Dealing with Complexity

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Dealing with Complexity

• Peter Andras
• Department of Psychology
• University of Newcastle
• peter.andras_at_ncl.ac.uk

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Overview

• What is complexity ?
• What is chaos ?
• Linking chaos and complexity
• Handling complexity Information
• External and internal complexity
• Generating matching complexity

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What is complexity ?
The buzz word complexity complexity of an
NHS trust (Guardian, February 12, 2002)
increasing complexity in natural resource
management (Conservation Ecology, January
2002) citizens add an additional level of
complexity (Political Behavior, March 2001)
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Complex micro-worlds

• gene interaction system
• protein interaction system
• protein structure

The system of functional protein interaction
clusters in the yeast (www.cellzome.com).
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Complex organisms
C. Elegans (devbio-mac1.ucsf.edu)

• complex cell patterns
• complex organs
• complex behaviours

C. Elegans ventral ganglion transverse-section
(www.wormbase.org)
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Complex machines
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Complex organisations
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Complex eco-systems
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Algorithmic complexity
Task calculate the total area of the shape
Question how many operations does it take to
find the total area
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Algorithmic complexity
The complexity of a computational problem is
given by the length of the sequence of operations
that are need to solve the problem. In principle
there is a universal way to to find out the
complexity of a problem, which is the finding of
the shortest program that a Turing machine
requires to solve the problem. In practice this
cannot be applied.
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Language dependent complexity
Problem to describe a phenomenon, an object, a
solution of some other problem Description
complexity the length of the description in
language units (words) Description complexity
depends on the language.
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Language dependent complexity
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What is chaos ?
The buzz word chaos managing at the edge of
chaos (Guardian, February 19,
2002) the brain as a system near the edge of
chaos (Journal of Consciousness Studies,
July, 2000) chaos theory is used metaphorically
to address aspect of creative process
(Creativity Research Journal, no.3-4, 2000)
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Randomness as chaos
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Chaos in nature
Light reflection from four spheres
(www-chaos.umd.edu)
Lung (micro)
Lung
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Fractals
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Mathematical chaos
Equational description of the phenomena or
object E.g. xt1 xt xt yt yt
a yt1 2 xt yt b It is chaotic if shows
sensitive dependency on the initial conditions
(on x0 and y0 in the case above). Sensitive
dependency small initial changes may lead to
large changes later.
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Mathematical chaos
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Chaos and unpredictability
Key feature of mathematical chaos unpredictabil
ity, due to the sensitive dependency on
initial conditions Practical unpredictability
links the deterministic chaos to the randomness.
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Complex fractals
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Simple fractals
z (x,y) z0 z zt1 zt zt z0 n(z) is the
first t for which zt gt 4
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Describing chaos
Different languages can be used to describe the
same chaotic phenomena. These languages may
differ in the length of descriptions that are
required for a given level of precision. Mathemat
ical chaos appears complex if we use a
description language which requires long
descriptions to achieve a desired level of
precision.
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Chaos, unpredictability, complexity
The unpredictability of chaos guarantees that the
description of the chaos requires long
descriptive sequences in most of the
languages. Finding the appropriate language that
allows compact description of a given chaotic
phenomena is far from trivial, and the search for
the appropriate language may be itself very
complex (in the sense of Turing computability).
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Handling complexity Information
How to survive within an environment ? How to
find the appropriate response to a given
environmental situation ? First step
DIFFERENTIATING between states of the
environment. Being able to differentiate between
environmental states means that information can
be gathered about the environment.
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Making a choice
Having the criteria for differentiation is not
enough. It is important that the observer is able
to make a choice, and use the criteria for
differentiation to choose between the possible
states of the environment. On the basis of this
choice the observer provides the appropriate
response. Information is the difference that
makes a difference. (Bateson, 1971)
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Sequence of choices
The environment is described by a sequence of
choices for the observer. The choices are the
description language units for the observer. The
length of the choice sequences gives the
perceived complexity of the environment for the
observer.
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Response generation
The level of inappropriateness of the selected
responses shows to what extent the description
language of the observer captures the real
complexity of the environment. The observer
always ignores those features of the environment
that cannot be evaluated using its
differentiation criteria. The ignored features
create the mismatch between the perceived and
real complexity of the environment.
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Information processing structures
Information processing means the effectuation of
choices. Information processing structures of
the observer perform this choices by selecting
their own appropriate action.
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Specialized information processing
