Usually, the founding-father status for Chaos and Complexity theory is given to Edward Lorenz in the 1960’s. He was a weatherman interested in long-term forecasting using mathematical models. He found that a small error in the input to his computer (0.506 instead of 0.506127) led to extremely divergent patterns of weather.
Fig.1: How the two weather patterns diverged.
From nearly the same starting point, the computer generated patterns of weather grew further and further apart, until all similarity disappeared.
Image 1: A sunny Day
Image 2: A stormy day
This phenomenon is known in Chaos theory as ‘sensitive dependence on initial conditions’, otherwise popularised as “The Butterfly Effect”. This characteristic of chaotic systems means that weather, and other naturally occurring systems are difficult to predict with any degree of accuracy far into the future.
Butterfly Effect:
The statistics that we use in psychology, (even the sophisticated ones), are associated with linear dynamics. We are used to ‘cause-and-effect’ relationships that can be calculated to give a predictable result. These linear systems work within clear definable limits; examine the assumptions for using parametric statistical tests for instance, or the idea of isolating all influences on the dependent variable apart from the one being manipulated by the experimenter. In this world of linear dynamics, the orderly and methodical are the norm; ‘things add-up’ to give predictable outcomes. It’s a world of clockwork; discover how the bits work and we can predict the time (as told by the clock!); generalising this research paradigm, we can discover how other ‘bits’ work and go on to discover the rules for the weather and even people. This will allow us to predict weather and people behaviour and thus ultimately control both.
(Un) fortunately, linear systems exist mainly in theory. Outside of the laboratory and mechanistic theorising, living beings and natural eco-systems are non-linear. A non-linear system cannot be described with traditional equations. The relationship between inputs and outputs in such systems is non-linear e.g.
Fig.2 Mathematical examples of linear and non-linear systems
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In a nonlinear system the outcome cannot be quantified simply with additive equations. And, as can be seen above, the output is not proportional to the input (as with linear systems), a small change in input can produce an enormous change in the output. Although the non-linear system’s future behaviour is fully determined by the initial conditions (i.e. there are no random variables involved), they remain unpredictable, and represent deterministic chaos.
Also in linear systems change is relatively easy to predict. Based on previous experience e.g. 3 -> 6, we can predict 8 -> 16 and 28 -> 56 and so on. In non-linear systems change is not so predictable. It is discontinuous with ‘crises or ‘tipping’ points. Change happens with sudden unpredictable jumps and whole systems can transform themselves qualitatively e.g. the phase change states of water, ice->water->steam. At the boundaries of each change, transition across the boundary results in a dramatic reorganization (of molecules).
Fig. 3 Example of a logistic plot of population growth
Image. 3: Bifurcation in nature
Animal or vegetable?
This concept of chaos is extremely difficult for researchers who want to change one variable at a time and explore simple linear and causative relationships using traditional parametric measurements. Outside the laboratory, real life is both elaborate and seemingly erratic; relationships are unpredictable and capricious; twisted causal paths are interrupted and variables continuously affect each other in a network of rebounding feedback loops. And yet there are discernable patterns in this chaos e.g. traffic flow, weather changes, cardiac arrhythmias, crowd behaviour.
Another example of a chaotic system is Lorenz’s waterwheel:
Fig. 4: Design your own waterwheel
Chaotic Waterwheel:
Double Pendulum:
http://www.youtube.com/watch?v=8VmTiyTut6A&feature=related
If the behaviour of the waterwheel is plotted in time and space (phase space)[1], it turns out that the system isn’t that chaotic at all, and we get a recognisable pattern emerging. Admittedly, the pattern is not predictable with linear statistical models. The patterns of behaviour that can be plotted by observing chaotic systems are known collectively as strange attractors. is a stable, non-periodic state or behaviour exhibited by some dynamic systems, especially turbulent ones, that can be represented as a non-repeating pattern in the system’s phase space.
