Complex adaptive systems

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Lecture 9

• Complex adaptive systems

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In the beginning...

• Newtonian sciences
• Initial conditions, laws and predictability
• If the initial conditions of the system are
  completely specified it will be possible to
  compute its further states precisely
• God-created, optimal universe
• Universe is optimal and infinitely precise
  because it was created by God
• Determinism and reductionism
• We can completely understand the functionality of
  the whole if we break it into parts and
  understand the functionality of its parts

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Paradigm is shifting...

• Quantum mechanics
• Non-determinism
• It is only possible to measure speed or location
  of elementary particle with precision of Planks
  constant
• Our own interference, our apparatus disturb the
  path of the particle
• Probabilistic universe
• Gödel Turing
• Limitations of logic
• It is not possible to construct mathematical
  system based on logic, such that it is both sound
  and complete
• Unpredictability in computing
• Halting problem

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The Flow

• Dynamical systems
• We find ourselves among ever-changing systems
• There is an intractable number of branches
• Feedback
• Systems change and develop by receiving feedback
  from the environment and responding to
  environment. Thus systems are inextricable parts
  of the environment
• Self-reference
• The systems around us are heavily recursive,
  self-bootstrapping
• Co-evolution
• There is no stand alone evolution, everything is
  co-evolving.
• Everything is dependent and influences everything
  else.

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Cybernetics

• Norbert Wiener
• Trying to understand how control communication
  worked
• Greek kybernetes (steersman) (Web of life pp..
  97)
• We are but whirlpools in a river of ever-flowing
  water
• Self-regulation
• We are not stuff that abides, but patterns that
  perpetuate themselves

Situation Assessment
Action
Impact on environment
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Ilya Prigogine

• Second law of thermodynamics
• In closed system, the amount of entropy in a
  given system does not decrease
• Entropy means disorder
• Living organisms and equilibrium
• Living beings are in order, away from equilibrium
• Open thermodynamical systems
• Nonlinear equations
• Self-Organization

Equilibrium (ice)
Order (edge of chaos)
Chaos (gas)
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Gaia theory

• James Lovelock and Lynn Margulis
• Search of life on Mars
• Earth is open system, away from equilibrium
• Life on Earth regulates atmosphere
• 25 increase of heat from sun
• Gaia - the living system
• Adaptation to available resources
• Crucial dependents and interdependence of living
  and non-living systems
• Symbiosis

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Cellular automation

• John von Neumanns cellular automation
• grid of cells, each cell can be in some state
• discrete space and time, synchronous updates
• updates are based on local interaction rule
• equivalent to Turing Machine in computational
  power!
• John Conways Game of Life
• if ( of neighbors lt 2 or gt 3 ) die
• if ( of neighbors 2 and you are alive live )
• if ( of neighbors 3 new cell is born )

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Classification of CA

• Stephen Wolfram

Single attractor (dies out)
Periodic attractors (oscillations)
Complex structures (increasing)
Strange attractors (chaos)
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Artificial Life

• Chris Langton
• Interpreting the classification

I II
IV
III
Complexity
Chaos
Equilibrium
Solid
Phase Transition
Fluid
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Fractals

• Bernoit Mandelbrot
• geometry of irregular natural phenomena
• language to speak of clouds
• Julia sets
• Z -gt Z2 C, for different Z
• Why are we fascinated with fractals?
• We are looking for patterns in nature
• Abstractions created by human brain

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How did it all come about?

• Stuart Kauffman
• Skeptics
• Probability and complexity
• Autocatalytic sets closures
• Self-bootstrapping properties

Catalyst/Adapter
A
C
B
A
BA
AB
B
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Santa Fe Institute

• Formed in 1985
• Think tank to deal with complexity
• Scientists from all areas including physics,
  chemistry, biology, computer science, economics,
  ecology, sociology, history, etc.
• http//www.santafe.edu

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John Holland

• Complex adaptive systems
• BACH group in University of Michigan
• Burks, Axelrod, Cohen, Hamilton
• Genetic algorithms
• Quotation from Complexity

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Seven basic elements of CAS

• Aggregation
• Economy and markets
• Body and nervous, immune, endocrine system
• World economy and country economies
• Emergence as a result of interactions
• whole gt sum of the parts
• higher level of organization
• meta agents

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Seven basic elements of CAS

• Tagging (mechanism)
• Identification of alike agents
• Grouping
• Attribute
• contracts between firms
• form of adaptation - delegation
• Divisions in a firm Equities, Fixed Income, etc.
• collaboration, formation of aggregate and
  diversification via tagging

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Seven basic elements of CAS

• Nonlinearity (property)
• aggregation tagging
• threshold of emergence (H gtsum(P))
• predator/prey interaction
• One of the standard example of nonlinear
  dynamical model is predator/prey interaction.
  Observe that increases in either population
  increase the likelihood of a contact. Let
  Predator(t), and Prey(t) be number of predators
  and prey at some time t, and let c be the
  constant that reflects efficiency of a predator.
  We can calculate the number of interactions per
  unit of time as cPredator(t)Prey(t). That is,
  with c 0.5, Predator(t) 2 and Prey(t) 10,
  we would have 10 encounters. Now, let us double
  each population so that Predator(t) 4 and
  Prey(t) 20, then we will have 40 encounters.
• nonlinearity is a result of a product instead of
  a sum

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Seven basic elements of CAS

• Flow (property)
• nonlinearity induces flow
• multiplier effect
• feedback and cycles

Dead
Alive
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Seven basic elements of CAS

• Diversity (property)
• arise from exploration of multitude of
  possibilities (local adaptations)
• firms enter and leave market
• mimicry

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Seven basic elements of CAS

• Internal models (mechanism)
• anticipation
• survival of the fittest
• subconscious mode

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Seven basic elements of CAS

• Building blocks (mechanism)
• decomposition
• quark, nucleon, atom, molecule, organelle, cell
• generation of internal models

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What is complexity?

• Complexity is digested information
• It is order out of chaos
• It is inevitable, it is intricate part of nature

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Information theory

• Definition of entropy
• measure of uncertainty in the random variable
• how many bits are necessary to describe an event
  (coin flip)
• We learned to see patterns around us
• Patterns represent information which can be
  compressed as oppose to random information
• Why do math professor stare at the ceiling when
  they speak?

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Modeling issues

• Emergence of behavior
• Global properties based on local interactions
• No optimum, the only measure of fitness is
  survival
• Free interactions
• Least amount of rules

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References

• Complexity
• by Mitchell Waldrop
• Hidden order How adaptation builds complexity
• by John Holland
• At home in the universe
• by Stuart Kauffman
• The web of life
• by Fritjof Capra