Towards a Comprehensive Framework for Environmental Statistics: A Stress-Response Approach

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2016 Berlin Conference on Global Environmental Change: Transformative Global Climate
Governance après Paris on 23 and 24 May 2016
System of Accounts for Global Entropy-Production (SAGE-P): A Coherent
Accounting of the Econosphere, Sociosphere, and the Ecosphere formalised in
Topological Domain Spaces (TDS)
Anthony Friend, (University of Ottawa)
abstract
This paper describes the accounts beyond GDP, described by the TDS of the Econosphere, Sociosphere and
Ecosphere governed by the Second Law of thermodynamics. Defined are complex input/output algorithms of the
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entropic process reduced to nonlinear double-entry bookkeeping for the flow variables of ’production’ defined as
‘neg-entropy,’ the flow variables of ‘consumption’ defined as entropy and the stock variables of capital
accumulation, defining the Low Entropy Fund (LEF) available for human-consumption. The balance sheet of
SAGE-P assumes a pluralistic-value formulation in the following states of the LEF: (a) steady-state: (i.e., rate of
neg-entropy production t+n = rate of entropy production t+n), (b) surplus-state: (i.e., rate of neg-entropy production t+n
> rate of entropy production t+n), and (c) deficit-state: (i.e., rate of neg-entropy production t+n < rate of entropy
production t+n). The roots of SAGE-P may be found in the labour theory of value coupled with the Malthus-
Ricardian (long-term) prediction of wages falling to subsistence, profits falling to zero and rents rise to a maximum.
Contrast this to the neoclassical (long-term) prediction of growing efficiency in production satisfying human wants,
through the hypothetical supply and demand curve governed by rational choices of the agents of production,
consumption and investment. Introduced to the reader are the equations of the entropic process described by G-R
Flow-Fund Model. The object of the accounts is to translate the quantitative (material) production of the
Econosphere (i.e., values conserved-in-exchange) into the distinct language of qualitative immaterial product of the
Sociosphere (i.e., values conserved-in-use) and the quantitative/qualitative material product of the Ecosphere (i.e.,
values conserved in themselves, or existential). Central, and unique, to SAGE-P is the clear distinction made
between the accounting of ‘physical objects/functions’ that occupy space and time, and ‘abstract objects/functions,’
that occupy time but not space. This type of accountings enables the mapping of material world on the immaterial
world and vice versa. Another unique feature of SAGE-P is the implicit hierarchical structure of values where the
objects and functions of the Econosphere is an implied sub-set of the larger Sociosphere, which in turn, is a subset of
the still larger Ecosphere. The SAGE-P provides the conceptual framework for the coherence of production,
consumption and capital accumulation of the whole Planet, and yet, like any coherent structure, enables the user to
define the boundary conditions of the accounting objects and function to fit their analytical frame. The attached
Appendices provide the reader with some of the formalism described discursively in the text
Prologue
Entropy Production and the Econosphere
The law that entropy always increases -second law of thermodynamics-holds, I think, the supreme
position among the laws of Nature. If someone points out to you that your pet theory of the
universe is in disagreement with Maxwell's equations -then so much worse for Maxwell's
equations. If it is found to be contradicted by observation -well, these experimentalists do bungle
things sometimes. But if it is found to be against the second law of thermodynamics I can give you
no hope; there is nothing for it but to collapse in deepest humiliation. (Sir Arthur Eddington, The
Nature of the Physical World, 1927)
The value conserved in the System of Accounts for Global Entropy-Production (SAGE-P) is the
flow of services drawn from the consumption of the Low Entropy Fund (LEF) composed of
economic, social and ecological objects. Boulding (1949) pointed to the desirability of
We have chosen the concept of Topological Domain Space (TDS) because of its generalisation of a mathematical
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object defined as any set of points that satisfy a set of postulates. These are postulates applied here are those
expounded in the G-R Flow Fund Model, see Appendix I.

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governments to design policies which maximise the service flows (benefits) and minimise the
entropy production (cost) of the national economy, to wit:
It is not the increase in consumption or production that makes us rich, but the increase in capital, and any invention
which enables us to enjoy a given stock of capital and a smaller amount of consumption and production, out-go or
income, so much the gain.
Boulding clearly saw that the objective function of economic policy is to maximise the flow of
service income from capital as opposed the current accounting of GDP, (i.e., money-income
generated from the gross domestic product. Efficiencies applying Boulding is the maximization
of values conserved in use of economic, social, human and natural capital. While recognised in
the discourse on sustainability, it is rarely practiced in a market economy. On the contrary,
conserved values-in-exchange dominate the assessments of economic performance as per capita
GDP. The protocols of longterm sustainability (i.e., intergeneration equity), cannot be developed
from the quantitative metric of GDP. For this to be done, a mapping of the qualitative variables of
the human welfare measure on GDP is a sine qua non.
Mayumi (2001) proposed that sustainability is best measured as deviation from the ‘socially
acceptable’ minimum rate of entropy production for any well-specified measure of GDP
expanded to a composition of inclusive capital – economic, social, human and natural. In effect, a
cultural choice of the social efficiency matrix of capital, or, in Georgescu-Roegen (1971) terms
the rate of replenishment of the consumed stock of a well-define LEF.
Ecological Economic theory permits the mapping of quantitative data, (i.e., cardinal-valued
metrics) on qualitative. (i.e., ordinal-valued metrics) to measure qualitative change of the human
welfare function, (Georgescu-Roegen, 1971, Daly and Cobb. 1989). Further, the theory infers an
a priori judgment of preferred future states of the system,. In other words, inferred is a pre-
analytical vision statement, based on ethical principles that enter, in important way in the
evolving discourse of the globalisation of the economic process which exhibit unequal
distribution, and unequal access, to the Global Law Entropy Fund, (Matinez-Alier, 1987).
1. Entropy Production.
The rate of entropy production is proportional to, and symmetric with, the economy’s material
rate of consumption. While symmetry remains, the proportionality assumption is dropped with
respect to the immaterial economy. The objects consumed in the Econosphere is represented as
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a set of values conserved-in-exchange, applying the convention of price (p) and quantity (q),
conserved value = p(q). For every object (or element) in the matrix A (low entropy Fund), there
exists a corresponding outflow matrix B (high entropy Product) permitting the mapping of a
objects → b objects. The arrow depicts the algorithm of a structure-preserving mapping
The immaterial economy, composed of the production, consumption and accumulation of abstract objects, is
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indirectly subject to the entropy law. For example if the abstract object is directly linked to a material function, then
the output is a dependent on the rate of entropy production of the source. However, if the output of the abstract
object is dependent on another abstract function, like the generation of information, the entropy has no physical
source, see discussion on information entropy, (Shannon, 1948).

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(homomorphism): A → B. Literally, entropy production is the rate of heat dissipation (i.e.,
unavailable energy for further work) in the transformation of the set of low entropy a objects into
an equal valued set of high entropy b objects, (i.e., waste).
The inverse of entropy production, as one might expect, is negentropy production, represented by
the inflow matrix B'. The net-value of entropy production is obtained from the structure
preserving mapping of B → B'. The result is a two-way mapping for inflows of objects to the
Fund, B' → A (i.e., the rate of replenishment), and for outflows of objects from the Fund, A → B
(i.e., the rate of dissipation).
Thus, SAGE-P may be presented to decision-makers, and the pubic-at-large, as a continuous
space-time mapping of net-valued entropy production and the results recorded in the balance
sheet of the LEF. If the result is: (i) B' > B = A(+), this may be interpreted as a ‘surplus’ with a
potential for further growth of the Fund (i.e., sustainable+); (ii) B' < B = A(-) , this may be
interpreted as a ‘deficit’ with a potential for the Fund to collapse, (i.e., unsustainable-); and (iii)
B' = B = A, this may be interpreted as a ‘steady-state’ with cyclical fluctuations returning to the
same level of low entropy stocks available for human consumption. Since the equations represent
inequalities over differential time periods, the assessment of sustainability are time functions of
the rate of replenishment of b' objects. If these objects are non-renewable, sustainability is
measured at its rate of consumption, or b objects. (Note that substitution is not allowed as the
substituted object, is another object, inside its own production/consumption matrix.
The Fund A is a construct of all objects available for human consumption, which includes, in the
entropy formulation, all factors of production consumed to produce the output of the economy.
The net-value of output – that is, the part not required to reproduce itself – is represented by the
object categories of the B' matrix. The b' objects enter the Fund as capital stocks. The b' object’s
qualitative properties determine its membership to the categories of the nested spheres:
Ecosphere > Sociosphere > Econosphere, (see Figure 1: SAGE-P ). Thus, we may classify the b'
objects – the elements of the set – as belonging to: (i) Economic Fund Ae; (ii) Social-
Demographic Fund As; and (iii) Ecosystem and Natural Resource Fund An. Note that these
categories are by convention classified to economic capital Ke, social-human capital Ks, and
natural capital Kn. However, Ks of economic analysis are redefined to the boundary conditions
of the SAGE-P categories, (i.e., direction of the vectors of entropy production in LEF).
The innate properties of physical and abstract objects are mutually exclusive to the categories in
any well-defined TDS, (i.e., economic, social or ecological function). The same objects mapped
from one category to another, while maintaining their innate properties, conserve values in
accordance to function. Thus, like the Bauhaus architectural and urban planning design where
form follows function, entropy accounting design is where form follows ‘entropy efficiencies’
unique to the categories of production, consumption and capital accumulation. The chameleon
colour change with respect to the immediate surroundings may be viewed as analogous the three
facets of valuation method referred to as Pluralism of Values, (see Figure 1: Pluralism of
Values).

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For instance a living tree is valued for its ecological function in the Ecosphere Accounts, (e.g.,
photosynthesis & habitat), its social function in the Sociosphere Accounts, (e.g., recreational &
aesthetic) and its economic function the Econosphere Accounts, (e.g., wood products). Thus, the
same object conserves values unique to its function: (i) conserved value-in-exchange
(Econosphere); (ii) conserved value-in-use (Sociosphere); and (iii) conserved value in
themselves, or exstential, (Ecosphere).
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Intrinsic values are either infinite or zero. While this may hold true for the individual, the society may express
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through culture, myth, memory etc., a value for objects and function unrelated to usefulness or economic gain. This
value is best summed up as existential value which must be conserved for its own sake. There is no direct matrix for
existential value, the society nonetheless expresses these values indirectly through allocation of funds, such as
conservation of assets (i.e., low entropy fund), like establishment of a system of national parks, protection of
historical monuments, museums etc., and through mass protests and politics. In the case of the latter wars have been
fought to protect the Nation’s abstract values like integrity, honour and freedom.
ECOSPHERE
Figure 1: Pluralism of Values
Objects/Functions
Exchange-value
Use-value
&
Existential-
Objects/Functions
Existential-value
Objects/
Functions
Exchange-value
& Existential-value
Objects/Functions
Use-value
(participation)
Objects/
Function
Exchange-value
& Use-value
Objects/Function
exchange-value
(prices)
Objects/
Functions
Use-value
& Existential-
value
Households
Institutions &
Governments
Ecosystems
&
Homo sapiens
ECONOSPHERE
SOCIOSPHERE
Ecosphere
Business
&
Trade