[1] Such dynamical systems can be represented as a fixed rule (equation) that describes the behaviour of a point in terms of time dependence in geometrical space.
Chaos in a traffic jam:
[1] Such dynamical systems can be represented as a fixed rule (equation) that describes the behaviour of a point in terms of time dependence in geometrical space.
Another very important area of chaos theory is the study of mathematical functions known as fractals. Fractal functions behave like logistic equations in chaotic systems, a small change in the starting value can change the outcome in dramatic ways. Fractals are figures or surfaces that are generated by successive subdivisions of a simpler polygon or polyhedron, according to some iterative process.
Scale:
Snowflake Fractal (Koch-curve-fractal)):
Fractals in nature:
The Golden Ratio 1:1.618:
Frost Fractal:
Fractal Tree:
Fractal Brain?
Chaos in the Human Brain?
Scale:
Hopefully, the above has given you some insights into the understanding of Chaos Theory. Formally, Chaos theory is the study of relative simple systems and how they can give rise to complex and unpredictable behaviour.
Complexity is a sub-section of Chaos theory. Complexity theory has its focus on systems that contain many elements, and how multiple interactions between these elements can lead to well-organized and predictable behaviour.
Complexity
In a sense the complexity of a system depends on the perceptions of the person observing the system and trying to understand it. Limits of complexity are measured using a term borrowed from cognitive psychology, namely the Hrair limit[1]. The Hrair limit (in the context of cognitive ergonomics) is the maximum number of subroutines that should be called up from the main program. It is a number between 5 and 9. The limit is proposed not because exceeding it will confuse the computer, but it will overload the cognitive capacity of the operator.
Complex adaptive system denotes systems that have some or all of the following attributes:
- The number of elements in the system and the number of relations between the elements is non-trivial (non-linear) – however, there is no general rule to separate “trivial” from “non-trivial”;
- The system has memory or includes feedback;
- The system can adapt itself according to its history or feedback;
- The relations between the system and its environment are non-trivial or non-linear;
- The system can be influenced by, or can adapt itself to, its environment;
- The system is highly sensitive to initial conditions.
Spontaneous Order
Emergent processes or behaviours can be seen in many places e.g. traffic patterns, nature and human organisations. Wherever there is a multitude of individuals interacting with one another, there often comes a moment when disorder gives way
[1] Yourdan, E. (1979). Modern Structured Analysis. Prentice Hall.
to order and something new emerges: a pattern, a decision, a structure, or a change in direction.
‘Swarming’ is a well-known behaviour in many animal species from marching locusts to schooling fish to flocking birds. Emergent structures are a common strategy found in many animal groups: colonies of ants, mounds built by termites, swarms of bees, shoals/schools of fish, flocks of birds, and herds/packs of mammals.
Emergence:
Groups of human beings, left free to each regulate themselves, tend to produce spontaneous order, rather than the meaningless chaos often feared.
A classic traffic roundabout is a good example, with cars moving in and out with such effective organization that some modern cities have begun replacing traffic lights at problem intersections with roundabouts.
Broken Lights:
Emergence
The notion of ‘emergence’ is encountered in systems that have qualities not directly traceable to the system’s individual components. Emergent properties come into being from the interaction of the system’s components.
These new qualities are irreducible to the system’s constituent parts.
The whole is greater than the sum of its parts.
