During the last three decades the World has been converging to a value of resilience of around 70%. The World, as a system, has been becoming more complex at a steady rate since the 1970s. After 2004 the rate of complexity growth has accelerated, peaking in 2007. Since 1998 the rate of global entropy production doubles. The same may be said of the entropy-complexity gradient ratio which quantifies the efficiency of a given system. Countries with higher complexity may be viewed as more 'advanced' but also less governable, and implementing reforms in such countries may be more difficult.

1. Sustainability – New
Quantitative Approaches,
New Indices
Preserving Value in a Turbulent Economy
The paper focuses on complexity and entropy-based
proxies and measures of sustainability
February 2015

2. 2Complexity-based measures of sustainability
Sustainability, Complexity and Resilience
Sustainability is a popular subject nowadays Sustainability implies permanence, a sort of
steady-state, almost some kind of equilibrium. However, in today’s world, speaking of
permanence or steady state is a contradiction to say the least. From an energetic-
thermodynamic standpoint a system or a process is sustainable if there is sufficient long-term
energy supply to keep it running (possibly without damaging side-effects). But the question is,
sustainable for how long? And with what efficiency? Inefficient systems can function for a long
time, as long as energy is supplied. So when politicians or economists speak of sustainability,
what do they really mean? What is really meant when we hear “eco-friendly and sustainable”?
Are we speaking of 50 years, 100 years or more? And what about efficiency? Does sustainable
also mean highly efficient? Are we looking at 30%, 70%, or 90% efficiency. One thing is clear – in
order to speak of and to “manage sustainability” one should be able to define it and measure it
or, in alternative, provide some proxy thereof. Managing something means measuring that
something in order to drive its value to some desired target. Otherwise, it’s just talk. Serious
science starts when you begin to measure.
Good metrics start with good definitions. In Wikipedia one finds this:
“Since the 1980s sustainability has been used more in the sense of human sustainability on
planet Earth and this has resulted in the most widely quoted definition of sustainability as a
part of the concept sustainable development, that of the Brundtland Commission of the United
Nations on March 20, 1987: “sustainable development is development that meets the needs of
the present without compromising the ability of future generations to meet their own needs.”
That is about as imprecise as it can get! How do you measure and manage that? A good
definition is one that hints a metric. The one above doesn’t.
Sustainability hinges on the following four “systemic attributes”: Resilience, Interdependency,
Complexity and Entropy. All these factors impact Governability, without which little can be
achieved. These attributes need to be measured if we want to speak of sustainability in a new,
systemic and quantitative fashion.
Wikipedia defines “resiliency thinking” as:
“Resiliency in ecology is the capacity of an ecosystem to absorb disturbance and still retain its
basic structure and viability. Resilience-thinking evolved from the need to manage interactions
between human-constructed systems and natural ecosystems in a sustainable way despite the
fact that to policymakers a definition remains elusive. Resilience-thinking addresses how much
can planetary ecological systems withstand assault from human disturbances and still deliver
the services current and future generations need from them.” How can this be applied
practically to the World as a system?
Based on data from the World Bank we have measured the resilience of the World (as
described by hundreds of variables per country, spanning the economy, finance, education,
healthcare, transportation, energy, pollution, mortality rates, crime, etc.) over the past 5
decades. The result is illustrated in Figure 1 (Global Resilience Index™).

