1. 24
Intuitively, most of us know that
our global society has become
more complex than that of our
parents, grandparents, and their
predecessors. We are much more
interconnected, we have more
options, more freedom. Our society
is fuzzier and more bureaucratic,
more unpredictable, chaotic, and
likely to become more so. Our
world is more complex than it was,
and many of us have instinctively
realised this has implications. But
intuition is not science, since if you
can’t measure something, you can’t
claim to be doing serious science,
and how can you manage what you
can’t measure? Or, as Italian-based
Dr Jacek Marczyk, the aeronautics,
aerospace and civil engineer
who founded Ontonix, a private
company that specifically deals
with complexity, says, “Why do you
think managing complex systems
is more difficult than managing
simpler ones?”
One can accurately measure a
country’s monthly trade balance,
the average rainfall at a particular
location,how many votes a candidate
received in an election, the height
and weight of a person, how many
cars travelled down a certain piece of
road on any given day. But try making
complete and precise statements
summing up the economy, the
climate, politics, and highway traffic
patterns. “To understand complexity
you have to accept the conundrum
– the more complex the system, the
You walk into a meeting of a
project important to you and the
ambient discussion is about how
things are going to be optimised for
sustainable development. Faster,
better, cheaper using the top-of-
the-line processors to ensure the
most detailed models. Would you
drift off reassured by these usual
platitudes, or would you find
yourself in a cold sweat? If it is the
latter, you probably understand
something about complexity.
24
The unravelling
of the world
A killer whale interacting with its environment is a
complex system because it is hard to predict.
Complex

2. February 2007 25
less precisely it can be measured,”
Marczyk says. This is known as
the Principle of Incompatibility:
high complexity is incompatible
with high precision.
So, how can we ever hope to
quantify something as complex
as our global society? Marczyk,
whose company has developed
a unique system, OntoSpace,
for measuring and managing
complexity, has done just that.
He used OntoSpace to analyse
raw data collected by the CIA’s
World Fact Book, and the outcome
is the predicted collapse of our
global society sometime between
2040 and 2045. Marczyk says, as
with all predictions, the timing
is uncertain and could be off
by several decades, but the one
thing he is 100% certain of is that
it will happen. This projection is
based on no additional modelling
and assumptions, but on using
the raw data and calculating
global society’s upper complexity
boundary. Every system possesses
its own upper limit of complexity
beyond which it cannot naturally
evolve. Systems close to this limit
are known as critically complex.
“We have seen that the yearly
growth of complexity is about
5% to 6%,” Marczyk says. In
essence Marczyk’s OntoSpace
software determines the fragility
of a system, which he has
formulated into an equation:
Complexity x Uncertainty = Fragility.
Or as Thomas Frey, executive
director and founder of the
Colorado-based, DaVinci Institute,
a non-profit futurist think-tank,
says, “As complexity of a system
increases, the costs associated
with it increase exponentially, to
the point where the costs approach
infinity, and collapse is a certainty.
It can be argued that every major
civilisation in history such as the
Egyptian,Greek,or Roman empires,
including smaller civilisations
like the Mayans, each reached a
point where an ever-increasing
bureaucracy coupled with an ever-
increasing number of rules, simply
overloaded the administrators’
ability to comply with them, and
the systems collapsed.”
Frey points out that modern
technology has given us the
ability to manage far more
complex systems than those of
these ancient civilisations, and
notes that thanks to Moore’s Law
(which predicts the doubling of
computing processing power
about every 18 months), our
ability to automate has kept up
with our ability to complicate. He
says that the breaking point will
not be the automated systems,
but rather the human interface,
where systems such as income
tax in many parts of the world
have gone beyond the pale of
understandability and “exist as
nothing more than a confusing
blur to the tax-paying public.”
Frey says the complexity
has reached a point of being
irreversible, causing the system to
unravel around the edges.
The more complex a system, the
more functions it can perform, so
we can do more than the Romans
did. But our global civilisation
does have a critical complexity
threshold. With complexity, both
robustness and fragility increase.
This duality – robust yet fragile – is
the salient characteristic of highly
complex systems. However, in the
proximity of critical complexity,
the system in question becomes
fragile, difficult to manage, and
therefore vulnerable.
