20th December 2009
Uncritical Strategic Dependence on Little-known Metrics
the Gaussian Copula, the Kaya Identity, and what else?
- / -
-- Gaussian Copula: investment risk
-- Kaya Identity: emissions
-- Sustainability metric
-- Other fundamental "metrics"?
-- Secret formulae?
-- Metrics: a measure other than human?
of Mythopoeic Insights to Global Challenges
-- Metrics with a "human face"?
-- Neglected geometric "metrics"
-- Mythopoeic insights of relevance?
-- Cognitive drama of the disciplines
-- Human remedial capacity: a ninefold challenge?
Cycles Vital to Sustainable Self-Governance
-- Cognitive unsustainability
-- Embodiment: how "one" engages with reality
-- Interweaving singular metrics
-- Emergent integrity of a configuration of cognitive cycles
-- a "Lord of the Rings"
Produced on the occasion of the problematic culmination of the United Nations
Climate Change Conference (2009) apparently based on a particular use of a single
The unprecedented financial crisis of 2008 revealed the uncritical dependence
of the global financial community and, by extension, the economic system,
on the innovative risk-management formula of David
X. Li known as the Gaussian
Copula function -- subsequently described as "the secret fomula
that destroyed Wall Street".
The debate on climate change, informed by the report of the United Nations
Intergovernmental Panel on Climate Change, culminating in the United Nations
Climate Change Conference (Copenhagen, 2009), has essentially been based
on the Kaya
Identity. This is an equation, little known to climate debaters and
negotiators, relating factors that determine the level of human impact on
climate, in the form of emissions of the greenhouse gas carbon dioxide.
As metrics both formulae have been positioned, with little question, as
fundamental to global strategic initiatives. The first example indicates
the danger of such dependence. The second raises questions about the coherence
of the debate on climate change -- at a time when scientists are vigorously
claiming a global consensus on the matter. But of greater concern is the
possible existence of other such metrics which have been placed at the heart
of strategic initiatives -- unknown to those who might question this tendency
to single-metric dependence, the validity of the metric, or the use of other
such metrics as the basis for other vital strategies, whether now or in the
The theme follows from an earlier exploration of Comprehensive
Formulations and their Cognitive Challenge (2009), itself part
of a continuing interest summarized in Unexplored
Potential of Mathematics and Geometry -- in reframing psycho-social challenges (2008).
It also relates to concern for indicators of the capacity to act
in the light of indicators of problematic conditions, as originally explored
in the context of the Goals, Processes and Indicators of Development
GPID) project of the United Nations University (Remedial
Capacity Indicators Versus Performance Indicators, 1981).
Gaussian Copula: investment risk
The innovative formula of David
X. Li with regard to the Gaussian
Copula function is of interest since its successful use is alleged
to be at the root of the overconfidence of the global financial community
in taking the high orders of investment risk which led to the global financial
crisis of 2008, and its consequences. It is admirably described by Felix
for Disaster: the formula that killed Wall Street, Wired,
17.03, March 2009) -- or on the title page of the issue as The Secret
Formula that Destroyed Wall Street. As Li had indicated in 2005 "Very
few people understand the essence of the model" (Mark Whitehouse, Slices
of Risk, The Wall Street Journal, 12 September 2005).
A second description is offered by Kevin Drum (The
Gaussian Copula, Mother Jones, 24 February 2009).
Li's original paper (On
Default Correlation: A Copula Function Approach, Journal
of Fixed Income 9, 2000, pp. 43-54) was the first appearance of
the Gaussian Copula models for the pricing of collateralized
debt obligations (CDO's). This quickly became a tool for financial
institutions to correlate associations between multiple securities --
allowing CDOs to be accurately priced for a wide range of investments
that were previously too complex to price, such as mortgages. In this
respect they were at the core of the subprime crisis.
Expressed succinctly, the formula is:
An articulated expression of the formula is:
probability that any two potential sources of risk
(A and B)
in a proposed investment will both default
couples the individual probabilities
associated with A and B
|TA = amount of time between
now and when A may be expected to default
||Φ-1 (FA(1)) = probability of
how long A is likely to survive before defaulting
|TB = amount of time between
now and when B may be expected to default
||Φ-1 (FB(1)) = probability of
how long B is likely to survive before defaulting
||γ = correlation
parameter, reducing correlation to a single constant
Kaya Identity: emissions
The Kaya Identity was developed by Japanese energy economist Yoichi Kaya.
