Transcript Slide 1

lecture 4: complexity
– parallel developments that are joining
together:
• systems literature
• complexity literature
– most systems of interest to IE/OR are
complex
– to understand the causes that gave rise to
these developments we need to understand
how science and the scientific method work
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science and the scientific method
• ways to knowledge:
– authoritarian and mystical mode versus the rational mode
– the Enlightenment, Galileo and Newton
– Newtonian mechanics
• aims of science – seeking reality and truth
– explanation and prediction
– understanding
• the scientific method - positivism
– objectivity
– the research cycle: theory-hypothesis-observation and
experimentation-generalisation-theory
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• calculus and analytic functions
– analysis
– reduction
• the Newtonian paradigm
– objective knowledge is possible: subject-object
duality
– cause and effect act linearly
– nature is deterministic or predictable
– reduction works
• Newtonian science has been a great success;
it has created today’s technological
society
• the Newtonian view of the world dominates
our thinking even today
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complexity
• quantum mechanics, biology, climatology etc
• Heisenberg’s principle of uncertainty
• insufficiency of analytical thinking
• failure of calculus in studying complex shapes
• realisation that nature is more complex than previously
thought led to the development of the new
field of complexity studies.
• complexity theory is as yet not fully developed
• its aim is to discover unified laws governing complex
systems through interdisciplinary inquiry
• it is early to say whether this aim will be achieved
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chaos
nonlinear dynamics
− phase-space
– the two-body and the three-body problems
– chaos in time : STIC, unpredictability
• the butterfly effect
• glasses, mountains, earthquakes etc.
− predictability: edge-of-chaos; strange attractors
– chaos in space : fractals
– all nonlinear systems are chaotic in some regionof
their phase-space
– hence complexity implies chaos but chos can also
occur in simple systems
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• complex systems have several scales;
– chaos can be observed at a lower scale
– but perhaps not at the higher scale above it
• to understand complexity and its relation to
chaos we recall the laws of thermodynamics
• the first law of thermodynamics says that the
total amount of energy remains unchanged in an
isolated system
• if there is a gradient such as a difference of
pressure or temparature in the system then work
can be done
• but our ability to turn energy into work is reduced
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• for example, work can be done when gas flows from a
high pressure area to low pressure areas until there is no
longer a pressure gradient; ie when the pressure
gradient is reduced to zero there is no possibility of using
it to do work
• when such a reduction takes place we say that “entropy
has increased”
• gas will not flow back on its own and separate itself into
high and low pressure ares; spontaneous change is
irreversible, entropy always increases in an isolated
system; this is the second law of thermodynamics
• energy is still there but we cannot use it again, only low
entropy energy is useful to us such as electricity, which
is energy of the highest grade
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• the maximum amount of work that a system can do on
its surroundings can be defined as exergy; it is the
component of energy that can do useful work
• there are four types of exergy:
– kinetic exergy associated with relative motion;
– potential field exergy associated with gravitational or
electromagnetic field gradients
– physical exergy associated with pressure or temperature
gradients, and
– chemical exergy associated with chemical gradients
• exergy is non-zero when the system under consideration
is distinguishable from its environment in one or more
of these four dimensions; therefore exergy is the most
general measure of distance from thermodynamic
equilibrium or of the degree of distinguishability.
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• distinguisibility here has the same sense as order, as
structure, as differentiation or as organisation
• entropy on the other hand, is a measure of the degree
of disorder of a system; or its degree of
indistinguishability or disorganisation or lack of
structure
• the state of maximum entropy therefore is a state of
randomness, a case in which all states in the phase
space have the same likelihood; when this happens the
states in the phase-space are uniformly distributed
• open thermodynamic systems maintain a state of
disequilibrium by the transport of material and energy
across their boundary; such systems are known as
dissipative structures
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• dissipative systems dissipate gradients and maintain
disequilibrium in a locally reduced entropy state
• this is done at the cost of increasing the entropy of the
larger system in which the dissipative structure is
imbedded
• dissipative systems self-organise into structures that
dissipate gradients, ie. self-organisation is one way to
counter and reduce gradients
• life itself can be viewed as a sophisticated dissipative
structure away from equilibrium that has emerged to
counter the gradient imposed by the sun; mainly by
photosynthesis
• complexity can be defined as the degree to which the
system maintains a thermodynamic disequilibrium
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complexity
• a complex system self-organises onto an attractor
• Baranger summarises the properties of complex systems
as follows:
1. complex systems contain many constituents
interacting nonlinearly
2. the constituents of a complex system are
interdependent
3. a complex system possesses a structure
spanning several scales
4. a complex system is capable of emergent
behaviour
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– emergence is the fundamental property of
systems
– emergent behaviour at a higher level of scale
arises from lower levels of scale although the
mechanisms involved are difficult to
comprehend
– emergence can be complex or simple
– emergent properties will be lost to reduction
– if all states were equally likely then there would
be no emergence
– it appears that relatively few configurations are
special or privileged in some way; these
configurations are what we call attractors
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−
the combination of structure and emergence leads to
self-organisation that occurs when emergent
behaviour creates new structure
5. complexity involves an interplay between chaos and
non-chaos:
– while chaos may reign on a scale, the coarser scale above it
may be self-organising, which in a sense is the opposite of
chaos
– complex systems, such as living organisms, manage to modify
their environment so as to operate as much as possible at the
edge-of-chaos, the place where self-organisation is most likely to
occur
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– two way interaction between the system and the environment
results in adaptation, or learning under changing conditions
e.g. the stock market players acting on local information,
consistent with Simon’s bounded rationality: individuals are
unable to forecast the higher level consequences of their actions
and so they optimise locally; yet the resultant behaviour has an
emergent logic
– evolution occurs as a result of collective adaptation over
generations
6. complexity involves an interplay between cooperation
and competition
e.g. firms compete with each other in markets but they
also cooperate and act collectively to prevent
government intervention in markets
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measures of complexity
– the degree of complexity can be expressed in terms
of structural aspects, the complexity of structure
– it can also be measured in terms of function
– a mathematical measure of complexity is given by
the amount of information needed to describe it
– the length of the binary string that can contain 2
messages is 1; for 4 or 22 messages, it is 2; for 8
or 23 messages it is 3 where log2(8)=3 etc.
– for a complex system with k possible states we need
N bits of information where N = log2(k)
– these ideas originated in communication theory and
are relevant in combinatorial mathematics also as
the problem of computational complexity
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systems thinking and complexity
• many of the attributes that define complexity also define
systems
• the commonalities between systems thinking and
complexity studies are strong; especially
because almost all human-activity systems are
complex
• it is not clear yet if the mathematical constructs and
results from complexity research can be directly
applied to the study of socio-economic or sociotechnical human systems
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• originally, OR searched for models and theories that
could simplify the essence of the world so that we
might capture a part of social reality for decision
making
• although OR knew that the world was complex, the
world also appeared to allow us produce robust
models that could be used in applications
• with the growing realisation that,
– complexity is more problematic to deal with than thought
before
– and that prediction appears to be getting out of reach
– the concern of OR has been moving away from solving
well defined problems towards structuring debate about
a complex world
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• many of the attributes of complex systems are
certainly shared by human activity systems
• the fundamental generalisations about selforganisation and complex adaptive systems
are especially relevant to OR
• hence an understanding of complexity can help
us better understand human activity systems
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