Complexity and Freedom

Complexity and Freedom Lessons from nature about human networks and life on the edge

Complexity

Complicated: Containing many intricately combined parts. Hard to figure out.

Complex: Exhibiting systemic properties that aren’t apparent even when you understand its parts.

http://www.people.vcu.edu/~mikuleck/ON%20COMPLEXITY.html

Equilibrium

Complexity

Chaos

Nature is not in equilibrium

It self-organizes towards criticality

Sand piles How do avalanches work?

self-organized criticality

In physics, self-organized criticality (SOC) is a property of (classes of) dynamical systems which have a critical point as an attractor. Their macroscopic behaviour thus displays the spatial and/or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to precise values.

First identified by Per Bak, Chao Tang and Kurt Wiesenfeld, 1987

(http://en.wikipedia.org/wiki/Self-organized_criticality)

Self-organized criticality

Population distribution

Traffic patterns

Income distribution

Market prices

Sociology

Music popularity

Social networks

Website links and traffic

Language

Avalanches

Earthquakes

Coastlines

Rivers

Extinctions

Evolution

Weather patterns

Cosmology

Neurobiology

Human Activities Natural Phenomena

Power Laws

A straight line in a double logarithmic coordinate system

Some quantity N can be expressed as some power of another quantity S

A power law is any polynomial relationship that exhibits the property of scale invariance.

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

Zipf’s Law

Self-Organized Criticality

is critical-point phenomena

that are characterized by…

fractal geometry

1/f noise

power laws

that can be simulated or reproduced by …

cellular automata

SOC is typically observed in slowly-driven non-equilibrium systems with extended degrees of freedom and a high level of nonlinearity.

Social Networks

Scale invariance

In physics and mathematics, scale invariance is a feature of objects or laws that do not change if length scales (or energy scales) are multiplied by a common factor

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

Scale-free network

In scale-free networks, some nodes act as "highly connected hubs" (high degree), although most nodes are of low degree. Scale-free networks' structure and dynamics are independent of the system's size N, the number of nodes the system has. In other words, a network that is scale-free will have the same properties no matter what the number of its nodes is.

http://en.wikipedia.org/wiki/Scale-free_networks

1/f noise « fractals in time »

Contains periodic signals of all frequencies. The signal/power is stronger for low frequencies.

Pink noise or 1/f noise is a signal or process with a frequency spectrum such that the power spectral density is proportional to the reciprocal of the frequency. Pink Noise has an equal amount of energy per octave. The name arises from being intermediate between white noise (1/f 0 ) and red noise (1/f 2 ), more commonly known as Brownian noise).

http://en.wikipedia.org/wiki/1/f_noise

Fractal

It has a fine structure at arbitrarily small scales.

It is too irregular to be easily described in traditional Euclidean geometric language.

It is self-similar (at least approximately or stochastically).

It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve).

It has a simple and recursive definition.

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

Cellular Automaton

A cellular automaton is a collection of cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules based on the states of neighboring cells. The rules are then applied iteratively for as many time steps as desired.

Game of Life

The Game of Life is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is the best-known example of a cellular automaton.

http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life

Sandpile simulation

Propagating avalanche in the sand pile model. The colors gray, green, blue and red indicate heights of 0, 1, 2 and 3, respectively. Light blue indicates columns that have toppled at least once.

http://thy.phy.bnl.gov/www/xtoys/gallery/gallery.html

Sandpiles

Once the sandpile model reaches its critical state there is no correlation between the system's response to a perturbation and the details of a perturbation.

Generally this means that dropping another grain of sand onto the pile may cause nothing to happen, or it may cause the entire pile to collapse in a massive slide.

http://en.wikipedia.org/wiki/Bak-Tang-Wiesenfeld_sandpile

Forest fire

http://en.wikipedia.org/wiki/Forest-fire_models

Model of evolution

http://en.wikipedia.org/wiki/Bak-Sneppen_model

http://cmol.nbi.dk/models/bs/bs.html

Dynamic Efficiency

« The critical state is the most efficient state that can actually be reached dynamically. »

- Per Bak

Self-organized criticality

Things have self-organized so that they’re wound up, ready to go

If something happens, something else is likely to happen

Mostly small things will happen, but sometimes big things will happen

Butterfly effect

Very small actions in a complex system can have potentially very large and unpredictable consequences.

Usually illustrates chaos theory, but applies just as easily to self-organized criticality.

You send an e-mail… Something random happens Something potentially useful could happen Nothing much happens Chaos Complexity Equilibrium

What does that have to do with freedom?

Freedom

the ability to act in accordance with the dictates of reason;

the ability to act in accordance with one's own true self or values;

the ability to act in accordance with universal values (such as the True and the Good); and

the ability to act independently of both the dictates of reason and the urges of desires, i.e. arbitrarily (autonomously).

http://en.wikipedia.org/wiki/Freedom_(philosophy)

Degrees of Freedom

Degrees of freedom is a general term used in explaining dependence on parameters, and implying the possibility of counting the number of those parameters. In mathematical terms, the degrees of freedom are the dimensions of a phase space.

Freedom

The potential to do small actions that make a big (positive) difference

Degree of leverage (amplification) in your choices

Degree to which you’re in the right place at the right time, and the right things happen

Freedom?

Are your toys wound up?

My Theory

You have more freedom within a complex network

Your freedom is potentially more useful if the network is in a critical state

The value of a network is proportional to its complexity

Sarnoff’s Law

The value of a (broadcast) network is proportional to the number of members (listeners, viewers)

David Sarnoff, ~1930

http://en.wikipedia.org/wiki/Sarnoff%27s_law

Metcalfe’s Law

The value of a (telecom) network is proportional to the square of the number of users of the system (n²)

Robert Metcalfe, 1970

http://en.wikipedia.org/wiki/Metcalfe%27s_law

Reed’s Law

The utility of large networks, particularly social networks, can scale exponentially with the size of the network.

David Reed, 1999

http://en.wikipedia.org/wiki/Reed%27s_law

http://www.reed.com/dpr/

My Law

The value of a network is proportional to its complexity

Flow

Flow is the mental state of operation in which the person is fully immersed in what he or she is by a feeling of energized focus, full involvement, and success in the process of the activity.

The Edge