3. Complexity-based measures of sustainability
Figure 1. Global Resilience in the period 1972
The World as a systems appears to be stabilizing at approximately
coincides with that of the vast majority of countries and macro
Is 70% sufficient for long-term sustainability
ourselves to shocks and disasters it very well could be, but how do you guarantee that? Evidently,
high resilience comes a cost in terms of performance, flexibility, efficiency and adaptability.
Because the world is interconnected – today the degree of
discussion of sustainability must be of global systemic nature. As interdependency increases,
local isolated analyses will become less relevant and a broad
mandatory. It is not only the economy which binds us all, it is also travel, telecommunications,
migrations, international finance, as well as conflicts, climate, natural disasters, etc.
Complexity is quantified in cbits (or complexity bits)
development, sophistication and evolution. A system which evolves becomes more complex
think of our biosphere – and can perform more functions. The complexity of the World has been
growing more or less steadily over the past five decades. Thi
which shows the evolution of the Global Complexity Index™
has been used in our analysis. Over 260000 parameters have been taken into account from 196
countries (these are the same parameters
Global Resilience Index). The bumps correspond to crises or
prominent of these is the current crisis which had started to build up in 2004. The drop which
started in 2008 gives an idea of how severe the crisis is.
3
in the period 1972-2012. Data source: World Bank.
to be stabilizing at approximately 70% resilience. This value
coincides with that of the vast majority of countries and macro-regions which we have analyzed.
term sustainability of our global society/economy? If we don’t expose
ourselves to shocks and disasters it very well could be, but how do you guarantee that? Evidently,
high resilience comes a cost in terms of performance, flexibility, efficiency and adaptability.
today the degree of interdependency is 62% – any
discussion of sustainability must be of global systemic nature. As interdependency increases,
local isolated analyses will become less relevant and a broad-scope analysis is therefore
mandatory. It is not only the economy which binds us all, it is also travel, telecommunications,
migrations, international finance, as well as conflicts, climate, natural disasters, etc.
(or complexity bits) and is a measure of the degree of
development, sophistication and evolution. A system which evolves becomes more complex –
and can perform more functions. The complexity of the World has been
growing more or less steadily over the past five decades. This is illustrated in the graph below
Global Complexity Index™. Again, data from the World Bank
has been used in our analysis. Over 260000 parameters have been taken into account from 196
s which have been used to compute the evolution of t
. The bumps correspond to crises or destabilizing events. The most
prominent of these is the current crisis which had started to build up in 2004. The drop which
started in 2008 gives an idea of how severe the crisis is.
regions which we have analyzed.
of our global society/economy? If we don’t expose
ourselves to shocks and disasters it very well could be, but how do you guarantee that? Evidently,
mandatory. It is not only the economy which binds us all, it is also travel, telecommunications,
and can perform more functions. The complexity of the World has been
ata from the World Bank
has been used in our analysis. Over 260000 parameters have been taken into account from 196
the
During the last
three decades the
World has been
converging to a
value of resilience
of around 70%.

4. Complexity-based measures of sustainability
Figure 2. Global complexity in the period 1972
But let’s turn our attention to entropy. The creation of entropy (
disorganization) is inevitable every time we transform energy to perform work. Development,
growth and evolution inevitably involve the creation of entropy. Until 1998, for nearly three
decades, entropy has been increasing at a steady pace, jus
1997 the rate of entropy production (the
change of slope indicated by the second red dotted line. In practice, until 1998, the
Entropy/Complexity ratio has been constant
after 9/11, the World changes dramatically
Figure 3. Global entropy in the period 1972
4
complexity in the period 1972-2012. Data source: World Bank.
. The creation of entropy (‘waste’, chaos,
disorganization) is inevitable every time we transform energy to perform work. Development,
growth and evolution inevitably involve the creation of entropy. Until 1998, for nearly three
decades, entropy has been increasing at a steady pace, just like complexity. In approximately
1997 the rate of entropy production (the entropy gradient) has increased dramatically – see
change of slope indicated by the second red dotted line. In practice, until 1998, the
Entropy/Complexity ratio has been constant. After 1998 the ratio more than doubles. In 2001,
the World changes dramatically, see Figure 3.
in the period 1972-2012. Data source: World Bank.
disorganization) is inevitable every time we transform energy to perform work. Development,
. After 1998 the ratio more than doubles. In 2001,
The World, as a
system, has been
becoming more
complex at a
steady rate since
the1970s. After
2004 the rate of
complexity growth
has accelerated,
peaking in 2007.

5. Complexity-based measures of sustainability
With all likelihood, 9/11 has consolidated the change
for each increase in complexity (growth) the amount of waste that is
100%. This is what happens at global, planetary level.
increase in entropy production. These causes have a lot to do with society, less with economy.
A new systemic index can now be introduced: the
reflects the efficiency of a generic evolv
much waste is generated for a unit of development or growth. Since approximately 1998 the
index doubles, from 20 to 40, meaning that our society needs to produce twice as much
waste for a unit of development as it did in, say, the 70s or 80s. The evolution of the E/
is depicted below:
Figure 4. Evolution of the global entropy/
Data source: World Bank
It is still too early to say if the current E/C value of 40 is excessive and for how long it can be
maintained. However, the fact that it has doubled almost suddenly isn’t a good omen.
In terms of single countries – which have b
source: World Bank) – the situation in 2012
Complexity is a versatile quantity and pro
vitality, sophistication and intricacy. Ultimately, it reflects the culture of a country. Countries with
higher complexity may be viewed as more
governable. Implementing reforms in such countries may be more difficult.
5
With all likelihood, 9/11 has consolidated the change – entropy is now growing very quickly:
for each increase in complexity (growth) the amount of waste that is produced increases by
l, planetary level. We identify the possible causes of this
tropy production. These causes have a lot to do with society, less with economy.
A new systemic index can now be introduced: the Entropy/Complexity gradients ratio which
ving system. Basically, the E/C index measures how
is generated for a unit of development or growth. Since approximately 1998 the
index doubles, from 20 to 40, meaning that our society needs to produce twice as much
waste for a unit of development as it did in, say, the 70s or 80s. The evolution of the E/C ratio
/complexity gradients ratio in the period 1972-2012.
Data source: World Bank
It is still too early to say if the current E/C value of 40 is excessive and for how long it can be
maintained. However, the fact that it has doubled almost suddenly isn’t a good omen.
which have been analyzed adopting similar parameters (data
the situation in 2012 is indicated in Table 1 below.
ovides, from a very general perspective, a reflection of
. Ultimately, it reflects the culture of a country. Countries with
may be viewed as more ‘advanced’ (not technologically!) but also less
governable. Implementing reforms in such countries may be more difficult.
entropy is now growing very quickly:
produced increases by
e identify the possible causes of this
which
system. Basically, the E/C index measures how
is generated for a unit of development or growth. Since approximately 1998 the
index doubles, from 20 to 40, meaning that our society needs to produce twice as much
C ratio
f
. Ultimately, it reflects the culture of a country. Countries with
Since 1998 the
rate of global
entropy production
doubles. The same
may be said of the
entropy-complexity
gradient ratio which
quantifies the
efficiency of a
given system.