Marczyk does not suggest
that our global civilisation will
suddenly implode, or that the
complexity ceiling when reached
will result in some cataclysmic
wrenching apart. It could just
be that a saturation point is
reached. “The key message here,”
Marczyk says, “is that we reach
limits to all things in life. The
concept of sustainable growth is
a slap in the face of the second
law of thermodynamics, which
states that a system will always
tend towards its highest state
of entropy, thus highest state of
chaos. Sustainable growth is not
possible – the rules of complexity
set limits as to the complexity to
which any system can naturally
evolve and grow.”
The more a complex
system is optimised for a
specific situation, the more
fragile and brittle it is, should
circumstances change. Or
as the Roman proverb goes,
Corruptio Optimi Pessima (when
something is optimal, it can
only get worse). The closer a
system gets to its complexity
boundary, the less robust, the
more fragile it is. There are two
ways a system that is close to
1
2 3 4 5 6 7 8
9 10 11 12 13 14
15 16 17 18 19 20 21
22
A typical business flow sheet often
has many components but relatively
low complexity.
Complicated

3. its complexity boundary can
increase its robustness. It can
devolve until it recedes from the
complexity boundary, or it can
grow (by adding infrastructure)
to increase the critical limit.
In the case of companies near
their complexity limit, they
can drain entropy, reduce
chaos by shutting down certain
divisions, or they can expand so
their critical complexity limit is
higher – hence the enthusiasm
for mergers and acquisitions.
However, Marczyk points out
that 70% of mergers fail because
this is an area of complexity
where too many variables
interact, and the outcome is
not a foregone conclusion.
And now the science of
understanding and managing
complexity demonstrates its
significance. Thanks to the work
of Marczyk and his colleagues
we can now take a system and
calculate how far it is from its
complexity threshold?We can now
tell how much scope a system has
to cope with unexpected shocks
and how healthy the system
is. In other words, Ontonix has
established a radical new way of
understanding and managing risk.
We can now answer the question
every executive would dearly like
to know – how much a global
corporation is at risk – how far
from critical complexity are we?
But before we can measure
complexity, we also need to
understand clearly what we are
talkingabout.“Theso-calledscience
of complexity has been around
for a couple of decades,” Marczyk
says, “and there are numerous
research centres around the world
that study complexity. The strange
thing is that there is no established
definition of complexity and no
rational measure either! We need to
define it, and dictionary definitions
are not particularly helpful here.
Renowned dictionaries make
26
The mechanical workings of a clock while complicated are not complex because of limited degrees of freedom.
Complicated

4. February 2007 27
mistakes and confuse complex
with complicated. To understand
complexity you need to understand
the difference.”
A mechanical watch is a very
complicated system, with its
numerous springs, shafts and
gears, which must all work
precisely together. But, because
each component can only do
one thing, each having only one
degree of freedom, it cannot do
anything spontaneously. It has a
very limited capacity to surprise.
A mechanical wrist watch is thus
complicated, but not a system
with a high level of complexity. In
contrast, take a family comprising
three or four humans, spending
an afternoon in a park. Predicting
the actions of such a system is
much more difficult, because it
has a much greater capacity to
surprise – the human family is
a system with a much higher
level of complexity. It is thus
not sufficient to have a large
number of connections between
numerous components to speak
of high complexity. To speak of
high complexity we also need
an element of uncertainty – the
capacity to surprise.
Numerous tools exist for
simulatingcomplexsystems.These
have been around for decades and
use stochastic simulation, in other
words based on probabilities, via
the Monte Carlo method. This
method, named after the famous
casino because of its probabilistic
nature, is the approach used to
estimate the amount of water in
a reservoir based on the random
distribution of rainfall and water
usage. The Monte Carlo method
determines what area a circle
takes up within a square by
sampling a random distribution
of points and seeing what
percentage of these are within the
circle. In engineering, and other
systems, where the distribution
is not completely random, for
example, Gaussian (Bell Curve),
distribution patterns describing
the probabilities of a phenomenon
are used when undertaking Monte
Carlo simulations.
