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					          Complex
   Evolutionary
     Systems
              Part Three
The Philosophy of Systems Study,
Hysteresis, and Self Organization,
   And the Earth as a System
           What is a System?
                   Clarification Five
                         Again
  A naturally occurring group of interacting, interrelated, or
      interdependent elements, forming a complex whole,
   existing far from equilibrium, that have evolved together
 through time, forming a dynamic network where everything
   is connected to everything else by positive and negative
    feedback, such that a change in one component affects
    the states of the other components, exhibiting sensitive
 dependence, fractal organization, and avalanche behavior
             that follows a power-law distribution.”
Much of our difficulty with thinking about systems is tied up with, . . .
   How we think about systems. This a problem of history, and
                     philosophy, and psychology.
The Pendulum as a Limit Cycle
      Limit Cycle Attractor




                                                 -   Position   +
                                      +




                                      Velocity
                                      0
                                      Velocity
                                      +



                                Point Attractor


Can the Behavior of a Pendulum Evolve???
        The Pendulum as a Limit Cycle


                  The pendulum is an important
                  system because throughout
                  history it has been the emblem
                  of classical mechanics and the
                  epitome of clockwork regularity.
                                                         Pierre Simon de Laplace
                                                               (1749-1827)


In the 19th century the great French mathematician Laplace said: If
we were to know with precision the positions and speeds of all the particles
in the universe then we could predict the future with certainty.
      The Pendulum as a Chaotic System
Yet, Henir Poincare in a 1903 essay titled
“Science and Method” said this:
   If we knew exactly the laws of nature and the situation of
the universe at the initial moment, we could predict exactly
the situation of that same universe at a succeeding moment.
but even if it were the case that the natural laws had no longer
any secret for us, we could still only know the initial situation
approximately.

                                                                             Henri Poincaré
                                                                              (1854-1912)
If that enabled us to predict the succeeding situation with the same approximation, that is all
we require, and we should say that the phenomenon had been predicted, that it is governed
by laws. But it is not always so; it may happen that small differences in the initial conditions
produce very great ones in the final phenomena. A small error in the former will produce an
enormous error in the latter. Prediction becomes impossible, and we have the fortuitous
phenomenon.
 This tension between the need for complete
predictability and certainty, and the real world in which
we live - which is anything but predictable - has always
existed. But, the question comes down to, does the
real world work as classical science says it does? Or,
more directly
• Can a system that behaves like a classic pendulum -
swinging with complete regularity - evolve and change?

• And, what would be required for it to evolve and
change?
     ? How can we test these ideas
                  ?



                     Run Pendulum
          Properties of Complex Evolutionary Systems

1.0
       The Pendulum as a Strange Attractor

            1.1




1.12




           1.22




1.35




           1.5




                               http://hubble.physik.uni-konstanz.de/jkrueger/phsi362/
Observe that the pendulum bifurcation diagram in
  the last slide shows the same period doubling
 pattern as the Xnext bifurcation diagram below.
                   Classical Science and
               Evolutionary Systems Science
   Classical Science                       Evolutionary Systems
1. Reductionist                         1. Holistic and Emergent
   To understand a system we must       The whole is more than the sum of the
   take it apart and understand the     parts; the whole must therefore be
   pieces.                              studied in its own right.

2. Linear                               2. Non-Linear
   A system where the effects are       Of or relating to a system of equations
   proportional to the causes.          whose effects are not proportional to their
                                        causes - sensitive dependence. Such a
                                        set of equations can be chaotic.

3. Clear Boundaries                     3. Diffuse Boundaries
   The best system is self-contained,   Organic. Coevolving. Because complex
   isolated, complete in itself so it   systems are open they must exchange
   can be understood without            energy and information with the
   distractions or outside influence.   surroundings–the environment.
                                        Therefore, boundaries are not distinct.
                   Classical Science and
               Evolutionary Systems Science
   Classical Science                      Evolutionary Systems
4. Discrete Solutions                   4. Qualitative
   Numeric solutions—answers.           The interactions among the agents are
   There is a right answer, and the     beyond logical analysis, but the outcome
   more precision we have the better.   of the interactions produce patterns
   The devil is in the details.         easily observed and compared. The eye
                                        is quicker than the mind.

5. Centralized Control                  5. Interconnected Systems
   Straight forward cause and effect    Every component affects every other
   relationships, or clear chains of    component in a complex network of
   command.                             positive and negative feedback. There is
                                        no centralized control.
               Classical Science and
           Evolutionary Systems Science
       OK, OK. But, really, just how common are
              these complex systems?

    “It has been said that if the universe is an elephant,
then linear theory (classical science) can only be used
to describe the last molecule in the tail of the elephant
and chaos (read complex systems) theory must be used
to understand the rest. Or, in other words, almost all
interesting real-world systems are described by non-
linear (complex) systems.”




                                              http://en.wikipedia.org/wiki/Chaos_theory
 What Self Organized Criticality and Deterministic Chaos are
saying is abhorrent to classical science – the science taught in
                       most classrooms.




 "In my graduate school courses, we were always taught that large nonlinear systems
 were monsters, practically impossible to solve. Yet here was one and it was beautiful. It
 didn't even seem that hard to understand."