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2. Domain Nesting of Entropic Processes: Econosphere → Sociosphere → Ecosphere.
The economic domain (Econosphere) is conceptualised as a proper subset of, and thus fully
integrated in, the social-demographic domain (Sociosphere), which, in turn, is a proper subset,
and fully integrated in, the ecological domain (Ecosphere). Each domain is represented by the
statistical datasets describing the quantities, qualities, and spatial distribution where relevant, of
fixed, and circulating capital: Econosphere (economic capital) → Sociosphere (human/social
capital) → Ecosphere (natural capital). Figure 2 presents the hierarchically-structured datasets of
the low entropy Fund. The directions of the arrows represent material-energy flows from lower-
to higher-order (trophic) structures, and reversed arrows, from higher- to lower-orders of the
trophic chain.
The accounting objects and functions in the low entropy Fund are uniquely expressed in the
conserved values of the domain. Thus, we have all objects expressed in exchange-values
belonging to the economic domain, use-values in the social domain, and existential-values in the
ecological domain. As such, objects in the low entropy Fund of the Ecosphere, with an exchange-
value, like the commercial timber value of a forest, are objects of the economic domain. The
recreational values of the same forest are objects in the social domain, and its existential-values
are objects of the ecological domain. Note, here, that that human life of the individual, and ipso
facto, the population, are existential-valued objects, belonging, like any other species, to the
ecological domain. However, if wages are paid in exchange for work, the objects (i.e., the labour
Figure 2:
ECOSPHERE

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force) belong to the economic domain. Similarly, population participation in activities where no
money is exchanged, are objects of the social domain.
The highest order value, in which all other entropic events are dependent functions, is the inflow
of solar radiation, and the outflow of heat dissipation from the Earth. Vitousek et al. (1986)
estimate that humans currently appropriate approximately 25 per cent of the potential total global
Net Primary Productivity (NPP), and 40 per cent of the terrestrial potential. It is important to
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recognise that the overwhelming quantity of solar energy is heat absorbed/reflected and only a
minuscule amount of solar energy fuels ‘living organisms’ (i.e., photosynthesis/respiration). The
solar energy balance sheet includes the NPP indirectly appropriated by humans (agriculture,
forestry, fisheries etc.,) and the direct solar energy captured for heating and useful work
(photovoltaic cells, wind, hydro, tidal, etc.).
Georgescu-Roegen argued that the economy is a process of transformation of low entropy
resources into high entropy objects – the ultimate end of the temple is a pile of rubble! Thus,
entropy production must be purposeful and has an ordinal-value. To wit:
Since the economic process materially consists of a transformation of low entropy into high entropy, i.e., into waste,
and since this transformation is irrevocable, natural resources must necessarily represent one part of the notion of
economic value. And because the economic process is not automatic, but willed, the services of all agents, human
and material, also belong to the same facet of that notion. For the other facet, we should note that it would be utterly
absurd to think that the economic process exists only for producing waste. The irrefutable conclusion is that the true
product of that process is an immaterial flux, the enjoyment of life. This flux constitutes the second facet of economic
value. Labor, through its drudgery, only tends to diminish the intensity of this flux, just as a higher rate of
consumption tends to increase it. (Georgescu-Roegen, 1971, p. 18)
Central to the valuation of the entropic process is defining the efficiency measure of the
immaterial flux. Irving Fisher (1906), in The Nature of Capital and Income, saw income (flow)
and capital (stock) as two facets of the same object – income being the accumulated flow of
abstract services measured over a period of time, and capital being a (low entropy) fund
measured as material wealth at an instant in time:
[Income] ...is a flow through a period of time and not, like capital, as a fund at an instant in time, ... consisting of
abstract services and not, like capital, of concrete wealth. The income from any instrument is thus the flow of
services rendered by the instrument. The income of a community is the total flow of services from all its instruments.
The income of an individual is the flow of services yielded to him from his property. (Fisher, 1965, p. 102)
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NNP = solar energy captured by plants and other photosynthetic organism minus that used by the organisms
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themselves for respiration.
In the Fisher analysis, abstract objects in SAGE-P, like bank accounts, assume a material object of ‘concrete
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wealth’. What this really means is that wealth is an instrumental means to produce more wealth (i.e., capital) or an
instrumental means to sustain or enjoy life (i.e., consumption). For this condition to hold, economic instruments
must have attached property rights, which are owned either by an individual or a collective, such as a community.
Note that in SAGE-P ‘property rights’ represent the higher order (abstract) institutional objects of the sociosphere.

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Kenneth Boulding expanded the Fisher service-flow income from stocks to include the entropy
efficiency of capital consumption itself:
I shall argue that it is capital stock that we derive satisfaction, not from additions to it (production) or subtractions
from it (consumption): that consumption far from being a desideratum, is a deplorable property of the capital stock
which necessitates the equally deplorable activities of production: and that the objective of economic policy should
not be to maximize consumption or production, but rather minimize it, i.e. to enable us to maintain our capital stock
with as little consumption and production as possible. It is not the increase in consumption or production that makes
us rich, but the increase in capital, and any invention which enables us to enjoy a given stock of capital and a
smaller amount of consumption and production, out-go or income, so much the gain.’ (Boulding, 1949)
Georgescu-Roegen argued that understanding the nature of the economic process is contextual to
historic experience of peoples and the capacity to adapt to technological change (i.e., exosomatic
evolution). To wit:
And paradoxical as though it may seem, it is the Entropy Law, a law of elementary matter, that leaves us no choice
but to recognize the role of cultural tradition in the economic process. The dissipation of energy, as the law
proclaims, going on automatically everywhere. This is precisely why the entropy reversal as seen in every line of
production bears the indelible hallmark of purposive activity. And the way this activity is planned and performed
certainly depends upon the cultural matrix of the society in question. There is no other way to account for the
intriguing difference between some developed nations endowed with a poor environment, on the one hand, and some
underdeveloped ones surrounded by an abundance of natural riches. The exosomatic evolution works it way through
cultural tradition, not only through technological knowledge.’(Georgescu-Roegen, 1971, p. 18)
3. SAGE-P: roots in the classical model of fixed and circulating capital
The key, and unique feature of SAGE-P, is the articulate accounting principles of the LEF. The
ethical principles concerning the distribution and access to Global low entropy fund is echoed in
the opening sentence of the Report of the World Commission on the Environment and
Development, a.k.a. the Brundtland Report, to wit:
‘The Earth is one but the world is not. We all depend on one biosphere for sustaining our lives. Yet each community,
each country, strives for survival and prosperity with little regards for the impact on others. Some consume the
Earth’s resources at a rate that would leave little for future generations. Others, many more in number, consume far
too little and live with the prospect of hunger, squalor, disease, and early death.’ (WCED, 1987, p. 27)
We shall argue that the issue raised by the Brundtland report has deep roots the distribution issue
in classical economics, and well articulated in the Malthusian Spectre considered a critical factor
in David Ricardo’s end state of Capitalism, (Malthus, 1959, Ricardo, 1973, Robinson, 1980.).
LEF in classical economics is composed of fixed (i.e.,physical objects) and circulating capital
(i.e., abstract objects). Further distinctions were made between the stock of objects available for
immediate consumption and the stock of objets necessary to replenish LEF at its rate of
consumption. While characteristically these were the seeds for reproduction, the work and
materials required to maintain structure was fully recognised.
Sraffa’s (1960) essay: The Production of Commodities by Means of Commodities acerbic
demonstration of the circulating capital model of the economy without the fictional driver of the
producer supply and the consumer demand curve. The production function is internalised by its
own factors of production with the classical distinction of: (a) a labour fund replenished at its rate

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of subsistence, (i.e., wages), (b) a capital fund replenished at its rate of surplus production (i.e.,
profits) and (c) a land fund replenished by Nature’s reproductive capacity, (i.e., rent). The latter,
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while a limiting factor for economic growth, is not in itself, a factor of the share of production
between wages and profits. All values are determined by the thermodynamic relationships of
factors of production: land, labour, and capital. Joan Robinson admired the logic of Sraffa’s I/O
Model of Production reduced to circulating capital, to wit:
Evidently we are in a capitalist economy, but to avoid ambiguity which have clustered around the word, capital is
never mentioned. There is profit, but no enterprise; wages, but no pay-packets; prices, but no markets. Nothing is
mentioned but but the equations of production and the necessary conditions of exchange, Robinson, 1980: 144-150.
While rooted in Ricardian economics and the labour (or work) theory of value, the Sraffa I/O
Model of circulating capital may be viewed as a precursor of G-R Flow-Fund Model of the
entropic process, (Robinson, 1980, Mayumi, 2001; Friend, 2005).
With the advent of the general equilibrium system, circa the 1870s, the supply theory of value
was rejected, and replaced by a demand theory of value where the consumer is sovereign. Thus
freeing economic analysis from the traditional constraints of the ‘dismal sciences’ of population
growth and land scarcity. The unbounded optimism was based on the ever expanding frontier of
technology, productivity of the producer, expanding income of the producer, and where
constraints of natural resources appeared, the substitution theory prevailed, (Simon, 1981).
Alfred Marshall, the great apologist of the neoclassical model, was a little more sanguine on this
point:
‘Even when cultivation has reached a stage after which each successive dose applied to a field would get less
return than the preceding dose, it may be possible for an increase in the population to cause a more than
proportional increase in the means of subsistence. It is true that the evil day is only deferred: but it is deferred. The
growth of population, if not checked by other causes, must ultimately be checked by the difficulty of obtaining raw
produce; but in spite of the law of diminishing return, the pressure of population on the means of subsistence may be
restrained for a long time to come by the opening up of new fields of supply, by the cheapening of railways and
steamship communication, and by the growth and organization of knowledge. Against this must be set the growing
difficulty of getting fresh air and light, and in some cases fresh water, in densely peopled places. The natural
beauties of a place of fashionable resort have a direct money value which cannot be overlooked; but it requires some
effort to realize the true value to men, women and children of being able to stroll amid beautiful and varied scenery.’
(Marshall, 1947, p. 166)
While Alfred Marshall’s warning was left unheeded by the economic growth optimists, the
entropy production feedback loop, if left unchecked, would lead to the ruination of the aesthetic
qualities of the planet Earth. Indeed, as noted by some social analysts (e.g., Ellul, 1964;
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Nonrenewable resources like fossil fuels and minerals are not circulating capital, other than recycling, and treated
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as appropriated in distributional relationship of the wage-profit cycle.
Theodore Roosevelt (1906) said: ‘We have become great because of the lavish use of our resources. But the time
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has come to inquire seriously what will happen when our forests are gone, when the coal, the iron, the oil, and the
gas are exhausted, when the soils have still further impoverished and washed into the streams, polluting the rivers,
denuding the fields and obstructing navigation.’