It is the subject of his book Environment, Energy, and Economy: strategies
for sustainability co-authored with Keiichi Yokobori as the output of
the Conference on Global Environment, Energy, and Economic Development
(1993 : Tokyo, Japan). It states that total emission level can
be expressed as the product of four inputs: population, GDP per capita, energy
use per unit of GDP, carbon emissions per unit of energy consumed. This equation
is very simple and tricky, as it can be reduced to only two terms, but it
is developed so that the carbon emission calculation becomes easy, as per
the available data, or generally in which format the data is available.
F = P*(G / P)*(E / G)*(F / E) = P*g*e*f
- F = global CO2 emissions from human sources,
- P = global population,
- G = world GDP
- g = (G/P) is global per-capita GDP,
- E = global primary energy consumption and e=(E/G) is the energy
intensity of world GDP
- f= (F/E) is the carbon
intensity of energy.
The Kaya identity plays a core role in the development of future emissions
scenarios in the IPCC Special
Report on Emissions Scenarios prepared for the Third
Assessment Report (TAR) in 2001. The scenarios
set out a range of assumed conditions for future development of each of the
four inputs. Population growth projections are available independently from
demographic research; GDP per capita trends are available from economic statistics
and econometrics; similarly for energy intensity and emission levels. The
projected carbon emissions can drive carbon cycle and climate models to predict
future CO2 concentration and climate change.
As a contribution to the Fourth Assessment Report (Rogner,
H.-H., D. Zhou, R. Bradley. P. Crabbé, O. Edenhofer, B.Hare (Australia),
L. Kuijpers, M. Yamaguchi, 2007: Introduction.
In Climate Change 2007: Mitigation. Contribution of Working Group III to
the Fourth Assessment Report of the Intergovernmental Panel on Climate Change)
it is stated that:
The Kaya identity (Kaya, 1990) is a decomposition that
expresses the level of energy related CO2 emissions as the product of
four indicators: (1) carbon intensity (CO2 emissions per unit of total
primary energy supply (TPES)), (2) energy intensity (TPES per unit of
GDP), (3) gross domestic product per capita (GDP/cap) and (4) population.
The global average growth rate of CO2 emissions between 1970 and 2004
of 1.9% per year is the result of the following annual growth rates:
population 1.6%, GDP/cap12 1.8%, energy-intensity of -1.2% and
carbon-intensity -0.2% ....
At the global scale, declining carbon and energy intensities have been unable
to offset income effects and population growth and, consequently, carbon
emissions have risen....
The challenge - an absolute reduction of global GHG emissions - is
daunting. It presupposes a reduction of energy and carbon intensities at
a faster rate than income and population growth taken together. Admittedly,
there are many possible combinations of the four Kaya
identity components, but with the scope and legitimacy of
population control subject to ongoing debate, the remaining two technology-oriented
factors, energy and carbon intensities, have to bear the main burden....
With regard to the Kaya Identity, at the time of the Copenhagen negotiations
on climate change, might its discoverer, Yoichi Kaya, have echoed the words
of David Li regarding the Gaussian Copula before the financial crash of 2008: "Very
few people understand the essence of the model"?
Following the consequences of any "binding agreement" in Copenhagen,
as with the financial crisis, might there be occasion for an article entitled
something like Recipe
for Disaster: the formula that crashed the climate
-- or perhaps as The Secret
Formula that Destroyed the Global Climate?
Is the unquestioning global confidence in the Kaya Identity to be compared
with that in the Gaussian Copula -- notably in the light of the unprecedented
resources invested in each?
