Complexity and Freedom

Slide 1: Complexity and Freedom Lessons from nature about human networks and life on the edge

Slide 2: 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

Slide 3: • Equilibrium • Complexity • Chaos

Slide 4: Nature is not in equilibrium It self-organizes towards criticality

Slide 5: Sand piles How do avalanches work?

Slide 6: 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)

Slide 7: Self-organized criticality Natural Phenomena Human Activities • Avalanches • Population distribution • Earthquakes • Traffic patterns • Coastlines • Income distribution • Rivers • Market prices • Extinctions • Sociology • Evolution • Music popularity • Weather patterns • Social networks • Cosmology • Website links and traffic • Neurobiology • Language

Slide 9: 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

Slide 12: Zipf’s Law

Slide 14: 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.

Slide 15: Social Networks

Slide 16: 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

Slide 17: 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

Slide 18: 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/f0) and red noise (1/f2), more commonly known as Brownian noise). • http://en.wikipedia.org/wiki/1/f_noise

Slide 19: 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

Slide 20: 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.

Slide 21: 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

Slide 22: 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

Slide 23: 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

Slide 24: Forest fire • http://en.wikipedia.org/wiki/Forest-fire_models

Slide 25: Model of evolution • http://en.wikipedia.org/wiki/Bak-Sneppen_model • http://cmol.nbi.dk/models/bs/bs.html

Slide 26: Dynamic Efficiency « The critical state is the most efficient state that can actually be reached dynamically. » - Per Bak

Slide 27: 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

Slide 28: 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.

Slide 29: You send an e-mail… Equilibrium Complexity Chaos Something Something Nothing much potentially random happens useful could happens happen

Slide 30: What does that have to do with freedom?

Slide 31: 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)

Slide 32: 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.

Slide 33: 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

Slide 34: Freedom?

Slide 39: Are your toys wound up?

Slide 40: 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

Slide 41: Sarnoff’s Law

Slide 42: 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

Slide 43: 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/

Slide 44: My Law The value of a network is proportional to its complexity

Slide 45: 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.

Slide 46: The Edge • Freedom is on the edge - the edge between equilibrium and chaos • The edge is potentially dangerous, but it is stable, although constantly evolving

Slide 47: Freedom • Not all freedom is worth having • The freedom you want is where you have the most options, and you get the most bang for your buck • The usefulness of freedom depends on the complexity of the system around you

Slide 49: Flemming Funch • Toulouse, France • Blog: http://ming.tv • Mail: ffunch@cr8.com • Facebook: http://www.facebook.com/profile.php?id=511572735 • Skype, Twitter, Jaiku: ffunch

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