What OntoSpace does, using
results of Monte Carlo simulations,
or any kind of measured data, is
to first determine all the possible
modes of behaviour a particular
system can exhibit. Even
apparently innocent systems
can possess a multitude of
modes, and it becomes clear how
simplistic it would be to say that
the behaviour of complex systems
can be represented by just one
global correlation map. The
package then distinguishes hubs,
critical variables that concentrate
the fragility of the system. Now,
when the system is a complex
one with many variables, none
dominant, its overall performance
is determined by the collective
behaviour of the many. And you
don’t try and determine which
variables run the show; instead
you determine the hubs, the
variables that connect to the
highest number of other variables.
In other words the nodes with
the highest degree. The loss of a
hub creates massive damage to
the mode, and possible loss of
functionality. A multi-hub system
is thus more robust, more resilient
than a system dependent on a
smaller number of hubs.
For some the Israel-Palastine situation may be clearcut but the interactions of Israel, Palestine, the USA and the Arab states make the
Middle East a very complex situation.
February 2007 27
Palestinian military expenditure
Palestinian economic development
US support of Palestine Israeli recognition of Palestinian
Israeli violence
Israeli military expenditure
Arab support of Palestinian violence Israeli economic development
Palestinian violence US support of Israel
Complex
------->

5. 28
A society with more diversified
hubs of political and economic
power won the Cold War
against a society with fewer
and more concentrated hubs.
And conversely, in spite of all
its technological, political and
military might, the USA is failing
in Iraq because it is trying to
combat an enemy that has many
hubs. A targeted attack on a single
hub system may bring the system
down, such as an ecosystem that
suddenly crashes due to the loss
of what biologists call keystone
species. The problem with
complex systems such as our
biosphere is that we don’t know
what these hubs are.
Marczyk also uses his knowledge
of complexity to warn against how
it is almost too easy for engineers
to over-rely on modelling systems.
“It is the path of least resistance
to use existing processing power
to build detailed models that
refine below a level of natural
precision.” One is not going to
squeeze out more information
than this natural precision allows,
and taking into account that high
complexity = less precision, this
particularly refers to long range
climatic, political, traffic, and
economic models.
“It is incongruous that one
models something to extreme
levels of detail, such as is the case,
in one example, of motor vehicle
safety parameters. The modelling
is typically detailed in the extreme,
but the results are presented to
the market as a rating of one to
five stars, i.e. in fuzzy terms. There
is no balance in this.”
And Marczyk points out that
this is not a new concept, as it was
Aristotle who said, “An educated
mind is distinguished by the fact
that it is content with that degree
of accuracy which the nature of
things permits, and by the fact that
it does not seek exactness where
only approximation is possible.”
Every time a company executive
says how that company has been
optimised, understand therefore
that its risk profile has increased.
At the moment we are optimising
our world economy with first-world
countries exporting high-tech
and using cheap off-shore labour.
Drives for more profit with lower
investment means companies
under such pressure are doing less
real research and development.
This seeking of maximum
profit with minimum risk, and
minimum investment in the
shortest possible time all equates
to fragility. The same applies to
engineering systems, which have
nowadays evolved to impressive
levels of complexity, sophistication
and performance. Like the Space
Shuttle with a faulty O ring, they
can fail with surprising ease, and
frequently due to very simple and
trivial causes.
“It could be 2025, or 2085, but our
society will reach its complexity
boundary, become very brittle and
probably collapse.” The only hope
is that it will be a soft decay, and to
ensure that is the case, Marczyk is
trying to promote healthier goals
than pursuit of ultimate returns.
“If we use the laws of entropy and
complexity wisely we can have a
lot, but we can’t have it all.”
If we are going to manage the
coming complexity boundary our
civilization faces, we are going to
have to become much more serious
about understanding and managing
complexity. This means giving up
certain cherished ideas. “We cannot
push performance to the limit.
We cannot design for perfection.
Sustainable growth is impossible.
Everything reaches a peak and
then, as much as we may not like it,
decays – the universe, civilizations,
and human beings.”
The human family, though consisting of only four people, is very complex because of its
capacity to surprise.
Heinz Pagels (1939-1988),
the physicist and writer of
several science books including
The Computer and the Rise
of the Sciences of Complexity
said “The nations and people
who master the new science
of complexity will become
the economical, cultural and
political superpowers of the
next century.”