In a White
Paper on All the Options for Managing a Systemic Bank Crisis (2008),
Bernard Lietaer, Robert
Ulanowicz and Sally
Goerner provide an overview
of an approach to the financial system in the light of a single
metric derived more generally from the Stability
and Sustainable Viability in Complex Flow Systems:
now scientific evidence that a structural issue is indeed involved. The
theoretical origin of this evidence may be surprising to the economic or
financial community, although it wouldn't be such a surprise for
scientists familiar with natural ecosystems, thermodynamics, complexity
or information theory. The science that explains this issue rests on a
thermodynamic approach with deep historical roots in economics. In this
view, complex systems, such as ecosystems, living organisms, and economies
are all seen as matter-, energy-, and information-flow systems. For example,
the famous food chain is actually a matter/energy flow-network built of
complex relationships among organisms. Plants capture the sun's
energy with photosynthesis; animals eat the plants; species then eat each
another in a chain to top predator, only to have all organisms die, decompose,
and their energy/matter be recycled by bacteria. Similarly, economies are
circulation networks consisting of millions of businesses and billions
of customers exchanging different products and services, which when taken
as a whole, are supposed to meet the needs of all participants....
Consequently, as Goerner (1999) says about universality: 'all [flow]
systems, no matter how complex, fall into one of a few classes. All members
of a class share certain common patterns of behavior.' Similarly,
Cvitanovic explains: 'The wonderful thing about this universality
is that it does not matter much how close our equations are to the ones
chosen by nature, as long as the model is in the same universality class…as
the real system. This means that we can get the right physics out of very
crude models.' The existence of parallel patterns and dynamics
explains why similar energy flow concepts and analysis methods apply to
economic systems as well as natural ones....
Sustainability of a complex flow system can therefore be defined as the
optimal balance between efficiency and resilience of its network. With
these distinctions we are able to define and precisely
quantify a complex system's sustainability in a single metric. Indeed,
there is now a way of quantitatively measuring all the relevant components
separately: total throughput, efficiency, and resilience. Furthermore, the underlying
mathematics are well-behaved enough so that there exists only one single
maximum for a given network system....
It is critical to understand that the findings described so far arise
from the very structure of a complex network system, and therefore that
they remain valid for any complex network with a similar structure, regardless
of what is being processed in the system: It can be biomass in an ecosystem,
information in a biological system, electrons in an electrical power distribution
network, or money in an economic system. This is precisely
one of the strong points of using a web-like network approach instead of
The details of this systemic approach are described in a separate paper,
with technical and mathematical proof (Robert Ulanowicz,
Sally Goerner, Bernard Lietaer and Rocio Gomez, Quantifying
Sustainability: Efficiency, Resilience and the Return of Information Theory,
Journal of Ecological Complexity. 6, 2009, pp. 27-36). Complementary
arguments are provided separately by the authors (Sally J. Goerner, Bernard
Lietaer, and Robert E. Ulanowicz, Quantifying
economic sustainability: Implications for free-enterprise theory, policy
Economics, 69, 2009, pp. 76-81)
Other fundamental "metrics" ?
Depending on how "metric" is understood, the following suggest
other possibilities for a single metric:
- business: various approaches have been taken to determing
a single measure of business performance (Dave Trimble, How
to Measure Success: uncovering the secrets of effective metrics,
BPR OnLine Learning Center, 2001)
- physics: this is the possibility of a hypothesized Theory
of Everything (TOE) in theoretical
physics. This would fully explain and link together all known physical
phenomena, and, ideally, has predictive power for the outcome of any experiment
that could be carried out in principle. Presumably such a theory would explain
or subsume all physical constants. These include: universal
of light in vacuum, the gravitational
constant, and reduced
Planck constant); electromagnetic
and nuclear constants; physico-chemical
constants. One of the difficulties is that there are multiple Theories
of Everything (John D. Barrow, New Theories of Everything: The Quest
for Ultimate Explanation, 2008).
- symmetry: this may itself constitute a form of metric.
Given the beauty of symmetry as
an attractive indicator of truth (cf Ian Stewart, Why
Beauty Is Truth: the history of symmetry, 2007), and despite
the "monstrous" complexity
of the highest forms of symmetry (cf Mark Ronan, Symmetry
and the Monster: one of the greatest quests of mathematics, 2006),
it is possible that the governance challenges of "globalization" call
for a form of marriage between "beauty" and such a "monster" -- but of
a quite unexpected order of complexity. The significance of the Monster is
briefly well-summarized by Marcus
du Sautoy (Patterns
that Hold Secrets to the Universe) and in a more technical manner
by Richard E. Borcherds (What
is the Monster? Notices of the A.M.S., 2002). It is indeed
suspected that the Monster is built in some subtle way into the structure
of the universe -- the ultimate metric?