                                               Steve Strogatz, 2003 , Sync: The Emerging Science of
                                               Spontaneous Order
                       GO TO
                      Hysteresis
                           and
Bistable Behavior
                             State 1
 Bistable Variab le




                              State 2


                         Driving Variable
                 The Problem
So far, all this is well and good, but it still does not
provide explainability for the fundamental problem –
. . . .how do systems become more complex with time,
without resorting to a teleological argument.
. . . .By what mechanism does complexity increases with
time.

For example, how does a large city operate without
central planning?
 • Millions of people, thousands of stores and merchants.
 • All working more or less independently, each looking after
 their own selfish interests.
• Yet the store shelves are always full.
         The Problem of Problems
   General Solutions to the Problem
3. Naturalism
                           An Inquiry into the Nature and Causes of
                                 the Wealth of Nations, 1776

           As every individual, therefore, endeavours as much as he can both to
           employ his capital in the support of domestic industry, and so to
           direct that industry that its produce may be of the greatest value;
           every individual necessarily labours to render the annual revenue of
           the society as great as he can. He generally, indeed, neither intends
           to promote the public interest, nor knows how much he is promoting
           it. By preferring the support of domestic to that of foreign industry,
           he intends only his own security; and by directing that industry in
           such a manner as its produce may be of the greatest value, he intends
           only his own gain, and he is in this, as in many other cases, led by
           an invisible hand to promote an end which was no part of his
           intention. Nor is it always the worse for the society that it was no
           part of it. By pursuing his own interest he frequently promotes that of
           the society more effectually than when he really intends to promote
           it.
                          The Problem of Problems
   General Solutions to the Problem
3. Self Organization (the new Naturalism)
Self-organization is a process where the organization of a system
spontaneously increases without this increase being controlled by
the environment or an encompassing or otherwise external system.
A process of evolution where the effect of the environment is minimal, i.e. where the development of new,
complex structures takes place primarily in and through the system itself.


Prigogine called systems which continuously export entropy in order to maintain their organization
dissipative structures.


It is an “invisible hand”, like the invisible hand of commerce. But, that is like saying the “invisible hand of
God.” It puts it in the realm of the supernatural, or magic.



Are there any systems or natural mechanisms to explain self
organization?
             The Problem of Problems
   General Solutions to the Problem
3. Self Organization Theories and Models
 Self Organized Criticality
              The Problem of Problems
    General Solutions to the Problem
 3. Self Organization Theories and Models
Autocatalytic Networks




                     Stuart Kauffman
              The Problem of Problems
    General Solutions to the Problem
 3. Self Organization Theories and Models
Cellular Automata
            Cellular Automata and Self Organization
Cellular Automata (CA) are simply grids of
cells, where the individual cells change      Local Rules/Global
states according to a set of rules. The CA
may be one dimensional, or linear, like a         Behavior
string of cells in a row (below), or two        Sample Local Rules
dimensional, like a checkerboard
                                             Survival Rules – number                         of
                                             surrounding cells necessary to make it to the next
                                             generation.

                                             Birth Rules –           number of surrounding cells
                                             necessary for a dead cell to come alive the next
                                             generation.




                                                       Life3000
                                                        LifeWin
                                             Merick’sCelebration
            Cellular Automata and Self Organization
Cellular Automata (CA) are simply grids of
cells, where the individual cells change         Local Rules/Global
states according to a set of rules. The CA
may be one dimensional, or linear, like a            Behavior
string of cells in a row (below), or two       Optimal Local Rule Set
dimensional, like a checkerboard
                                             Survival Rules – 2/3 a live cell
                                             survives to the next generation if at least 2 but no
                                             more than three of the surrounding 8 cells are alive.
                                             Less than 2 and it dies of loneliness; more than 3 and
                                             it dies of over crowding.-

                                             Birth Rules – 3/3                     a dead cells comes
                                             alive the next generation if 3, any 3, of the surrounding
                                             8 cells are also alive.




                                                                Life3000
                                                                 LifeWin
                                                     Merick’sCelebration
                                                                   Applet
Cellular Automata and Power-Law Relationships
           What is a System?
                    Clarification Six

So, to refine our definition:
    A “system” is a group of naturally occurring interacting, interrelated,
    or interdependent elements, forming a complex whole
   • existing far from equilibrium,
   • that have evolved together through time,
   • (self organized by bottom-up processes)
   • forming a dynamic network where everything is connected to
        everything else by positive and negative feedback,
   • such that a change in one component affects the states of the other
        components,
   • exhibiting:
        sensitive dependence,
        fractal organization,
        and avalanche behavior that follows a power-law distribution.
         The Earth and Everything
           On It Are A System!
• They cannot be understood in reductionist terms
• They cannot be understood in linear terms.
• They cannot be understand through only 1 or 2 disciplines.

     It is all about how the lithosphere, hydrosphere,
  atmosphere, and biosphere connect – the links among
 them - and the positive and negative feedback relations
           among them that must be understood.

 Many of the ideas we need to understand, and we need
 to learn, have not been taught to us. But, we have to
 begin somewhere and this is as good a place as any, so
 let’s start here.

				
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posted:8/16/2012
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