The information processing structures deal with a
restricted complexity environment that is the
real environment filtered through an appropriate
part of the description language Such structures
are specialized on processing of information that
can be gathered by applying a restricted set of
the differentiation options and related choices.
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Example 1 Proteins
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Example 2 Photoreceptors
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Example 3 The legal system
From the point of view of the legal system the
single issue is whether something is legal or
illegal. If an action or a state cannot be
assessed from this point of view, it is just
outside of the interest of the legal system, it
is ignored. In all cases when an action or state
falls in the interest of the legal system, the
single question about it is whether it is legal
or not, and all the investigations consider only
the definitions, guidelines, rules and other
formal components of the legal system in deciding
the legality.
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External complexity
The external complexity is the complexity of the
environment. Environment the Earth, a city, the
university, a cave, a skin patch of an animal,
the programs that are running in a computer, etc.
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Internal complexity
The internal complexity is the complexity of the
information processing structures of a system
that acts in an environment. Internal
complexity system of adaptive protein folding,
sensory discrimination and adaptive response
generation system of an animal, the internal
structure and functional rules of an
organisation, the input interpretation and output
generation system of a computer program
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Information processing
The information processing structures and
processes can be viewed as a description language
of the external complexity. This language gives
the perceived complexity of the environment.
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Matching complexities
The system performs well in an environment (its
adaptive actions fit to the environmental
conditions) if its internal complexity matches
the external complexity of the environment. The
information processing sub-system of the system
can be described in many ways, using many
description languages. The key is that using at
least one of these languages the internal
complexity fits to a good extent the external
complexity.
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Competition of information processing structures
In a world of co-existing systems (e.g.,
individual animals, animal species, cars, etc.)
those have better survival chances that gather
and process information more efficiently. Those
systems that develop internal complexity that
matches better their external complexity perform
better, their adaptive responses fit better to
the environmental challenges. If these systems
reproduce (directly or indirectly), those will
become dominant that have better information
processing sub-systems.
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Evolution of world descriptions
The evolution of information processing
sub-systems can be viewed as an evolution of
world descriptions. The better world descriptions
capture better the real complexity of the
environment (the relevant part of the world for
some systems inhabiting that part). Generating
better descriptions of the world the systems are
able to deal more efficiently with the complexity
of their environment.
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Example 1 Genes
Mutant genes may encode proteins that are able to
transform environmental energy resources into
internal energy storage of the cell. Cells having
these mutant genes have a better description of
their environment, and will conquer the living
space of those which do not have the mutant genes.
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Example 2 Organ evolution
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Example 3 Politics
The governing parties change at elections. Those
get more votes who provide a better description
of the world, which fits better the perceived
complexity of the world, as it is perceived by
the voting public. Those politicians who use a
better language to address the real world
problems are more likely to be voted and more
likely to put in practice their views as members
of the government.
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Generating matching complexity
How to build / generate information processing
sub-systems that capture the complexity of the
environment to a large extent ? How to generate
internal complexity that matches the external
complexity ?
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Generating complexity by chaos
Deterministic chaos offers the advantage that it
has a very simple and a very complex
description. Generating it is simple, by using
the simple description language. It can be used
to capture high complexity descriptions by using
the complex description of the deterministic
chaos.
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Self-similarity
A simple way to generate complex deterministic
chaos is by the application of self-similar
expansions at smaller scales.
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Self-reference
Self-reference is the extension of the
self-similarity concept to generic
systems. Systems operating by self-referential
expansion are able to generate high complexity
deterministic chaos that can capture high levels
of environmental complexity.
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Self-referential expansion
Self-referential expansion is possible in
effective way if the simple description language
is available. Highly specialized components of
the information processing sub-system can develop
their internal language that is highly
standardized and communicates information
efficiently (with low ambiguity and in a
compressed form). Such standardized internal
languages can constitute the basis for effective
self-referential expansion.
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Standardized languages

• Possible examples of standardized languages
• nucleic acids of the DNA / RNA
• spikes in the neural system
• the spoken human language
• the price of goods and services

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Match criterion
Two description languages have matching
complexity if their information encoding capacity
is close.