- systems: the Viable
Systems Model (VSM) is a model of the organizational structure
of any viable or autonomous system organized
in such a way as to meet the demands of surviving in the changing environment,
namely through adaptive capacity. The model is an abstracted cybernetic
(regulation theory) description that is applicable to any organization
that is a viable system and capable of autonomy.
- generalized periodic table: this possibility has been
explored by Edward Haskell (Generalization
of the structure of Mendeleev's periodic table. In: Full
Circle - The Moral Force of Unified Science, 1972)
Mathematics might be understood as the study of metrics and as such to itself
constitute a (meta)metric. Insights into its nature might even be achieved
through metaphor (Towards a Periodic Table of Ways of
Knowing -- in the light of metaphors of mathematics, 2009). Various
approaches are taken to reduce multiple metrics to a single metric.
One concern is the extent to which any single metric might be elaborated
and used in secret for competitive advantage. This is evident in the approach
taken by institutions in developing formulae used in trading on the financial
markets. Such management of risk is similarly evident in gambling where gamblers
may each develop and use their own secret formula.
It is to be expected that intelligence agencies would develop a secret metric
to assess "points of interest" calling for heightened attention. Of particular
interest is the metric through which levels of threat are assessed to determine
an appropriate Defense Readiness
Condition (DEFCON), especially in response to terrorism (Distinguishing
degrees of fear and terror, 2004). The threat of terrorism itself
offers a kind of singular "metric" (Promoting
a Singular Global Threat -- Terrorism: Strategy of choice for world governance,
A related approach is evident in the use of copyright to protect a formula
or to prevent others from using it -- as in the practice of "patent
squatting". The possibility that the world might be held to ransom
for its food by potential "terminator
seeds" has long been recognized with
concern -- but more intriguing is the possibility that access to vital insights
might be withheld by practices analogous to such genetic
use restriction technology. Perhaps a form of "memetic use restriction
Coping Strategies: beyond the constraints of proprietary metaphors,
Variants of such secretive possibilities are evident in secret societies
organized to offer access progressively to deeper knowledge -- presumably
more integrative and singular -- through a succession of initiations.
It is however also the case that commercial barriers to access to copyrighted
publications may render "secret" to the majority the models they
Another form of metric is that used for page
ranking of results
from a search engine query, such as with Google. This could prove to be of
increasing relevance in shaping global knowledge society through secret
rules for including, excluding or weighting certain results -- possibly under
commercial, religious, political or security pressures (as recently highlighted in debate over access to Google in China). According to
Wikipedia, a generic page rank equation is as follows:
Metrics: a measure other than human?
The challenge with respect to any singular metric of global strategic significance
is whether it has a "human face". This was the theme of the classic
challenge of UNICEF to the metric used by the International Monetary Fund
in determining the necessary "structural
in developing countries (UNICEF, Development
with a Human Face, 1997). A related argument has been made by the
UNFPA (Thalif Deen, Development:
UNFPA Puts Human Face on Climate Blowback, IPS, 18 November 2009)
and with respect to climate change more generally (Ellen
Goodman, The 'human' factor
is missing in Copenhagen, The
Boston Globe, 11 December 2009).
There is thus a sense that there is an inappropriate dilution of an essentially
human dimension by the use of the kinds of metrics favoured by economists
and related disciplines:
- economic development (typically understood as quantitative growth) --
as with models of structural adjustment
- financial risk management -- as with the Gaussian Copula -- and despite
the risks to the livelihoods of many
- population factor -- as with its marginalization in relation to climate
change in use of the Kaya Identity
- sustainability -- as with the single metric proposed for sustainable
viability in complex flow systems
The issue seems to be a combination of:
- recourse to mathematical abstraction, avoiding the challenge of humanity
-- ignoring implications of the Renaissance recognition of "man
as a measure of all things"
- avoidance of complexity and preference for (reduction to) single factor
- preference for formulaic expression -- appropriate to simplistic policy
- a tendency to freeze categories and patterns, constraining future flexibility
and development -- effectively colonizing the future
These suggest a reason for the use of images with "human interest" to
frame a period.
Continued in Part 2: Relevance
of Mythopoeic Insights to Global Challenges