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Koestler, 1967; Schumacher, 1973; and Bataille, 1988), the feedback loop of Machine Age
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harboured its own inner logic of the Tragedy of the Commons, (Hardin, 1968). Productivity of
the input costs and the output benefits, has only driven the explosive growth of the human
population and its parallel material consumption, but subjugated continuous biological time for
the discrete time units of the machine time.
Today, the exponential rate of entropy production associated the material consumption is openly
discussed in terms of sustainability of high consumer societies, (Arrow et al., 2004). The concern
of material consumption identified with environmental degradation, at least in Britain in the
1840s, elegantly expressed in John Stuart Mill’s essay on the Stationary State, to wit:
It is scarcely necessary to remark that a stationary condition of capital and population implies no stationary state of
human improvement. There would be as much scope as ever for all kinds of mental culture, and moral and social
progress; as much room for improving the Art of Living, and much more likelihood of its being improved, when
minds ceased to be engrossed by the art of getting on, (Mill, 1970, p. 116)
The labour theory of value includes the notion that Nature work along with Man but as a ‘free
good,’ to wit:
In agriculture, too, Nature labours along with man; and though her labour costs no expense, its produce has its
value, as well as that of the most expensive workman. (Smith, 1994, p. 393).
Services, while recognised as the necessary condition to maintain order and structure of a
Society, as well as pleasure and enjoyment, could not add to the Wealth of Nations the work “…
perish the very instance of its production.” The oft quoted passage in the Wealth of Nations
makes this point clearly and unambiguously as follows:
The labour of some of the most respectable orders in society is, like that of the menial servants, unproductive of any
value, and does not fix or realize itself in any permanent subject, or vendible commodity, which endures after labour
is past, and for which an equal quantity of labour can be procured. The sovereign, for example, with all the officers
both of justice and war who serve under him, the whole army and navy, are unproductive labourers....In the same
class must be ranked, some both of the gravest and most important, and some of the most frivolous professions;
churchmen, lawyers, physicians, men of letters of all kinds; players, buffoons, musicians, opera-singers, opera-
dancers, etc. ...Like the declamation of the actor, the harangue of the orator, or the tune of the musician, the work of
all of them perish the very instance of its production. (Smith, 1994, p. 364)
While abstract objects, referred to as non-tangible, are denied contribution to wealth, the physical
objects that make-up this stock of wealth offer the paradox use-value with no exchange-value and
exchange-value with no use-value, to wit;
The word VALUE, it is to be observed, has two different meanings, and sometimes expresses the utility of some
particular object, and sometimes the power of purchasing other goods which the possession of that object conveys.
Georges Betaille’s philosophical concern is the logic that ‘surplus product’ must ultimately ‘destruct’. This led to
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the examination of the human experience with respect to the distribution (power) and destruction (choice) of the
‘economic surplus’. The annual flood of the Nile River aquatic ecosystem (i.e., a low entropy Fund) created the
‘surplus funds’ to construct the tombs of the Pharaohs – a useless object. In the more literal sense of destruction, the
economic surplus provides the capacity for nation’s to wage wars or to build-up arms for the politically-motivated
(imaginary) pseudo-wars, like the Cold-War.

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The one may be called “value in use”; the other, “value in exchange”. The things which have the greatest value in
use have frequently little or no value in exchange; on the contrary, those which have the greatest value in exchange
have frequently little or no value in use. Nothing is more useful than water: but it will purchase scarce anything;
scarce anything can be had in exchange for it. A diamond, on the contrary, has scarce any use-value; but a very
great quantity of other goods may frequently be had in exchange for it. (Smith, 1994, p. 57)
Adam Smith in the opening passage of the Wealth of Nations has an uncanny resemblance to
the G-R Flow Fund Model when the economy is described in terms of the annual product of
labour (negentropy) as inflow to, and the annual consumption this product (entropy) as outflow
from, the stock of LEF available for human consumption, to wit:
The annual labour of every nation is the fund which originally supplies it with all the necessaries and conveniences
of life which it annually consumes, and which consists always either in immediate produce of that labour, or what is
purchased with that produce from other nations. (Smith, 1994, p. lix)
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4. Emergence of dual valuation of land and labour in classical economics.
The Political Arithmetic of William Petty (1623-1687) calculated the value of the nation’s wealth
on a per capita income of £6 13s 4d per annum and a population of six million souls, thus
yielding a national income for England of £40m. On value, Petty continued the debate begun by
Aristotle, and chose to value the Wealth of the Nation in its natural denominations, land and
labour. Both of which are prime source of tax, land (i.e., Nature’s Œconomy) and labour, (i.e.,
Human Œconomy). Petty’s famously quoted valuation method: “LAND is the MOTHER of
WEALTH,” “LABOUR the FATHER of WEALTH.”
The Physiocrates, in the Tableau Economique identified the augmentation of value in the soil,
which clearly suggests that out of nothing, nature creates value (i.e., the primary product of the
Planet Earth). Labour, while productive, can only conserves value prescribed by the magnitude
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of fixed and circulating capital and the quantity of the labour product exchange in the market.
Adam Smith disagreed, while recognising that Nature is the primary producer, (i.e., natural
capital), considers wealth creation (i.e., augmentation of value) as coming into existence so to
speak through human industry and labour. to wit:
The materials of all wealth originates primarily in the bosom of the earth; but it is only by the aid of labour they can
truly constitute wealth. The earth furnishes the means of wealth; but wealth cannot have any existence, unless
through industry and labour which modifies, divides, connects and combines the various production of the soils so as
to render them fit for human consumption. (Smith, 1809, p. xxxvii).
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Economists have often pointed to the contradiction between ‘annual labour’, a flow concept, and a ‘Fund’, a
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stock concept. This can be resolved by replacing the word ‘annual’ with the word ‘potential’. The labour force is
thus a stock (a quantitative value) representing qualities of the potential work, in conjunction with nature, to supply
the nation ‘...with all the necessaries and conveniences of life which it annually consumes.’
Primary production is the synthesis of organic compounds from atmospheric or aqueous carbon dioxide. It
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principally occurs through the process of photosynthesis, which uses light as its source of energy.
The quote is from M. Garnier who wrote a introductory essay entitled “A Short View of the Doctrine of Smith
11
with that of the French Economists” included in the 1809 edition of “An Inquiry into the Nature and Causes of the
Wealth of Nations.”

!11
Mirowski (1989) detected in the reasoning of the Physiocrates the essence of the entropic process
inferring that the primary producer of photosynthesis (i.e., solar energy) is the origin of value.
The logic of recursive, hierarchically-structured, circulating capital seem to confirm the
hypothesis of conserved values in the following order: existential-value > use-value > exchange-
value. This is how Mirowski put it:
If one chooses, as did the Physiocrates, to locate the augmentation of value in a single sector, then it follows that
trade between sectors can readily be defined as trade of equivalents: this is the real meaning of the Tableau
Economique. In this schema, primary production is well defined as the locus of increase of the value substance;
secondary production, trade or circulation as where value substance is conserved, and finally, consumption as the
locus of final destruction. (Mirowski, 1989, p. 159). Note the words in italics were added to conform to the
Physiocrats thesis that secondary production (i.e., manufacturing) does not add value.
5. Georgescu-Roegen’s Flow-Fund Model (FFM)
Time as a factor of production
At Harvard University in the 1930s, Georgescu-Roegen studied under Joseph Schumpeter,. His
Theory of Economic Development (1934) was framed in the formalism of the dialectics of the
creative and destructive process, a precursor of the indeterminism entailed by the Entropy Law
(i.e., arrow of time). While not explicit, the General Equilibrium Model is framed in statistical
time series which predict the future from the probability of past events, (i.e., frequency
distribution). Determinism in economic analysis is based on the Newtonian equation of motion
and degree of belief in the Laplacian Demon.
12
The Entropy Law introduces to economic analysis the ultimate anti-Laplacian Demon, that of
pure randomness of events, both past and future. In the pure state of chaos there is no linkages
and connections among the observed events with a statistical probability of zero. Ilya Prigogine,
who studied the Entropy Law in chemical reactions and synthesis, concluded that what might
appear to the observer as a random event is the manifestation of the disequilibrium state of the
system at the limit, (i.e., far from equilibrium) where anticipated trajectories enter the zone of
bifurcation, like the mutation in evolutionary theory. Prigogine (1997) refers to this state
condition of the system in terms of nonlinear processes characterised as “emergent properties of
dissipative structures far from equilibrium,” (Prigogine 1997).
Schumpeter, studied under Eugen von Böhm-Bawerk, (1891) whose capital theory founded on
historical time assumed the dynamics of recursive functions of the Austrian School. While the
13
original ‘roundaboutness’ theory of capital assumed interdependency of current consumption to
We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect
12
which at a certain moment would know all forces that set nature in motion, and all positions of all items of which
nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a
single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an
intellect nothing would be uncertain and the future just like the past would be present before its eyes. (translated
from French), —Pierre Simon Laplace, A Philosophical Essay on Probabilities.
Von Böhm-Bawerk was a student of Karl Menger, who, along with Stanley Jevons and Leon Walrus, are
13
considered the founders of the Neo-classical School.

!12
past capital formation, the Neo-Austrian School expanded the interdependencies to include
complex pathways through the social and natural capital, (Malte et al., 1999).
Time recursion is a characterised in the FFM in the algorithms of hysteresis (i.e., lagged effect of
past state conditions on the present state conditions). This factor of time in evolutionary
14
processes requires information of the memory of the system, which, inter alia, assumes
knowledge of the initial state conditions of the system. Georgescu-Roegen argued that
(nonlinear) evolutionary processes cannot be predicted from a priori assumptions of equilibrium
state conditions entailed by the (Walrasian) General Equilibrium System.
The logic of the behaviour of economic agents framed in the analytical domains of complex,
adaptive, systems are irreducible to the linear regressions analysis of econometric models, no
matter how many exogenous variables are given. Predictions of the next event in the time series,
exception of near future events, are better framed in the theory of prior distribution or
anticipatory future event models identified with Bayesian Statistics, (see Appendix II: Bayesian
Statistical Methods, (Rosen, 1985; Malte and Proops, 1992).
A key distinction between the Neoclassical School and the Austrian School is that the latter
describes change of qualities as a dependent function of time itself, like the entropic process,
whereas, with the former, qualitative change in objects are given (de gustibus non est
disputandum) and, indeed, are empirically observed in consumer choice and preferences in the
market place. Government intervention, with respect to public goods, is similarly assumed as an
external factor in any statistical regressions of consumer and/or producer behaviour.
Schumpeter’s (1934) analytical method of creative-destruction assumes discontinuities in
production/consumption and capital accumulation cycles. Holling (1994) adapted the method to
the Figure Eight Model (see Figure 3) to describe dynamics of ecosystem restructuring at the
planetary-scale of the Anthropocene,, to wit:
The one overall conclusion is that discontinuous change is an internal property of each system. In a sense, key
structural parts of the system become “accidents waiting to happen”...There is both a destructive feature to such
changes and a creative one. Organisms are destroyed, but this is because of their very success in competing with
other organisms and in appropriating and accumulating the prime resources of energy, space and nutrients. The
accumulated resources, normally bound tightly and unavailable, are suddenly released by forces of change. Such
forces therefore permit creative renewal of the system. I call this ... ecosystem function “creative destruction”, a term
borrowed from Schumpeter's economic theory...The full dynamic behaviour of the system at an aggregate level can
therefore be represented by the sequential interaction of four ecosystem functions: exploitation, conservation,
creative destruction, and renewal. The progression is such that these functions dominate at different times: from
exploitation...slowly to conservation...rapidly to creative destruction...rapidly to renewal...and rapidly back to
exploitation. (Holling, 1994).
For instance the 2008 financial meltdown may be viewed as lag effect of deregulation of the Banking sector in the
14
1980s and the subsequent explosion of financial products created by traders in the 1990s, like derivatives, hedge-
funds, credit/default swaps etc. The secondary lag effect of the 2008 financial market are reverberating in the debt
crises of sovereign States.

