Self Organization

Compl ex

Evol ut ionar y

Syst ems

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.”

What is a System?Clarification Five

Again

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.

Can the Behavior of a Pendulum Evolve???

Limit Cycle Attractor

Position- +

Ve

loci

ty0

Ve

loci

ty

+

+

Point Attractor

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.

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.

Pierre Simon de Laplace (1749-1827)

The Pendulum as a Limit Cycle

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.

Yet, Henir Poincare in a 1903 essay titled “Science and Method” said this:

Henri Poincaré(1854-1912)

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.

The Pendulum as a Chaotic System

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

? How can we test these ideas ?

Run Pendulum

• 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?

Properties of Complex Evolutionary Systems

The Pendulum as a Strange Attractor1.0

1.12

1.35

1.1

1.22

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.

1. Reductionist 1. Holistic and Emergent

Classical Science Evolutionary Systems

Classical Science andEvolutionary Systems Science

To understand a system we must take it apart and understand the pieces.

The whole is more than the sum of the parts; the whole must therefore be studied in its own right.2. Linear 2. Non-Linear

A system where the effects are proportional to the causes.

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

3. Clear Boundaries 3. Diffuse BoundariesThe best system is self-contained, isolated, complete in itself so it can be understood without distractions or outside influence.

Organic. Coevolving. Because complex systems are open they must exchange energy and information with the surroundings–the environment. Therefore, boundaries are not distinct.

4. Discrete Solutions 4. QualitativeNumeric solutions—answers. There is a right answer, and the more precision we have the better. The devil is in the details.

5. Centralized ControlStraight forward cause and effect relationships, or clear chains of command.

The interactions among the agents are beyond logical analysis, but the outcome of the interactions produce patterns easily observed and compared. The eye is quicker than the mind.

5. Interconnected SystemsEvery component affects every

other component in a complex network of positive and negative feedback. There is no centralized control.

Classical Science Evolutionary Systems

Classical Science andEvolutionary Systems Science

“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.”

OK, OK. But, really, just how common are these complex

systems?

Classical Science andEvolutionary Systems Science

http://en.wikipedia.org/wiki/Chaos_theory

"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

What Self Organized Criticality and Deterministic Chaos are saying is abhorrent to classical science – the science taught in

most classrooms.

So far, all this is well and good, but it still does not provide explainability for the fundamental problem –

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 ProblemThe Problem

. . . .how do systems become more complex with time, without resorting to a teleological argument. . . . .By what mechanism does complexity increases with time.

The Problem of Problems

General Solutions to the Problem3. Naturalism

An Inquiry into the Nature and Causes of

the Wealth of Nations, 1776As 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 Problem3. 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 Problem3. Self Organization Theories and Models

Self Organized Criticality

The Problem of Problems

General Solutions to the Problem3. Self Organization Theories and Models

Autocatalytic Networks

Stuart Kauffman

The Problem of Problems

General Solutions to the Problem3. Self Organization Theories and Models

Cellular Automata

Cellular Automata and Self Organization

LifeWin

Life3000

Merick’sCelebration

Cellular Automata (CA) are simply grids of cells, where the individual cells change states according to a set of rules. The CA may be one dimensional, or linear, like a string of cells in a row (below), or two dimensional, like a checkerboard

Sample Local RulesSurvival 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.

Local Rules/Global Behavior

Cellular Automata and Self Organization

LifeWin

Life3000

Merick’sCelebration

Cellular Automata (CA) are simply grids of cells, where the individual cells change states according to a set of rules. The CA may be one dimensional, or linear, like a string of cells in a row (below), or two dimensional, like a checkerboard

Optimal Local Rule SetSurvival 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.

Local Rules/Global Behavior

Applet

Sensitive Dependence in Cellular Automata

Power-Law Relationships in

Cellular AutomataRun an random array until it stops, add a live cell at random, run again until it stops. Avalanche size is the number of generations from initiation until it stops. Most avalanches last only one or a few generations; others may last hundreds of generations. Plotted up the avalanches follow a power-law meaning Cellular Automata (with optimum local rules) are Self Organized Critical systems.

So, to refine our definition:A “system” is a group of naturally occurring interacting, interrelated, or interdependent elements, forming a complex whole

• that have evolved together through time,

• forming a dynamic network where everything is connected to everything else by positive and negative feedback,

• exhibiting: sensitive dependence,

and avalanche behavior that follows a power-law distribution.

fractal organization,

What is a System?Clarification Six

• existing far from equilibrium,

• (self organized by bottom-up processes)

• such that a change in one component affects the states of the other components,

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.

The Earth and EverythingOn 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.