpinning of the emergent global brain (cf
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
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:
- emerging trends towards "faith-based" governance and its possible
consequences for high levels of censorship of the web and the emergence of
isolated knowledge communities (cf Dynamically
Gated Conceptual Communities: emergent patterns of isolation within knowledge
- the increasingly recognized "clash of civilizations" and its potential
impact on the organization of knowledge space, if only in terms of language
preferences, but necessarily with their semantic consequences -- and despite
continuing hopes for a kind of "semantic Esperanto";
- the clash of cultures between those giving priority to "serious"
semantic content and those increasingly favouring an "edutainment"
emphasis on imaginative content, possibly minimizing the "reality-based"
dimensions -- and often poorly distinguished from the wishful thinking embodied
in strategic planning (whether for fund-raising, political, public relations,
or propaganda purposes);
- systematic misuse of the semantic web (as characterized in the "three
sets of books" of Table 2);
- the predicted increasing constraints on non-renewable resources [more],
may give rise to emergence of extreme pressures to use the semantic web as
a "Potemkin" device to minimize or focus public panic and to sustain
the belief system of world leadership (cf Globalization
within a Global Potemkin Society, 2000; Promoting
a Singular Global Threat -- Terrorism: Strategy of choice for world governance,
Initiation of Armageddon -- a heartfelt response to systemic negligence,
- dynamics arising from inherent discontinuities characteristic of the different
knowledge bases of communities with very different disciplines, experiences
or strategic objectives -- as formally described by Ron Atkin (cf Social
organization determined by incommunicability of insights, 1995).
The nature of the challenge of "semantic discontinuity" was explored
on the occasion of the United Nations Earth Summit (Rio de Janeiro, 1992) in
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
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.
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):
The difficulty is that bargains are typically discussed in the verbal and
textual mode. In this mode, notions of "giving up" in order to "get something
else" are understood in the simplest terms and therefore readily evoke opposition.
This opposition is indeed legitimate in terms of the "two-dimensional" images
(of "sides") through which they are currently discussed....
As in architecture, it is through balancing the stresses and tensions between
a set of complementary construction elements that the integrity of a building
is ensured. Richer structured imagery is required to facilitate understanding
of how the larger and more encompassing bargains can be achieved. It is through
such images of integrity, emerging from more complex structures, that the
logic of that integrity gives justification to issue-specific bargains with
greater effectiveness. It shows how they "fit". Structured images are required
to give precision to the vague notions of "checks and balances" conventionally
articulated in textual terms. Such images give precision to the notions of
"giving up", and tensional "trade offs", which readily lend themselves to
description in architectural terms, for example.;;;
... [The 3D
icosidodecaahedral structure] is one attempt to respond to this situation by
showing how different social functions, understood as strategic opportunities,
interfere with each other to engender a pattern of strategic dilemmas. In
that pattern each strategy may take a privileged role or may in turn be constrained
by other strategies. For example, when "environment" is a privileged function,
"well-being (+jobs)" may be sacrificed, whereas, when "well-being (+jobs)"
is the privileged function, sacrificing "environment" is the alternative option.
Neither option is satisfactory, but both appear to have their place. Any such
dilemma may of course be "resolved" by short-term measures, but the nature
of the dilemma renders such solutions unsustainable in the longer-term. Sustainable
development is a function of the pattern as a whole rather than of its components....
This approach points to new policy possibilities in which the degree of global
consensus required is reduced to a minimum (in a design sense) by localizing
the patterns of disagreement. In this way disagreement no longer acts globally
-- tearing apart the global community. Rather it is locally confined and understood
as a long-term strategic dilemma on which "consensus" can only be achieved
in the short-term. Sustainability thus lies at the global level not at the
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
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
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.
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:
The protocol is usually applied for groups ranging from 6 to 40 persons and
has been successfully used in more than one hundred of meetings in different
countries. Each member of the group plays three different roles: the role
of a participant, the role of a critic and the role of an observer. For a
group of 30 people the protocol is better explained by using an icosahedron
as a metaphor. Here, each person is represented by an edge whereas each vertex
corresponds to a topic, therefore in this case we have 12 topics. Usually
each vertex (i.e., a topic) is associated with a colour so each member of
the group is represented by two colours, the two colours that connect its
edge in the icosahedron. This structure implies that in order to discuss a
topic five participants meet in a place (i.e., five edges lead to a vertex).
In fact, according to the protocol, in order to keep a good tension on each
meeting, five other members join the discussion assuming the role of critics
during the meeting. Another five members can also attend a meeting, assuming
the role of observers. So, in each meeting of a particular topic we may have
15 persons at the same time (5 participants, 5 critics and 5 observers). This
means that with 30 people it is possible to run two meetings on two different
topics simultaneously. [more]
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:
For social tensegrity to exist in organisations a division of control is
required to establish a basis for competition and cooperation between control
centres and competition and cooperation for obtaining tenure as a member of
a control centre. Likewise, a compound board is required to provide a basis
for a watchdog board to be suspicious about the self-interest of managers
and to confirm their trust in them to be selfless stewards. A compound board
provides a forum for customers to check up on any suspicions on the integrity
of the goods and services of suppliers and provides a basis for establishing
trust to overcome the problems...
Construction of "semantic shelters" or "memetic
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,
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,
Michael R. Hyman. A Critique and Revision of the Multidimensional Ethics Scale.
Journal of Empirical Generalisations in Marketing Science, Volume One,
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.
- Evoking Authenticity: through polyhedral global configuration of local paradoxes?
- Framing NGOs in the Market for Change: comment on the report by SustainAbility,
- Personal globalization, 2001 [text]
- Psychology of Sustainability: Embodying cyclic environmental processes,
- Enhancing the Quality of Knowing through Integration of East-West metaphors,
- Coherent Policy-making Beyond the Information Barrier, 1999 [text]
- Spherical configuration of interlocking roundtables: Internet enhancement
of global self-organization through patterns of dialogue, 1998 [text]
- From Statics to Dynamics in Sustainable Community, 1998 [text]
- Spherical Configuration of Categories to Reflect Systemic Patterns of Environmental
Checks and Balances, 1994 [text]
- Groupware Configurations of Challenge and Harmony: an alternative approach
to alternative organization, 1979 [text]
Henning Kirkegaard. True Accounting - Myth or Possibility?
Peter Koenig. 30 Lies About Money: liberating your life, liberating your money. iUniverse, 2003
Bernard A. Lietaer:
- Mysterium Geld. Emotionale Bedeutung und Wirkunsweise eines Tabus. Riemann Verlag, 2000 [review]
- The Future of Money: creating new wealth, work, and a wiser world. Century, 2001 [overview]
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
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]
Markus 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]