Evolutions, changes
and emergences
(dynamical systems)

Restless and changing systems

Many processes and systems found in the natural world as well
as in human and social life are dynamical, as always changing.
Their equilibrium is rarely fully stable.

Their evolution are often hard to predict and modelize, they can
be non-linear and not fully obey simple random laws. Here we
have complex dynamic systems with many interactions.

When they cross a critical threshold they show drastic evolution
phenomena such as self organization, percolation, emergence.
Those mutations can be robust or temporary.

The economy is specifically prone to dynamical phenomena and
emerging systems.

It never stays the same!
Expect surprises at every street corner!


A dynamical system is a process, a system or an entity
(yes, all of us are dynamical systems ...more or less intensively!)
* That is dynamic always in motion and evolving,
* not always regularly, as sometimes in a complex complex and
  
uppredictable way  (complex dynamical system) with
   many
interactions between its components and that acquires
   its
"own life" through self-organization and the emergence of
   new traits)

From a moment to the other, a dynamical system is never exactly
the same
.

If it doesn't move anymore, then it is a dead system!

Where to find complex dynamical systems?

Such systems are found about everywhere:
  • In physics,
from our planet's behavior with its hurricanes, volcanoes,
earthquakes, to the evolution of the whole universe.
  • In biology (life is a typical dynamical system). 
Yourself are a dynamical system!
Therefore not fully
predictable!
Although, normally, quite well organized!
  • Also in sociology / economics
(evolution of societies, groups, states and other institutions,
markets....)

How a complex dynamical system evolves

Dynamical systems are areas of uncertainty about the future, but some
traits can be identified

1. Non-linearity

Sometimes, something breaks.

Such a system evolves in a nonlinear and complex way, as subjected to:
  • Ordinary volatility: small fluctuations / vibration  oscillations.
They are more or less self-correcting, like when riding a
bicycle.
Or they lead to only incremental changes, making you a
slightly better ...or worse cyclist.
  • Cumulative bifurcation bifurcations / divergences.
They lead to decisive changes of orientation, or of state, at
the end, the famous "butterfly effect".
  • Disruptions: fluctuation instantaneous crucial changes / mutations
of value, state or nature).
  • Percolations: 
They are decisive breakthroughs / mutations above some
"critical threshold" towards a higher organization
level
with the
hatchemerge emergence of new traits (as specifically
described below).


This "enrichment" is often a trait of open systems that
draw energy from the outside, a form of "negentropy"
(see below: entropy)
  • Sometimes decay (entropy)
to a lower / disorderly / chaotic organization state.
Or even collapse, extinction, death of the system.

2. Unstable equilibrium

Rock and roll.
A dynamic system equil equilibrium is never fully stable.

Actually the word equilibrium might be misleading when applied to
them.

OK, let us say "dynamic equilibrium / balance".

Of course not all dynamical system evolve in the same way, and with
the same degree of instability.
Some even live a rather restful life with long periods that show just a
few blips or oscillations / vibrations.

But in many of them there are alternations (*) between usually:
  • Periods of minor changes and near stability (stases).
  • sometimes also going back and fro, between opposite forces,
    like
    a pendulum or as if self-regulating around an optimal
    position of the cursor
    .
  • Episodic dramatic changes,
  • Accelerations or setbacks, luckpositive or dangernegative
    mutations (among them "percolations", described below).


    And even periods of chaos (transition). Whence the "chaos
    theory".

    Markets give sometimes typical examples of chaotic evolutions such as

    bubbles and crashes.

    (*) Well, those alternation are far from completely regular,
          no Swiss clock here
    .

    3. Percolation, self organization and emergence

    Hocus pocus, something new appears!

    As seen above, when the system crosses a critical threshold,
    under repeated pressure or accumulation, a percolation to a new
    state is said to occur.

    Ilya Prigonine, a Nobel prize, called it a "self-organized criticality".
    Like when your sock drawer is so full that it becomes critically hard
    to open, or can critically fall to pieces.

    Then the system
    • Reaches a new level of organization
    (self-organization, "negentropy")
    • Shows new (usually superior) traits (emergence).
    • Also, might gain speed, or grow in volume,
    sometimes in a "snowballing" way

    => Have fun with two examples of how - via a
            "mathematical
    attractor" - chaos can become
            organized:
    the
    Langton ant and the Conway
            game of life.

    Examples of "emerging systems" are "emerging countries".
    Sorry for dogmatic thinkers who limit the notion of percolation to the
    physico-chemical-biological world. Mutations, self-organization,
    emergence and percolations drive also social phenomena, which are
    developed below.


    Some changes / mutations can be irreversible, except if some crucial
    shock brings a backlash
    .

    4. Examples in the economy and in human societies

    sous The economy moved from farming - as the dominant activity -
    to industry, or from industry to services.
    And now it is dominated by knowledge and information.

    New structures and institutions emerge at each step. Others tend to
    decay
    .
    Those switches are sometimes referred to as Schumpeter's "creative
    destruction".


    Those striking events are found not only in the economic area, but also
    in many social / political fields.
    History is full of
    surprise surprises, including "rare events"
    (see
    probability)
    • Some of them change fundamentally the turn of events.
    • Other , however dramatic, have only temporary incidences
    (the system is then  said "robust" or "resilient").

    The last case should not be confused with a fully reactionless system,
    which is no more dynamical but fossilized.
    Is not the most conspicuous human / social evolution in the
    21st century a double emergence, probably still fragile, of
    * a "4th type" society driven  by
    knowledge information and
        knowledge,
    across the World ?
    * and a self-organization via
    network networks, which
        could take
    preeminence over more pyramidal structures?
       
    If those mutations get confirmation, can we expect to reach a
    still superior
    level, in which the world would federate into a
    "
    democratic globalization"?

    And what about a possible new diruption if a new critical step
    is crossed later and a further level is reached in case
    transhumanism, which is just a project at the moment becomes
    a reality?

    Can such a system be modelized?

    Mathematical tools such as "fractals" or "attractors" can represent
    some of those systems'
    evolutions.
    But those evolutions are not fully predictable,
    there is always a degree
    of
    uncertainty
    specially for complex dynamical systems with many
    interactions, 
    .

    In some areas (those linked to social sciences for example, in which
    people's behaviors intervene) projections made via classical
    computer
    models that use statistical probabilities (however crucial
    they are to avoid elementary errors in standard
    cases) become
    unreliable when evolutions diverge
    :
    • either from standard random laws (Gaussian distribution...)
    • and/or from past statistics.
    => Thus an alternative method is to imagine a éventail range of
            scenarios
    (including extreme ones, as "rare events" are ...not
            so rare) and subjective
    probabilities based on human
            anticipations.

    It does not make uncertainty disappear. But it might help to be readier
    (contingency plans) and to keep an open mind.

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    M.a.j. / updated : 18 July 2015
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