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Figure 3: Holling Figure Eight Model
5. Some observations of SAGE-P and adaptive logics
SAGE-P is a system of accounting of complex, nonlinear, evolutionary systems, where the
(accounting) objects and functions evolve and change over time and space. The algorithmic
mappings of category sets, therefore, require special adaptive logics to describe bifurcation
points of qualitative properties of objects, such that they are no longer the same object. This
question was explored in a paper on nonlinear accounting presented at the European Society for
Ecological Economics Conference, Ljubljana, Slovenia, in 2009:
Here, it should be noted, we make no assertions about which logic is the best fit for nonlinear accounting, but rather
offer adaptive logics as a possible first base from which to work. Adaptive logics are sensitive to, and can account
for, evolutionary processes. Further, the objective is to develop a formal logic framework to construct the analytical
space for an ordinal structured system of non-ergodic processes (Georgescu-Roegen, 1971; Friend, 2009). One of
the key features which we can reflect in adaptive logics is the idea that objects change properties over time, which at
some indefinite point, are no longer the same objects defined by their initial conditions. In other words, objects,
themselves evolve and change. (Friend and Friend, 2009)
In theory, each event recorded in a non-ergodic statistical database is deemed unique. In practice,
events in the Ecosphere, described by cycling systems, (i.e., atmosphere, hydrosphere and
lithosphere) and the reproductive processes of the ecosystems are of sufficient similarity in
coarse-grained data to be treated as recurring events. However, a measure of recurrence is a
problem in the statistical databases of the Econosphere and Sociosphere.

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The quantitative/qualitative properties of physical objects visibly change form and function over
space-time, enabling co-ordinate metric of entropy production and efficiencies. While the
statistical objects change qualities, the common denominator of entropy production does not.
Abstract objects, while changing volume and qualities over time, are not directly subject to a
metric of entropy production. However, SAGE-P permits an an algorithm of correspondence
mapping of abstract objects which by definition immaterial, on the associated physical objects.
Entropy production, and entropy efficiencies, are thus, the inverse correspondence mapping on
abstract objects/functions.
Adaptive logics permit relationships to be expressed, and normalised, in nonlinear statistical
events where, for instance: (i) inputs ≠ outputs ; (ii) the critical event horizon → limit function
15
→ bifurcation points (e.g., sudden collapse); and (iii) resilience to absorb stress (e.g.,
robustness). Algorithms of non-ergodic processes involve time-delay recursive statistical events,
expressed in stress-response vectors leading to system collapse (i.e., chaos → release →
reorganisation) and the emergent properties of dissipative structures far from equilibrium, (see,
Figure 3). The Stress-Response Model was proposed as a framework for the development of
environment statistics following the the first UN Conference on the Global Environment in
Stockholm, 1972, (Rapport and Friend, 1979)
Feedback loops are constructed from algorithms of statistical correspondence of objects/
functions that either amplify or dampen the rate of entropy production in the SAGE-P., (Rosen
1985, 1991, Lawvere and Schanuel,1997). Of interest, especially in the long-term analytical
frame for climate change policies, are the accounts of entropy production of new technologies,
such as Hydrolic Fracturing of shale rocks to release sequestered gas and oil. The long term
amplifying feedback loop of previous technologies are well-documented, (Ellul, 1964, Bataille,
1988).
While portrayed in the literature as progress, the underlying premise of SAGE-P is the paradox
of entropy efficiency. At the the micro-scale entropy efficiency increases in proportion to
technological progress, (i.e., per unit of consumption) but decreases in the same proportion at the
macro scale, (i.e., aggregate consumption as per GDP), (Jevons 1965, Polimeni et al, 2008). This
phenomena applies only to the material world of physical objects/function. The positive feedback
loop of abstract objects/function are not subject to the Second Law of thermodynamics. The
accounts of the LEF demonstrate this paradox as a function of increasing complexity to describe
the basic categories of negentropy, (production), entropy (consumption) and low entropy fund
available for human consumption, (capital).
While Ecological Economics theory was founded on uncertainty and on the principles of
complexity and nonlinear dynamical relationships, Neoclassical Economics was founded on the
premise of the rational economic behaviour of the fictitious Homo-economicus. Complexity and
This means that abstract objects do not obey the superposition principle which states that, for all linear systems,
15
the net response at a given place and time caused by two or more stimuli is the sum of the responses which would
have been caused by each stimulus individually.

!15
uncertainty, while real, and fully recognised as the exogeneous variable in theoretical model, the
neo-classical economists continued to apply linear regression analysis to the supply/demand
functions governed by the Walrasian General Equilibrium to predict the trajectories of new
technologies. The question raised was not basic premise of the linear analytical frame, (i.e.,
prediction the next event in the time series), but whether rational choices could be prevailed upon
the Homo-economicus to lead to a green and sustainable economy. This position is exemplified
in a paper authored by notable neoclassical environmental economists entitles, “Are we
consuming too much?,” (Arrow et al., 2004).
6. The Flow-Fund Model (FFM) of the entropic process.
16
The FFM is an accounting system of the LEF available for human consumption in the form of the
metabolic process. That is the inflow of low entropy objects and outflow of high entropy objects.
The Fund parameters represent the metabolic agents of transformation, (e.g., manufacturing).
The flow elements (Ei) enter as inputs to, and exit as outputs from, the Fund. The elements (Ep),
represent the factors of production and exist simultaneously in two states: (i) the ‘agents’ of the
process (i.e., the coefficient of the I/O matrix), and (ii) the elements used and/or acted upon (i.e.,
material-energy inflow/outflow). The flow E’s are defined, and empirically observed, at the I/O
boundary of the entropic process. What goes on inside the process remains forever a black box.
The entropy production, or the rate of consumption of the Fund, represents the efficiencies of the
human participation in the Fund elements, expressed as categories of consumption, C1, C2, C3 ...,
Cn. (i.e., the net-value entropy production per unit of consumption), (see Appendix 1:Georgescu-
Roegen’s Flow-Fund Model).
The net-value of entropy production is the difference between the quantity of input flow (i.e., low
entropy objects, like natural resources) to the fund – which is given a positive sign (negentropy)
– and the quantity of the output flow, (i.e., high entropy objects. like waste residuals) – which is
given a negative sign (entropy). Sustainability implies that the balance accounts of SAGE-P are
non-negative over some well-specified time period and/or spatial entity. If the result is positive,
the fund assumes a ‘surplus’ of low entropy stocks available for future consumption. If negative,
the fund assumes a ‘deficit’, which needs to be replenished at a rate greater than the present rate
of consumption. An example of ‘deficit’ is the rate of emissions of greenhouse gas emissions
(i.e., the present consumption of fossil fuels), which is greater than the absorptive capacity of the
Ecosphere carbon cycle, resulting in an inevitable build-up of the concentration of greenhouse
gases in the atmosphere.
FFM represents the dynamics continuous change in from and function. While recurrence of
entropic processes are observed in natural cycles and reproductive processes, Georgescu-Roegen
is careful to rule out illusion of recursion from the irreversible entropic process .Thus, the logic
of the Entropy Law decrees that all events in a statistical time series are non-ergodic (Friend,
2009). In practice, and in the short-term, however defined, it matters little to assume recurrence
For a Technical description see Appendix I: Georgescu-Roegen’s Flow-Fund Model.
16

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of events, as the error term is too small to be of any consequence for policies. This is not true for
the long-term as the small error (i.e., slight perturbation) amplifies in any algorithm of recurrence
in any positive feedback loop.
Georgescu-Roegen distinguished statistical probability in the abstract, (i.e., analytic a priori),
from the statistical probability of causal relationships, (i.e., synthetic a posteriori). The his view
two formulations of probability not only apply to different domains, but are fundamentally
antagonistic. While the latter assumes an irreducible ‘randomness’ in nature itself, the former
assumes incompleteness in knowledge, viz:
If probability is an ultimate element of nature, then forcibly its definition must rest on probability. And if the
centuries-old struggle with the problem of finding an analytical definition of probability has produced only endless
controversies between the various doctrines, it is, in my opinion, because too little attention has been paid to the
singular notion of random. For the dialectical root, in fact, lies in this notion: probability is only an arithmetical
aspect of it. (Goergescu-Roegen, 1971, pp. 56).
Erwin Schrödinger captures the essence of the entropic process in his 1944 essay on What is
Life? to wit:
A living organism continually increases its entropy – or, as you may say, produces positive entropy – and thus tends
to approach the dangerous state of maximum entropy, which is death. It can only keep aloof from it, i.e. alive, by
continually drawing from its environment negative entropy - which is something very positive as we shall
immediately see. What an organism feeds upon is negative entropy. Or, to put it less paradoxically, the essential
thing in metabolism is that the organism succeeds in freeing itself from all the entropy it cannot help producing while
alive.’ (Schrödinger, 1967)
The entropic process exhibits the behavioural parameters of complex, non-equilibrium,
thermodynamic systems. The Ecosphere bio-economics is caused by the inflow of solar radiation,
the production of of biomass, (i.e., primary productivity), and the outflow of heat to outer space.
(the Stuart Kaufman, (1995) put forward the idea that like the Newtonian Linear laws of Motion,
there must be a set of formalised general laws to enable the prediction of the behaviour of non-
equilibrium (material) systems. While there is progress in defining formalism and the
mathematics of non-equilibrium systems, the predictive cause-effect are missing. Morel and
Fleck (2006) propose an answer to Kaufman’s question with the proposition of the material
Fourth Law of Thermodynamics: The entropic processes (cause) increase entropy at the
maximum rate available to them. The Fourth Law:
“...brings the vast area of reacting systems within the domain of thermodynamics. By stressing the consistency of
system behavior, it explicitly incorporates the concept of causality into the formal foundations of thermodynamics.
The significance and manifestations of the Fourth Law are dramatic in far-from-equilibrium systems where
spontaneous investments in local ordering – in dissipative structures – inevitably increase the rates at which systems
increase entropy.” (Morel and Fleck, 2006)
The Morel-Fleck proposition formalises the Georgescu-Roegen material Fourth Law. Whether
this will hold up to scientific scrutiny is another matter, but the proposition is consistent with the
Aristotelean ‘efficient cause’ (i.e., instrumental means of change). The four Aristotelean causes
are defined: (a) material cause (the object), (b) formal cause (the boundary conditions of the

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object), (c) efficient cause (the instrumental means of object change) and (d) final cause (the
existential value of the object).
These definitions do not correspond to our modern understanding of causal relations in the
natural and social sciences. Rosen, (1991) redefined the four Aristotelean causes into a
hierarchical structure: (a) material cause corresponds to the change of object observed (e.g., tree
cut down) → efficient cause corresponds to the instrumental means (e.g., chain saw) for the
change of state of the object → formal cause corresponds to the human-designed structure (e.g.,
forest industry) that caused (a) and (b), → final cause corresponds to an abstract object (e.g.,
government policy regulating the forest industry) that caused (a), (b), and (c).
While the Entropy Law governs direction and volume of entropy production in a closed
thermodynamic system, the Fourth Law is exclusively applied to open thermodynamic systems
(i.e., temporary reversal) governing the causal relationship of (material) object and functions
arising out of complex, hierarchically-structured systems that a not predicted from extrapolations
of the past into the future characterised as “emergent properties of dissipative structure far from
equilibrium.”
The great idea of Georgescu-Roegen was to recognise that Newtonian Laws of Motion as
applied to the equations an production, consumption and capital accumulation, in other words the
quantitative economy, entrapped economic analysis to the one-dimensional mechanistic universe.
While the mechanism of quantitative analysis is important for low income countries, (i.e.,
relatively low entropy per unit of consumption), for high income economies the central question
is the qualitative change in the consumption function (i.e., to reduce to a minimum the rate of
entropy production per unit of consumption). The primary science of matter is non-Newtonian,
and the indeterminism and complexities of quantum mechanics is universal and applicable to
17
the macro-world of the social sciences, to wit:
The significant fact for the economist is that the new science of thermodynamics began as a physics of economic
value and, basically, can still be regarded as such. The Entropy Law itself emerges as the most economic of all
natural laws. It is in ...the primary science of matter that the fundamental nonmechanistic nature of economic
process fully reveals itself. (Georgescu-Roegen, 1971, pp. 3)
Georgescu-Roegen viewed the neoclassical project to reduce the behaviour of Homo economicus
into a set of deterministic laws of statistical mechanics, such as the Hamiltonian, an error of the
first order. This mania of the mechanical regression of statistics, (i.e., econometrics), he coined
the neologism “arithmorphism.” By this, he meant reducing the infinity of all other possible
numbers to a logical class of discrete and distinct objects represented by a single number. Indeed,
this is the neoclassical project of applying ‘Economics as Social Physics, and Physics as Nature’s
Economics’ – the secondary title to Mirowski’s (1989) book entitled: More Heat than Light,
A ‘quantum’ is a quantity of something, a very specific amount. ‘Mechanics’ is a study of motion. Therefore,
17
quantum mechanics is the study of motion in quantities. Quantum theory says that nature comes in bits and pieces
(quanta), and quantum mechanics is the study of this phenomena (Zukav, 1979, p. 45).