6. Complexity-based measures of sustainability
Table 1. Country complexity, entropy an
period 1972-2012.
Complexity is a measure of vitality, sophistication and intricacy from a general perspective.
Ultimately, it reflects the culture of a country. Countries with higher complexity
as more ‘advanced’ (not technologically!) but also le
countries may be more difficult.
From a complexity perspective, Italy, USA, France and Germany are the most
countries.
Entropy, as mentioned, measures the amount of
sense – and there are countries which clearly produce more than the average: Italy, USA,
Germany, France and India. Singapore, on the other hand, is far less entropy
significantly less complex. Japan is in a similar situ
function like ‘clockwork’.
From an ‘efficiency’ point of view, i.e. based on the E/C ratio, which measures the amount of
waste per unit of development, Italy, Germany, France and China present the best credential
USA and Japan have the worst E/C ratio. The Eurozone, surprisingly, boasts a ratio of 310, well
below that of its largest member states (so much for linear thinking!).
In conclusion, the E/C ratio may be a proxy
values indicate that a particular country is
may be more expensive to achieve and maintain. Countries with high complexity are generally
more advanced – their inhabitants may be more receptive to refo
sustainable less wasteful lifestyle – but are also less governable. Finally, since the E/C ratio is a
general feature of any evolving system, it may be applied to measure the sustainability potential
of corporations and to measure their impact on society in a more comprehensive
the CO₂ footprint.
References
[1] Marczyk, J. A New Theory of Risk and Rating
6
nd global entropy/complexity gradients ratio in the
2012. Data source: World Bank
Complexity is a measure of vitality, sophistication and intricacy from a general perspective.
Ultimately, it reflects the culture of a country. Countries with higher complexity may be viewed
(not technologically!) but also less governable. Implementing reforms in such
From a complexity perspective, Italy, USA, France and Germany are the most ‘advanced’
Entropy, as mentioned, measures the amount of ‘waste’ – again, the term is used in a very broad
and there are countries which clearly produce more than the average: Italy, USA,
Germany, France and India. Singapore, on the other hand, is far less entropy-heavy but it is also
significantly less complex. Japan is in a similar situation. In both these countries many systems
point of view, i.e. based on the E/C ratio, which measures the amount of
waste per unit of development, Italy, Germany, France and China present the best credentials.
USA and Japan have the worst E/C ratio. The Eurozone, surprisingly, boasts a ratio of 310, well
below that of its largest member states (so much for linear thinking!).
proxy of sustainability or sustainability-potential. High
e that a particular country is potentially ‘inefficient’. In such cases, sustainability
may be more expensive to achieve and maintain. Countries with high complexity are generally
their inhabitants may be more receptive to reforms necessary to lead to a more
but are also less governable. Finally, since the E/C ratio is a
system, it may be applied to measure the sustainability potential
eir impact on society in a more comprehensive manner than
A New Theory of Risk and Rating, Editrice Uniservice, 2009. ISBN 9788861784819.
may be viewed
ss governable. Implementing reforms in such
very broad
heavy but it is also
ation. In both these countries many systems
s.
USA and Japan have the worst E/C ratio. The Eurozone, surprisingly, boasts a ratio of 310, well
may be more expensive to achieve and maintain. Countries with high complexity are generally
rms necessary to lead to a more
but are also less governable. Finally, since the E/C ratio is a
system, it may be applied to measure the sustainability potential
than
9788861784819.

7. 7Complexity-based measures of sustainability
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