in this video we will be giving an
overview to the area of complexity
theory by looking at the major
theoretical frameworks that are
considered to form part of it and
contribute to the study of complex
systems
complexity theory is a set of
theoretical frameworks used for modeling
and analyzing complex systems within a
variety of domains complexity is proven
to be a fundamental feature of our
universe that is not amenable to our
traditional methods of modern science
and thus as researchers have encountered
it with in many different areas from
computer science to ecology to
engineering they have had to develop new
sets of models and methods for
approaching it out of these different
frameworks has emerged a core set of
commonalities that over the past few
decades has come to be recognized as a
generic framework for studying complex
systems in the abstract complexity
theory encompasses a very broad and very
diverse set of models and methods as yet
there is no proper formulation to
structure and give definition to this
framework thus we will present it as a
composite of our four main areas that
encompass the different major
perspectives on complex systems and how
to best interpret them including
self-organization theory nonlinear
systems Network theory and adaptive
systems theory
firstly self-organization and emergence
complex systems are composed of many
small parts without centralized control
examples being flocks of birds financial
markets social networks global logistics
networks or the human brain without
centralized control global organization
is an emergent feature of the local
interactions between the parts whereas
the term emergence is a general concept
referring to how new levels of
organization are formed as we put
component parts together the theory of
self-organization presents a number of
concrete models for understanding how
this process takes place the model of
self-organization draws upon information
theory to understand organization in
terms of information and entropy it
draws upon ideas and physics surrounding
synchronization and pattern formation
and ideas in chemistry surrounding
dissipative systems and far from
equilibrium processes here we are
looking at how elements governed by
simple rules synchronize their behavior
with the result being a process of
self-organization as patterns of
organization emerge from the bottom-up
researchers try to model complex systems
by capturing these local rules and using
computational tools like agent-based
modeling to try and simulate the process
through which order emerges out of
initially homogeneous or disordered
States
next nonlinear systems and chaos theory
non-linearity is an inherent feature and
major theme that crosses all areas of
complex systems a lot of nonlinear
systems Theory has its origins in quite
dense and obscure mathematics and
physics out of the study of certain
types of equations weather patterns
fluid dynamics and particular chemical
reactions has emerged some very
counterintuitive phenomena in the form
of the butterfly effect and chaos chaos
theory which is the study of nonlinear
dynamical systems was one of the first
major challenges to the Newtonian
paradigm that was accepted into the
mainstream body of scientific knowledge
our modern scientific framework is based
upon linear Systems Theory and this
places significant constraints upon it
linear Systems Theory is dependent upon
the concept of a system having an
equilibrium all the linear systems
theory often works as an approximation
the fact is that many of the phenomena
we are interested in describing are
nonlinear processes of change such as
regime shifts within ecosystems and
society happen far from equilibrium they
are governed by the dynamics of feedback
loops and not linear equations trying to
model complex systems by using
traditional linear Systems Theory is
like trying to put a screw into a piece
of wood with a hammer
we are simply using the wrong tool
because it is the only one we have
thus the areas of nonlinear systems in
their dynamics is another major part of
the framework of complexity theory that
has come largely from physics
mathematics and the study of far from
equilibrium processes in chemistry
next network theory network theory is
another major area to complexity theory
as almost all complex systems can be
understood and modeled effectively as
networks network theory is a formal
mathematical language but it has proven
a very practical tool for analysis and
thus has found widespread application in
many areas the study of networks is
probably the youngest and most active
area of complexity science again driven
by the rise of computation and the
fundamental role that networks are
starting to play in our world with the
advent of information technology with
the theory of networks and the
availability of new sources of data we
are starting to get a real picture to
what some of these complex systems that
make up our world actually look like we
can start to see the connections within
financial systems through which
contagion spreads the real time movement
of freight around the globe or
socio-political networks that influence
our lives this is a new kind of science
driven less by models and equations but
more by real time dense datasets this
means we are no longer left staring in
models but now have accessible
visualizations to give us a much more
rich intuitive and in many ways real
sense for what exactly these complex
systems are like the main contributions
to this area have come from the area of
mathematics called graph theory and
again computer science
the last major area to complexity theory
that we will discuss is that of complex
adaptive systems complex adaptive
systems are classical examples of
complex systems and people often use the
two words somewhat interchangeably
they consist of many parts acting and
reacting to each other's behavior like a
school of fish swimming together
nation-states within the international
political environment or businesses in a
market they are highly dynamic and
developed through an evolutionary like
process the central issue is that of the
process of adaptation and evolution the
idea of adaptation formed a central part
of cybernetics that contributed ideas
surrounding control systems and how
systems regulate themselves and their
environment in order to maintain
homeostasis
a key issue here is that of the dynamics
surrounding cooperation and competition
that form as adaptive agents interact
and try to pursue their goals
collectively one could also include game
theory here a branch of mathematics for
modeling the interaction between
adaptive agents of all kinds and the
dynamics of cooperation and competition
that form out of this when the idea of
adaptation is generalized to a whole
population of agents and takes place
over a series of life cycles it can be
termed evolution and the theory of
evolution is one of the major
contributions that ecology is made to
complexity theory we now have a number
of different models for understanding
evolution including evolutionary game
theory replicator equations Fitness
landscapes and genetic algorithms among
others this is an area that has grown
out of cybernetics computer science
economics and ecology
lastly we'll discuss a little of the
context and significance of the area of
complexity theory as it plays a somewhat
unique role within the framework of
contemporary science the website
scholarpedia describes complexity theory
as an emerging post-newtonian paradigm
there is a lot packed into this short
statement so let's try and unravel and
make sense of it the Newtonian framework
is based on linear Systems Theory this
has been a powerful tool for helping us
understand the world through the
contributions of millions of researchers
over the course of centuries we have
built up a large and sophisticated body
of scientific knowledge which is one of
humanity's greatest achievements
throughout the 20th century though the
Newtonian paradigm and linear Systems
Theory have become increasingly called
into question has general relativity and
then chaos theory proved some of its
most basic assumptions to be in fact
flawed the fact is that much of the
phenomena that we are really interested
in are inherently nonlinear such as
almost all socio-political ecological
and economic phenomena a core challenge
of 21st century science then is to
extend this framework into the world of
nonlinear systems and complexity and
this means going beyond the Newtonian
framework as scholarpedia puts it
developing a post Newtonian paradigm and
this is exactly what complexity theory
is doing
to summarize we have been giving a quick
overview to the area of complexity
theory which we defined as a set of
theoretical frameworks used for modeling
complex systems within a variety of
domains we looked at four of the major
modeling frameworks that fall under its
canopy we firstly talked about
self-organization and how it gives us
the tools to understand the process of
emergence where global patterns form out
of only local interactions we talked
about the theory of nonlinear systems
and how it has emerged out of the study
of chaotic physical and chemical
processes we then discussed network
theory as another major domain that
understands complex systems in terms of
connectivity and how things flow through
these systems the last major area we
looked at was the theory of adaptive
systems that tries to understand complex
adaptive systems in terms of the
interaction between adaptive agents
cooperation and competition and the
dynamics of evolution finally we tried
to provide some insight into the
significance and context of complexity
theory as I so called post-newtonian
paradigm as it tries to extend our
scientific body of knowledge into the
world of nonlinear systems