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which is a discourse on how the conservation of energy theories were hijacked to demonstrate the
mathematical proofs of the conservation-of-value in (linear) econometric models.
Solo (1974) in reviewing the Entropy Law and the Economic Process wrote:
Georgescu-Roegen central message is a devastating attack on mathematization in the social sciences in general and
economics in particular, and a wise critique of the values and limitations of mathematics in the analysis of human
behavior and social phenomena. He agues as follows: Mechanistic model building, and the arithomorphism of
theory, the consequences of an effort in by modern economics to conform to the formal cannons of classical physics,
has destroyed the relationship between statement (premise) and experience (observation), (brackets added).
While the First Law of Thermodynamics is an expression of the conservation of energy, it is the
Second Law that expresses the fundamental nature of irreversibility, indeterminism, and
complexity in Nature. Thus, unlike the neoclassical concern of reducing complexity to a set of
(static) equalities of conserved value, Georgescu-Roegen chose to examine the change of forms
and qualities of economic objects and functions by applying the (holistic) dialectic method. In
18
other words, it involved an analysis of the economic process as an ordinal progression in
continuous real time and real, as opposed to abstract, space.
19
Georgescu-Roegen’s exploration of the ‘physics of value’ led to the discovery of the new
discipline of ‘Bioeconomics’, which combined elements of evolutionary biology, ecology, and
conventional economics (Mayumi, 2001). Alfred Marshall anticipated Georgescu-Roegen’s
Bioeconomics :
20
The Mecca of the economist lies in economic biology rather than economic dynamics. But biological conceptions are
more complex than those of mechanics; a volume on Foundations must therefore give a relatively large place to
mechanical analogies; and the frequent use of the term "equilibrium," which suggests something of a statical
analogy. This fact, combined with the predominant attention paid in the present volume to the normal conditions of
life in the modern age, has suggested the notion that its central idea is “statical”, rather than “dynamical”. But in
fact it is concerned throughout with the forces which cause movement: and its key-note is that of dynamics, rather
than statics. (Marshall, 1947, pp. xiv)
Bioeconomics entails the parameters of complexity. Georgescu-Roegen proposed the dialectical
methods to study ‘emergence’ of novelty and to apply the entropic process to evolutionary
change that cannot be predicted by extrapolating the past into the future. The validity of
Fichtean/Hegelian Dialectics postulate that: (i) everything is transient and finite, existing in the medium of time;
18
(ii) everything is made out of opposing forces/opposing sides (contradictions); (iii) gradual changes lead to turning
points, where one force overcomes the other (quantitative change leads to qualitative change); and (iv) change
moves in spirals (or helices), not circles (sometimes referred to as ‘negation of the negation’).
For instance administrative boundaries are abstract space and can be changed from one instant to the next by
19
decree. Geographical space require that the boundary conditions be specified by observed differences in the qualities
of the biome or in hydrological/geological formation, river basins, mountain ranges etc.
Alfred Marshall similarly rejected the notion of a general equilibrium system. While the individual markets may
20
tend towards equilibrium, (i.e., supply = demand), the relationship among markets may tends towards disequilibrium
states, like the world oil market, international trade, and any market with political interference, subsidies, rationing,
currency, etc.

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statistical projections of the past into probable states of the unknowable future was challenges as
follows:
Social Scientists…apply mathematical operations on paper to any number they can can get hold of, or think of,
without stopping for one moment to consider whether these operations have any meaning at all. Do we not
frequently see economists adding discounted utilities to future dates -i.e., discounted future fluxes - as if they were
annuities paid in money (a cardinal variable)? … As I have intimidated, quantity cannot be regarded as a notion
21
prior to quality, either in the logical or evolutionary order, (Georgescu-Roegen, 1971.pp.99).
The dialectical theory was employed, largely by continental social scientists after Hegel (i.e.,
thesis → antithesis → synthesis), to identify the salient vectors of chronological trajectories of
future sates of the system. The alternative theory employed, largely by analytical social scientists
after Darwin chose ‘randomness’ of mutation as the salient vector of evolutionary processes.
Unlike the Hegelian dialectic, in which ‘emergence’ identified with the synthesis of paired
opposites (thesis/antithesis), randomness can built in the algorithm of the entropic process.
’Synthesis’ of conflictual, multi-dimensional, parameters identified in complex adaptive systems,
can be specified in the vector of convergence towards some well-identified ‘attractor.’ The
stabilisation of tha attractor draws the algorithm to a conclusion, (Prigogine,1997).
Rosen (1994) proposed the method of anticipatory modelling of formal systems parameters (i.e.,
algorithms of the Econosphere) mapped on the observed parameters of natural system (i.e.,
algorithms of the Ecosphere). Of interest is the deviation of the formal system trajectories, upon
which policy is based, from the observed trajectory of natural systems.
7. Entropy Production and the UN Agenda 21.
Entropy production, expressed as a rate of depletion of the low entropy ecological Fund (i.e.,
natural capital), came onto the world stage at the UN Conference on the Human Environment
(Stockholm, 1972). Twenty years later, the UN Conference on Environment and Development
(Rio de Janerio, 1972) produced an action plan to reduce the rate of depletion of this Fund under
the rubric of sustainable development. The plan, entitled Agenda 21, produced a comprehensive
blueprint for the conservation of the global fixed and circulating natural capital – in other words,
a plan to reduce the rate of entropy production at the global, national, and local level through
government, international and NGO actions.
While Agenda 21 was rich in semantics, there was a singular lack of a comprehensive, syntactical
structure to integrate the programme areas into a higher-order complex systems analytical
framework. The result, perhaps inevitable considering the number of experts involved, was to
advise on how to mitigate the material cause of events detailed in the programme areas of
desertification, deforestation, biodiversity, atmospheric pollution, and so forth. In an integrated
framework, the whole would be addressed before the particulars. In other words, the analysis,
The Stern Report (2007) present-value discount of income flows, albeit at 2-3 per cent of global GDP, in order to
21
avoid an even greater loss of income in the future, is an example of the neoclassical arithomorphism applied to the
wellbeing of future generation of unknowable values.

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and the a priori questions, would focus on formal causes, such as national economic and social
policies; final causes, such as social and cultural values; and time-delay feedback loops of
historical events (Gunderson and Holling, 2002).
Chapter 40 of Agenda 21 addresses the question of information and data. It is here that the
lack of syntax in Agenda 21 is most evident (Friend and Rapport, 1991). While macro-accounting
is referred to as important, necessary, and needs to be improved, there is no mention whatsoever
on statistical methods to integrate the social and natural science datasets into a single framework.
Nor is there any reference to the valuation of the global ecological debt. The latter is valued in
SAGE-P as the full accounting cost necessary to replenish, in the context of the steady-state, the
human-consumed stock of the low entropy ecological Fund. The advice on data was primary on
the development of ad-hoc indicators to measure the degree of sustainability as follows:
40.4. Commonly used indicators such as the gross national product (GNP) and measurements of
individual resource or pollution flows do not provide adequate indications of sustainability.
Methods for assessing interactions between different sectoral environmental, demographic, social
and developmental parameters are not sufficiently developed or applied. Indicators of sustainable
development need to be developed to provide solid bases for decision-making at all levels and to
contribute to a self-regulating sustainability of integrated environment and development systems.
40.6. Countries at the national level and international governmental and non-governmental
organizations at the international level should develop the concept of indicators of sustainable
development in order to identify such indicators. In order to promote the increasing use of some
of those indicators in satellite accounts, and eventually in national accounts, the development of
indicators needs to be pursued by the Statistical Office of the United Nations Secretariat, as it
draws upon evolving experience in this regard.
9. SAGE-P: Category Theory and the Homomorphism of Entropy Production
Category Theory, also referred to as conceptual mathematics, is a formalism for object/functional
mapping of: (i) object → objects; (ii) object → functions; (iii) function → objects; and (iv)
function → functions (Lawvere, and Schanuel, 1997; Friend and Friend, 2009). The formalism
assumes ‘structure preserving’ operations termed homomorphism (i.e., a transformation of one set
into another that preserves in the second set the relations between elements of the first). The
category set is a collection of elements defined by the boundary condition of the set, such as an
economy defined by national boundaries. Technically, the objects of the set are identified by
‘common properties’ and/or ‘common end-objectives’. The latter defines the function of objects
classified to the three fundamental category sets of SAGE-P – namely: (i) Econosphere; (ii)
Sociosphere; and (iii) Ecosphere.
The category sets are isomorphic structural accounts of the low entropy Fund (i.e., empirically-
observed data). In mathematics, isomorphism involves structure preserving mapping between
objects that shows a relationship between two properties or operations. If there is an isomorphism

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between two structures, we can call the two structures isomorphic. In a certain sense (i.e., if you
choose to ignore finer-grained differences that may arise from how they are defined), isomorphic
structures are structurally identical.
The (analytical) datasets are produced through the algorithms of correspondence mappings
(i.e., the homomorphism), which maps the rate of entropy production on the elements of the low
entropy Fund. The structure preserving algorithm is a set of isomorphism of conserved values
identified with specific objects and/or functions described in the datasets.
The fundamental category sets of the System of National Accounts (SNA) are: (i) production
accounts; (ii) consumption accounts; (iii) capital accumulation accounts; and (iv) trade with the
rest-of-the-world accounts (Stone, 1968). The Keynesian definition of the boundary conditions of
the institutional-market economy assumes an isomorphic structure of the System of National
Accounts (Keynes, 1960). These are the identifiers (or algorithm) of conserved values of Income
(Y), Consumption (C), Saving (S) and Investment (I). Figure 3.2 demonstrates the
correspondence mapping of the System of National Accounts on SAGE-P. Note, here, that
SAGE-P, as a more general and larger-scale description of the economic process, fully integrates
the System of National Accounts as a proper subset. However, the accounting methodology
remains as given, being a special case of the institutional-market economy.
Unlike the pluralism of SAGE-P valuation methods, the isomorphism of the System of National
Accounts assumes single-value methods denoted in prices to assess complex, interactive,
transformation processes, or equivalences (i.e., non-market valuation methods) (Norgaard, 1989;
Friend, 1993). While prices may, on occasion, correlate to conservation principles, such as a
22
carbon tax, the reliance on a single valuation method is dangerous, not only for policy decisions
(witness the resistance to the Kyoto Protocols due to the cost of reducing greenhouse gas
emissions), but because the integration of social and natural science databases is a sine quo non
for understanding complexity, qualities of human welfare, and the limit functions of the
(material) economy.
The SAGE-P isomorphism of transformations of entropic processes are of two types: (i) the
algorithm to construct statistical time series of object/function datasets, and (ii) the algorithm to
construct a geo-coded dataset of (i). While the latter is much easier to produce than the former,
the location of events is an invariable with its spatial co-ordinates, whereas objects in the former
change properties over time. These ‘events’ express the evolution of objects in the time series and
may appear and disappear in unpredictable, random ways.
A further distinction that needs to be made is between the correspondence mapping of abstract
and physical objects. Clearly, abstract objects in themselves cannot be mapped to co-ordinate
space. However, when abstract properties, like beauty of place, are attached to physical objects,
The non-market valuations drop out of the System of National Accounts, as these data are represented in the
22
money-valued elements in the social and environmental accounts. Thus, the System of National Accounts is freed
from imputations of equivalences between market and non-market objects.

!22
the mapping of abstract objects on spatial coordinates are possible. It is nonetheless a tricky
exercise, insofar as abstract objects are, for the most part, ephemeral and, above all, not subject to
the Second Law of Thermodynamics. In other words, abstract objects are not directly observable
objects, like ground cover from satellite imagery, but must be placed by the human imagination
or be institutionally defined, like geographical administrative spaces.
23
SAGE-P assumes nonlinearity in algorithms and associated vector analysis of entropic processes
and transformation functions. Category sets of the entropic process are: (i) the set of objects
24
that enter the Fund (i.e., the rate of negentropy production); (ii) the set of objects that exit the
Fund (i.e., rate of entropy production); and (iii) the set of objects which constitute the low
entropy Fund. While (i) and (ii) are measures of flows over a period of time and equivalent to
production and consumption in the System of National Accounts, (iii) is a measure of stock at an
instant-in-time and equivalent to the surplus/deficits in the balance sheets of the System of
National Accounts. The third category set thus represents the net-value of the Fund in three sub-
sets: (i) fixed capital (i.e., non-renewable objects, like fossil fuels); (ii) circulating capital (e.g.,
reproductive objects, like food and manufactured goods); and (iii) cycling capital (i.e.,
atmosphere, hydrosphere, and lithosphere).
SAGE-P proposes hierarchical, valued-structured, topological domain spaces of three basic
categories of objects and functions, viz:
•values conserved-in-exchange = economic objects/functions → Econosphere;
•values conserved-in-use = social objects/functions → Sociosphere;
•values conserved-in-themselves (existential) = ecological objects/functions → Ecosphere.
The low entropy Fund is an ordinal-valued dataset of objects and functions mapped from lower-
to higher-order categories as follows: (i) {[(Econosphere) → Sociosphere] → Ecosphere}; (ii)
the hierarchical structured mapping of efficiencies: {[(economic money-valued efficiency) →
social participatory-valued efficiency] → existential -valued eco-efficiency}; and (iii) the
hierarchical structured mapping of the welfare function: {[(economic well-being) → social well-
being] → ecosystem health and integrity}.
The objects of the SAGE-P fundamental category sets are usefully distinguished by being
material or non-material objects, the latter we shall call abstract objects, and the former, physical
objects. Since our central concern is to account for the rate of entropy production, we need to
identify the objects in the low entropy Fund which can be replenished and those which cannot.
Thus, we are able to make a distinction between reproducible physical objects, and non-
Administrative boundaries can sometimes be clearly observed from air by observing the patterns of land-use. The
23
US-Mexican border is observed sharply in contiguous urban and agricultural zones, but not in with the wild desert
zone.
Entropy production functions in complex systems need not be identified in the strict sense of causal relationships,
24
but rather in the weaker sense of probabilities. The precautionary principle is based on uncertainty, and the risk
factor is merely a probability function assumed by a priori knowledge. See the discussion on Bayesian statistical
methods.

!23
reproducible physical objects – the latter representing exhaustible resources, and the former,
renewable resources.
Abstract objects, by definition, do not occupy space. Therefore, while they may appear,
disappear, grow, and decay, they are not directly subject to the Second Law of Thermodynamics.
Nonetheless, abstract objects may be clearly identified with inflows, outflows, and entropic
processes. They may also be net-valued in the LEF, generalised as a stock of information
25
available for human use and, like physical objects, are conserved in the Econosphere as
exchange-values; in the Sociosphere as use-values; and in the Ecosphere as in existential-values.
Replenishing physical objects may be categorised circulating capital that: (i) occupy space; (ii)
are subject to the Second Law of Thermodynamics; (iii) are conditionally reproducible; and (iv)
26
cardinally measured in quantity units and ordinal measured in qualitative properties.
Non-replenishing physical objects may be categorised as a complex set of fixed and
27
(conditional) cycling capital that: (i) occupy space; (ii) are subject to the Second Law of
Thermodynamics; (iii) are non-reproducible; and (iv) cardinally measured in quantity units and
ordinally measured in qualitative properties.
Abstract objects may be categorised as the collection of objects in the immaterial world. The
boundary condition – for example, financial investment – may be identified either directly, or
indirectly, with causal factors associated with any well-defined entropic process. Abstract objects
are clearly identified in the economic process as the inflows and outflows of ‘services’ in
material production, consumption, and capital accumulation. Abstract objects may also be
mapped on other abstract objects to produce a new set of abstract objects. This, indeed, is the
familiar operational functions of the financial sector of the economy, but includes the boundary
conditions (i.e., inflow/outflow), the institutional structure of the Sciosphere – e.g., education,
governance, jurisprudence, religion, health services, entertainment, etc. – but not the
epidemiological dataset. The latter represent the ‘health status’ of physical objects of the low
entropy (population) Fund.
In information theory, entropy is a measure of the uncertainty associated with a random variable. In this context,
25
the term usually refers to Shannon entropy, which quantifies the expected value of the information contained in a
message, usually in units such as bits. Equivalently, the Shannon entropy is a measure of the average information
content one is missing when one does not know the value of the random variable. The concept was introduced by
Claude E. Shannon in his 1948 paper, ‘A Mathematical Theory of Communication’.
These are state conditions where the object, while replenished, changes properties. In economic analysis,
26
substitution assumes qualitative change of objects for equivalent values. In SAGE-P analysis, substitution reflects
the human acceptance of inferior qualities of objects in the consumption function, because the superior quality object
is unavailable or unaffordable.
Note that non-renewable processes generally decline at the rate of (human) consumption. While associated with
27
exhaustible resources in geological time, like fossil fuels, they include objects of human artifacts, like historical
monuments and, of course, extinct biological objects and/or irreversible ecosystem functions, like the collapse of the
cod fishery stocks off the Newfoundland coast. Cycling capital, atmosphere, hydrosphere, and lithosphere has been
included in this category. This is because, while circulating, the global quantitative value is fixed, but subject to the
distributional and qualitative change in values.

!24
While requiring some imagination, one can apply a physical analogue to the conceptual
framework of abstract object accounting. This is nothing less than the research program of
‘quantification’ in the social sciences. A useful distinction for the hierarchical structured
mappings of objects on objects, and functions on functions, is the recognition of ordinal causal
relationships. Here, physical objects are generally identified with material cause (observed state)
and efficient cause (instrumental-physical), while abstract objects are identified with formal
cause (instrumental-nonphysical) and final cause (social values). Like objects in the material
world, abstract objects may be similarly categorised into replenishable and non-replenishable
objects and similarly subdivided into fixed, circulating, and cycling capital. The properties of
abstract capital: (i) does not occupy space; (ii) is not subject to the Second Law of
Thermodynamics; and (iii) owes its existence to acknowledgement (informal) and/or entitlement
(formal).
The powerful isomorphism of SAGE-P that links physical with abstract objects permits the
mapping of ordinal values on the state (position), and the change of state (movement), of well-
defined accounting objects and functions. While immaterial things do not occupy space by
definition, they nonetheless may be presented by volume, density, or other metrics in imaginary
space – for example, global information pathways in the internet, the physical location of bank
accounts in Switzerland, or the cyclical movement in the New York stock exchange, etc.
28
Abstract objects mapped on other abstract objects provides the datasets of the higher-order effect
(i.e., formal cause) on the rate of entropy production in the material economy. For example, a
mapping of approvals of sub-prime mortgages → debit/credit swaps → toxic debts in bank
balances → 2009 Financial Crisis ← physical location and number of house foreclosures in
American suburbs.
Conserved values-in-exchange constitute the structure preserving the homomorphism of the
System of National Accounts. This is illustrated by the correspondence mapping of the elements
in the consumption function (demand) on the elements in the production function (supply) to
arrive at the equilibrium state of the economy (i.e., supply equals demand). The correspondence
mapping of GDP on the SAGE-P datasets results in the gross-value of entropy production, the
mirror image of the consumption function. The former is a linear price evaluation of output
denoted as GDP – an aggregation of abstract objects. In contrast, the former is a nonlinear
complex construct (i.e., algorithms) for mapping physical objects on physical objects to obtain an
aggregate entropy production matrix (i.e., the transformation of low entropy inputs into high
entropy outputs).
That does not mean that the abstract objects do not have spatial identifiers, like the enjoyment of scenery in the
28
Alps, or the enjoyment of the ballet in the Bolshoi Theatre in Moscow. The essential idea is that of mapping abstract
objects on abstract objects, like financial flows and balances, or the mapping of abstract objects on physical objects,
like prices on goods, but not services. Indeed, GDP may be viewed as a mapping of prices on all the (final) goods
(physical objects) and services (abstract objects) produced in the economy in one year. It should be noted that the
System of National Accounts is a method to reduce physical objects (material economy) and abstract objects
(immaterial economy) into the single denominator of market prices. In other words, it is a method to reduce complex
physical processes into a pure abstract value-object disconnected from the physical universe.

!25
Note that the objective function of SAGE-P is to measure entropy efficiency per unit of
consumption. Thus, the Flow-Fund Model, not too dissimilar to the input/output Tables of the
System of National Accounts, measures the material-energy ‘throughputs’ identified with the set
of macro-accounts on the consumption of (final) goods and services in the economy (Daly,
1977). The difference between the System of National Accounts and SAGE-P is that, while the
former maps price efficiencies on factors of production (cost per unit of output), the latter maps
entropy efficiencies on the set of factors of production identified with the entropic process.
Daly and Cobb (1989) have observed that the neoclassical method of mapping price efficiencies
on the consumption function results in the logical fallacy of ‘misplaced concreteness’. In other
words, abstract object → abstract object ≠ physical object. In this case, the abstract object is the
ordinal-valued utility function to be optimised, which measures the degree of satisfaction (or
service flows) from a well-defined material consumption function. The missing equation in the
neoclassical analysis is the mapping of abstract objects (values) on physical objects (entropic
process) to obtain ordinal-valued utility function, where the objective function is some well-
defined minima of a socially acceptable rate of entropy production (Mayumi, 2001).
10. Bayesian Statistical Methods: nonlinear statistics and evolutionary processes
SAGE-P permits non-discounted present day evaluations of risk and uncertainty of large-scale
future events, 30 to 50 years hence. The pluralistic valuation method provides data for policy
analysis unique to the entropy production algorithm of the TDS, (i.e., the Econosphere, the
Sociosphere and the Ecosphere). Rosen (1985) ‘anticipatory system’ concept provides a template
for the hierarchically-structure mapping of algorithms formal systems (models) on natural
systems (observations). The common denominator of algorithms is the I/O of any well-defined
entropic process. The Rosen’s anticipatory system assumes the Bayesian method of ‘prior
probability’ in unfolding event process, where a future is latent in the present structure of the
system, and thus detectable, if one knows what one is looking for, (see Appendix II: Bayesian
Statistical Methods).
The distinction needs to be made between statistical ‘uncertainty’, concerning bias in the sample
for instance, and scientific uncertainty, concerning evidence and proof. The issue of scientific
uncertainty embedded in complex systems was well-explored by Funtowicz and, Ravetz, (1991)
in “Uncertainty and Quality in Science Policy.” The conclusion drawn is that investigative
science of complex systems can no longer be treated as purely objective, and that ethical and
moral questions need to be considered in the evaluation of the quality of (science) data. A
secondary conclusion is importance of qualitative assessment of data requiring transparency and
openness in any well-designed policy at the the scale of climate change and transformation to
sustainable, green, economies.
The algorithms for mapping objects → objects; objects → functions; functions → objects; and
functions → functions in SAGE-P while constructed from a priori propositions (i.e., pre-set

!26
instructions of the programmer), the data entered into the algorithm are a posteriori proposition
(i.e.,observations), (Berlinski, 1999).
29
Kant’s analytic-synthetic distinction, also called the analytic-synthetic dichotomy, is helpful in
understanding the distinctions between scientific uncertainty. (i.e., a posteriori propositions) and
statistical uncertainty, (i.e., a priori propositions).
•analytic proposition: a proposition whose predicate concept is contained in its subject concept;
•synthetic proposition: a proposition whose predicate concept is not contained in its subject
concept.
These two propositions can be further classified with respect to:
•a priori proposition: a proposition whose justification does not rely upon experience;
•a posteriori proposition: a proposition whose justification does rely upon experience.
Combining the above definitions, we now have four types of proposition to construct the
accounting algorithms of SAGE-P :
1. analytic, a priori propositions;
2. synthetic, a priori propositions;
3. analytic, a posteriori propositions;
4. synthetic, a posteriori propositions.
Applying the above four proposition to the construction of the accounting algorithms for the
System of National Account (SNA) and SAGE-P we have:
SNA = analytic propositions, (i.e.,General Equilibrium System) with a correspondence mapping
of a priori propositions, (i.e., statistics pre-defined by analytic propositions for Production,
Consumption, Capital and Trade with the rest-of-the-world).
SAGE-P = synthetic propositions, (i.e., Entropic Process) with a correspondence mapping of a
posteriori propositions, (i.e., statistics defined by a posteriori propositions of the boundary
conditions for Negentropy, Entropy and Low Entropy Fund).
Note that the synthetic propositions of SAGE-P are symmetric (i.e., translation) to the SNA but
not the reverse. The reason: the SNA (Econosphere) is a proper subset of the SAGE-P
(Ecosphere).
11, SAGE-P: construction of synthetic, a posteriori, statistical databases
Bayesian statistics, a priori knowledge, also known as the prior distribution (θ) of the observed
events (Θ) is permissible under some ordinal set of well-defined causal protocols. SAGE-P
There is some ambiguity of what actually is being observed in statistical databases. Economic and social
29
statistical databases are largely constructed from surveys, with pre-defined categories. Demographic data is a direct
observation of the population and can be counted in numbers of people with specific time and location.
Environmental data is perhaps the least ambiguous observation if taken from satellite imagery, the location and time
of the data are exact. The data on spot checks and sampling of physical objects run into the same degree of
uncertainty as those of socio-economic surveys.

!27
adapts the Aristotelean causal protocols in the mapping of probability and limit functions on the
datasets of: (i) material cause (π1); (ii) efficient cause (π2); (iii) formal cause (π3); and (iv) final
cause (π4). These are mapped pairwise to produce joint prior distribution estimators of expected
events (i.e., π2 θ → π1 Θ = θ’; π3 θ → π2 Θ = θ’’; π4 θ → π3 Θ = θ’’’), where:
•θ represents a statistical distribution (e.g., observed events) of the material cause (π1);
•θ’ represents the prior distribution (e.g., technology) of the efficient cause (π2);
•θ’’ represents the prior distribution (e.g., policy) of the formal cause (π3);
•θ’’’ represents the prior distribution (e.g., socio/cultural values) of the final cause (π4);
Note that the material cause represents the observed data of the normal distribution of events
with accuracy of any particular prediction being informed by its standard deviations (σ) from the
mean (μ). Thus, Bayesian Methods provide the decision-maker (and the public) with the
estimators of probability distribution of events (x1 ….xn) representing the initial state conditions
of the material cause, π1 Θ = θ1 (data observed on the ground). The SAGE-P material dataset may
be modified under well-defined conditions representing probabilities of the change of state of the
system due to efficient cause π2 Θ = θ2 (technological conditions); formal cause π3 Θ = θ3 (policy
conditions); and final cause π4 Θ = θ4 (social value conditions).
Bayesian statistics fix the normal distribution of the observed event x a priori. While traditional
statistical average probability of an event x happening over the state conditions of the observed
sample itself: x ∈ Θ, the result is a (linear) extrapolation of probability function, assuming a
statistical correlation of past events into the future. Bayesian probability of the event x happening
is modified by ‘degrees of belief’ of a potential and/or hypothetical distribution of (probable)
events θ: x ∈ Θ. This is known as a generalized Bayes rule with respect to π θ. There maybe
more than one generalized Bayes rule, since the model may require multiple and complex
conditional relations between x and y. This may be generalized as mapping of different formal
systems, or models, on natural systems: θ ∈ Θ (e.g., What if? scenario modeling). Applying the
Rosen ‘anticipatory system’, the prior distribution (θ) predicts the probability of event x as a
mapping: θ → Θ, [i.e., mapping of a formal system (θ) on a natural system (Θ) to predict the
next event in Θ] (see Appendix 3.2 on Bayesian Statistical Methods).
12. Further observation of the Bayesian Method
Macro-accounting assumes, as given, the institutional structure of society and its social values.
While construction of the datasets may be scientific, applying sound statistical methods, the
social value structure, including political intervention (e.g., the definition of ‘unemployment’),
may not only bias the selection of data collected (i.e., administrative vis-à-vis scientific data), but
also the qualitative assessments of the state and the change of state of the observed datasets.
30
This was clearly recognized by the UN Statistical Office by permitting the social value bias to enter the System
30
of National Accounts. Here, the Marxist versus the capitalist bias entered the valuation of the ‘National Product.’ The
latter valued the annual goods and services at ‘willingness-to-pay’ basis, or market prices, while the former valued at
the cost of production of the material product – thus, assuming a labour theory of value. However, the UN Statistical
maintained its own bias with respect to the non-monetised sector of the national economies and thus the ‘product’ of
the household and the non-monetised ‘natural product’ was left out of the accounts. This can be corrected by a
‘service-flow’ income accounting.

!28
The latter is particularly sensitive to the order of the evaluation protocols, where, for example,
commercial values override cultural values (Maslow,1968). The Bayesian Method permits values
to be modified, and indeed evolve, with the change of social values.
In reality, the accounts are constructs of the accountant who assumes the role of the neutral
observer of ‘facts’. Bayesian parameters of ‘degrees of belief’ are thus ruled out of any
consideration for the objective function for the accounts. This, in the Bayesian language, is
illusionary, as degrees of belief are found in every fact, since there is no absolute certainty. This
becomes glaringly obvious in the assumption that willingness-to-pay equals willingness-to-sell,
the code-word for conserved values-in-exchange, which, under given conditions, represents in
the neoclassical model an unbiased sample of consumer preferences. Even under the condition of
‘perfect competition’, consumer preferences are not only manipulated by advertising, or pure
lack of information, but by time preferences of (discounted) future streams of consumption. The
belief in future state conditions of consumption is pure Bayesian and finds representation in an
index number of ‘consumer confidence’ following an economic crisis.
Even more problematical are the (inflexible) institutionally-defined objects and functions of
accounts, exacerbated by the penumbra of the boundary conditions of categories. For instance, is
‘housework’ value-added, or value-subtracted to the national product. Clearly the inflows
material products, like tools, cleaning fluids, household appliances and the human labour
performed, is no different labour performed by the producer and added to the low entropy fund
available of for consumption, albeit by same members of the household. While clearly not an
economic product for sale, with a definite exchange-value, it has indeed definite use-value and to
the extent that the family is a micro-ecosystem, existential value. If government policy is to
increase the national product, it would make sense add housework
The non-institutional SAGE-P there is no distinction made between household and market
production functions, and indeed, except for its factors of production, is a distinction made
between human and Nature’s production production, consumption and capital accumulation
functions. What is observed, and measured, is the direction of material inflows towards order,
disorder, or steady-state of dissipative structures.
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Future, Oxford University Press, Oxford.
Zukav, G. (1979), The Dancing Wu Lim Masters: An Overview of the New Physics,
William Morrow, New York.

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Appendix I
Georgescu-Roegen’s Flow-Fund Model
Factors of production are divided into two categories: the Fund elements, which represent the
agents of the process, and the flow elements, which are used or acted upon. Each flow element is
represented by one coordinate Ei(t). The fund element enters and leaves the process with its
efficiency intact. Specifically, we can represent the participation of a Fund Cσ by a single
function Sσ(t) showing the amount of services of Cσ up to the time t, where 0 ≤ t ≥ T.
The analytical presentation of a Process can thus be written [ ] , where the i subscript
represents input or output and σ represents both inputs and outputs.
As for the analytical coordinates of a partial process, analysis must renounce the idea of
including in the description of a process, either inside or outside it, the problem associated with
the happenings with a process reducing to recording only what crosses the boundary. For
convenience, we may refer to any element crossing the boundary from the environment into the
process as an input, and to any element crossing it from the opposite direction as an output. At
this juncture, analysis must make some additional heroic steps all aimed at assuming away
dialectical quality.
Discretely distinct qualities are still admitted into the picture as long as their number is finite and
each one is cardinally measurable. If we denote the elements that may cross the t boundary of a
given process by C1, C2, C3, … Cn, the analytical description is complete if, for every Ci, we have
determined two non-decreasing functions Fi(t) and Gi(t), the first showing the cumulative input,
the second, the cumulative output of Ci up to the time (t). Naturally, these functions must be
defined over the entire duration of the process which may be always represented by a closed time
interval such as [0, T]. The question of whether this analytical model is operational, outside
paper-and-pencil operations, cannot be decided without an examination of the nature of the
elements usually found in actual processes. Such an examination reveals that there exists
numerous elements for which either Fi(t) or Gi(t) is identically null for the entire duration of the
process. Solar energy is a typical example, which is only an input for any terrestrial process. The
various materials ordinarily covered by the term ‘waste’ are clear examples of elements which
are only outputs. In all these cases, we may simplify the analytical picture by representing each
element by one coordinate only – namely, by:
Ei(t) = Gi(t) – Fi(t)
For an output element, Ei(t) = Gi(t) ≥ 0; for an input element, Ei(t) = -Fi(t) ≤ 0. The sign of the
suffices indicate which is actually the case (Georgescu-Roegen, 1971, p. 215).
Georgescu-Roegen further distinguishes Ei(t), which are (basic) elements necessary to
maintain the production cycle at a steady-state (e.g., seeds → crops) and Ei(t), which are (non-
basic) elements that are surplus available for consumption, Ei(t) = Gi(t) – Fi(t) ≥ 0."

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Appendix II
Bayesian Statistical Methods31
Thomas Bayes addressed both the case of discrete probability distributions of data and the more
complicated case of continuous probability distributions. In the discrete case, Bayes’ theorem
relates the conditional and marginal probabilities of events A and B, provided that the probability
of B does not equal zero. Thus: P(A|B) = P(B|A) P(A)/P(B)
In Bayes’ theorem, each probability has a conventional name:
• P(A) is the prior probability (or ‘unconditional’ or ‘marginal’ probability) of A. It is ‘prior’ in
the sense that it does not take into account any information about !B; however, the event !B
need not occur after event!A. In the nineteenth century, the unconditional probability!P(A) in
Bayes’ rule was called the ‘antecedent’ probability; in deductive logic, the antecedent set of
propositions and the inference rule imply consequences. The unconditional probability!P(A) is
called ‘a&priori’.
• P(A|B) is the conditional probability of A given B. It is also called the posterior probability
because it is derived from or depends upon the specified value of!B.
• P(B|A) is the conditional probability of B given A. It is also called the likelihood.
• P(B) is the prior or marginal probability of B, and acts as a normalising constant.
Bayes’ theorem, in this form, gives a mathematical representation of how the conditional
probability of event A given B, is related to the converse conditional probability of B given A.
Bayes’ theorem with continuous prior and posterior distributions
Suppose a continuous probability distribution with probability density function!ƒΘ is assigned to
an uncertain quantity!Θ. In the conventional language of mathematical probability theory, Θ
would be a ‘random variable’. The probability that the event B will be the outcome of an
experiment depends on Θ; it is P(B!|!Θ ). As a function of Θ, this is the following likelihood
function:
L(θ) = P(B!|!Θ = θ)
The posterior probability distribution of!Θ (i.e.,!the conditional probability distribution of Θ,
given the observed data!B), has the probability density function:
fΘ(θ|B) = constant · fΘ(θ)L(B|θ)
where the ‘constant’ is a normalising constant so chosen as to make the integral of the function
equal to!one, so that it is indeed a probability density function. This is the form of Bayes’
theorem actually considered by Thomas Bayes. In other words, Bayes’ theorem says: ‘To get the
posterior probability distribution, multiply the prior probability distribution by the likelihood
Wikipedia entry on Bayesian Statistics.
31

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function and then normalise.’ More generally, still, the new data B maybe the value of an
observed continuously distributed random variable!X. The probability that it has any particular
value is therefore!zero. In such a case, the likelihood function is the value of a probability density
function of X given Θ, rather than a probability of B given Θ:
L(θ) = fx(x | Θ = θ)
Notation and Definitions
In the notation P(A|B), the symbol P is used only as a reference to the original probability. It
should not be read as the probability P of some event A|B. Sometimes the more accurate notation
PB(A) is used, but the use of complex events as index of the symbol P is cumbersome. Notice that
the line separating the two events A and B is a vertical line.
Conditional probability is the probability of some event A, given the occurrence of some other
event B. Conditional probability is written P(A|B), and is read ‘the (conditional) probability of A,
given B’ or ‘the probability of A under the condition B’. When in a random experiment, and the
event B is known to have occurred, the possible outcomes of the experiment are reduced to B,
and hence the probability of the occurrence of A is changed from the unconditional probability
into the conditional probability given B.
Joint probability is the probability of two events in conjunction. That is, it is the probability of
both events occurring together. The joint probability of A and B is written as P(A|B), P(AB), or
P(A, B). Marginal probability is then the unconditional probability P(A) of the event A; that is,
the probability of A, regardless of whether event B did or did not occur. If B can be thought of as
the event of a random variable X having a given outcome, the marginal probability of A can be
obtained by summing (or integrating, more generally) the joint probabilities over all outcomes
for X.
The conditioning of probabilities (i.e., updating them to take account of (possibly new)
information), may be achieved through Bayes’ theorem. In such conditioning, the probability of
A given only initial information I, P(A|I), is known as the prior probability. The updated
conditional probability of A, given I and the outcome of the event B, is known as the posterior
probability, P(A|B, I).
A continuous probability distribution is a probability distribution which possesses a
probability density function. Mathematicians also call such a distribution absolutely continuous,
since its cumulative distribution function is absolutely continuous with respect to the Lebesgue
measure λ. If the distribution of X is continuous, then X is called a continuous random variable.
There are many examples of continuous probability distributions: normal, uniform, chi-squared,
and others.
The probability density function, or density of a continuous random variable, is a function that
describes the relative likelihood for this random variable to occur at a given point. The
probability for the random variable to fall within a particular region is given by the integral of
this variable’s density over the region. The probability density function is non-negative
everywhere, and its integral over the entire space is equal to one."

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Appendix III:
SAGE-P datasets on the state and change of state of the Econosphere,
Sociosphere, and the Ecosphere
Propositions
Proposition I: An entropic Process in SAGE-P is an algorithm to map the transformation of
(statistical) objects from lower into higher entropic states (i.e., consumption), and its inverse
from higher into lower entropic states (i.e., production).
The proposed methods to construct the algorithm are prescribed Bayesian Rules for scalar
operators in any well-defined, hierarchical-structured, complex adaptive system in Topological
Domain Space (TDS), defined as:
Econopshere (E') ⊆ Sociosphere (E") ⊆ 0 (E"')
where ⊆ = subset.
Scalar operators of the ecological flow-fund are a slow moving, but much larger scale to the
socio-demographic Fund, which, in turn, is larger, but slower moving to the economic Fund (i.e.,
E"' > E"> E').
•The elements of the E' dataset belonging to the Econosphere TDS are characterised by fast
moving state, and change of state, variables described by emergent properties of dissipative
economic structures far from equilibrium: (i.e., domain properties of the low entropy
economic fund);
•The elements of the E'' dataset belonging to the Sociosphere TDS are characterised by slow
moving state, and change of state, variables described by emergent properties of dissipative
social-institutional structures near equilibrium (i.e., domain properties of the low entropy
socio-demographic Fund);
•The elements of the E''' dataset belonging to the Ecosphere TDS are characterised by very slow
moving state, and change of state, variables described by emergent properties of dissipative
ecosystem structures very near equilibrium (i.e., domain properties of the low entropy global
ecosystem Fund).
Proposition II: The homomorphism of SAGE-P datasets are conserved value mappings of objects
→ objects; objects → functions; functions → objects; and functions → functions among any
well-defined TDS:
•Econosphere: the homomorphism of economic objects/functions are the values conserved-in-
exchange;
•Sociosphere: the homomorphism of socio-demographic objects/functions are the values
conserved-in-use;
•Ecosphere: the homomorphism of socio-demographic objects/functions are the values
conserved-in-themselves (i.e., intrinsic value).

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Proposition III: SAGE-P functions are defined by the boundary conditions of processes unique to
any well-defined TDS. Objects are defined by the boundary conditions of the objects-in-
themselves, but change values with respect to function:
•Objects where values are conserved-in-exchange ∈ Econosphere
•Objects where values are conserved-in-use ∈ Sociosphere
•Objects where values are conserved-in-themselves ∈ Ecosphere
Proposition IV: SAGE-P qualitative properties of Objects change with Function:
•Social and ecological objects where qualities are values conserved-in-exchange ∈ Econosphere;
•Economic and ecological objects where qualities are values conserved-in-use ∈ Sociosphere;
•Economic and social objects where qualities are values conserved-in-themselves ∈ Ecosphere.
Structure of datasets
SAGE-P material datasets are observed phenomena (i.e., statistical database); all other datasets
are constructed from correspondence mappings of:
(i) objects → objects;
(ii) objects → functions;
(iii) functions → objects;
(iv) functions → functions.
Working definitions
Objects are a collection of statistical elements of the dataset, (E1-n = Θ), and represent numerical
cardinal/ordinal values of the quantitative/qualitative properties of physical/abstract objects.
Functions are a collection of algorithmic operators where the elements of the set are the
instructions, [f (E1-n) = π Θ], (i.e., vector mapping of objects on object, objects on functions,
functions on objects, and function on functions).
SAGE-P algorithmic operators are formalisms expressed in terms of entailment properties of
objects and functions. These may be classified to Aristotelean hierarchical structure of causes,
viz: material cause (π1) → efficient cause (π2) → formal cause (π3) ← final cause (π4). The
reverse arrow of π4 reflects the (abstract) socio-cultural values mapped on sustainable
development policy in terms of an intensity value measure of the socially acceptable rate of
entropy production.
Homomorphism is a structure preserving algorithm permitting one-to-one correspondence
mapping of the elements in the SAGE-P datasets – an example being the mapping of prices
(values conserved-in-exchange) on economic objects to construct the System of National
Accounting dataset (Note the symmetries conserved in linear datasets: inputs = outputs, and
broken in nonlinear datasets, inputs ≠ outputs).
SAGE-P datasets are hierarchically-structured matrices of entropic processes representing the
notion of:
•Production (Pe) (i.e., negentropic processes);
•Consumption (Ce) (i.e., entropic processes);

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•Capital Accumulation (Ke) (i.e., the low entropy Fund available for future consumption, or
Ke(t)= Pe(t-n) – Ce(t-n).
Category sets of the statistical database
SAGE-P datasets are divided into two separate and distinct categories, viz:
•Physical Objects/Function (Category I): material statistics subject to the Second Law of
Thermodynamics, where Category I = (Θp) and;
•Abstract Objects/Function (Category II): immaterial statistics not subject to the Second Law
of Thermodynamics, where Category II = (Θa).
Category I: Quantitative values of inflow/outflow of Physical Objects in any well-defined
entropic process and a parallel set of balance sheet accounts of the low entropy (physical) Fund:
•E' I → Econosphere → Θp'
•E'' I → Sociosphere → Θp''
•E''' I → Ecosphere → Θp'''
Category II: Quantitative values of inflow/outflow of Abstract Objects in any well-defined
entropic process and a parallel set of balance sheet accounts of the low entropy (abstract) Fund:
•E' II → Econosphere → Θa'
•E'' II → Sociosphere → Θa''
•E''' II → Ecosphere → Θa'''
Category III: Mapping of Qualitative Values Algorithms (π) on Category I and II, π' = exchange,
π'' = use, π''' = intrinsic
•E' III → (EI, EII) → π' Θ
•E'' III → (EI, EII) → π'' Θ
•E'' III → (EI, EII) → π''' Θ
Category IV: Mapping of Spatial Co-ordinate Algorithms (πs) on Category I (Note: Category II
objects, by definition, have no geographical co-ordinates), πs' = economic co-ordinate space, πs'' =
social coordinate space, πs''' = ecosystem coordinate space.
•E' IV → Econosphere TDS → πs Θp'
•E'' IV → Sociosphere → πs'' Θp''
•E'' IV → Ecosphere → πs''' Θp'''