“Although ‘strong’ emergence is logically possible, it is uncomfortably like magic. How does an irreducible but contingent downward causal power arise, since by definition it cannot be due to the aggregation of the micro-level potentialities? Such causal powers would be quite unlike anything within our scientific ken. This not only indicates how they will discomfort reasonable forms of materialism. Their mysteriousness will only heighten the traditional worry that emergence entails illegitimately getting something from nothing.”(Bedau 1997)[1]
“The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe. The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity. At each level of complexity entirely new properties appear. Psychology is not applied biology, nor is biology applied chemistry. We can now see that the whole becomes not merely more, but very different from the sum of its parts.”(Anderson 1972)[2]
“…..the debate about whether or not the whole can be predicted from the properties of the parts misses the point. Wholes produce unique combined effects, but many of these effects may be co-determined by the context and the interactions between the whole and its environment(s).” (Corning 2002)[3]
[1] Bedau, M. A. (1997).Weak Emergence. http://academic.reed.edu/philosophy/faculty/bedau/pdf/emergence.pdf
[2] Anderson, P.W. (1972), “More is Different: Broken Symmetry and the Nature of the Hierarchical Structure of Science”, Science 177 (4047): 393–396.
[3] Corning, Peter A. (2002), “The Re-Emergence of “Emergence”: A Venerable Concept in Search of a Theory”, Complexity 7 (6): 18–30.
Emergence in our World
Emergent change processes have latterly been used within Business Psychology in the field of group facilitation and organization development.
These are designed to maximize emergence and self-organization, by offering a minimal set of effective initial conditions e.g.
Leaderless Organisation:
Other examples include Appreciative Inquiry, Future Search, the World Cafe or Knowledge Cafe, and Open Space Technology.
Emergence on the WEB
The Internet offers many examples of decentralized systems exhibiting emergent properties.
For example, there is no central organization rationing the number of links, yet the number of links pointing to each page follows a power law in which a few pages are linked-to many times and most pages are seldom linked to, (hence SEO).
A related property of the network of links in the World Wide Web is that almost any pair of pages can be connected to each other through a relatively short chain of links. Although relatively well known now, this property was initially unexpected in an unregulated network. It is shared with many other types of networks called small-world networks. (Shared vocabularies)
Self-organization
Self-organisation is the process where a structure or pattern appears in a system without a central authority or an external element imposing it through planning. This globally coherent pattern appears from the local interaction of the elements that make up the system, thus the organization is achieved in a way that is parallel (the entire elements act at the same time) and distributed (no element is a central coordinator). Such systems have the following qualities:
- Strong dynamical non-linearity, often though not necessarily involving Positive feedback and Negative feedback
- Balance of exploitation and exploration
- Multiple interactions
Sometimes the notion of self-organization is conflated with that of the related concept of emergence. Properly defined, however, there may be instances of self-organization without emergence and emergence without self-organization.
Self-organization in human societies:
Tell-tale signs of self-organization are usually statistical properties shared with self-organizing physical systems (see Zipf’s law, power law, Pareto principle).
Examples such as critical mass, herd behaviour, groupthink and others, abound in sociology, economics, behavioural finance and anthropology.
Zipf’s law states that given some corpus of natural language utterances, the frequency of any word is inversely proportional to its rank in the frequency table. Thus the most frequent word will occur approximately twice as often as the second most frequent word, three times as often as the third most frequent word, etc.
The Pareto principle (also known as the 80–20 rule), states that, for many events, roughly 80% of the effects comes from 20% of the causes e.g.
In business:
- 80% of your profits come from 20% of your customers
- 80% of your complaints come from 20% of your customers
- 80% of your profits come from 20% of the time you spend
- 80% of your sales come from 20% of your products
- 80% of your sales are made by 20% of your sales staff
Therefore, many businesses have an easy access to dramatic improvements in profitability by focusing on the most effective areas and eliminating, ignoring, automating, delegating or re-training the rest, as appropriate.
Power Law: the power law relationship applies to phenomena such as income distributions. The richest 20% of the world’s population control 82.7% of the world’s income. Further, if we take the ten wealthiest individuals in the world, we see that the top three (Warren Buffett, Carlos Slim Helú, and Bill Gates) own as much as the next seven put together. Such inequality can be illustrated by the so-called ‘champagne glass’ effect.
Critical mass (sociodynamics)From Wikipedia, the free encyclopediaJump to: navigation, search
Critical mass is a sociodynamic term to describe the existence of sufficient momentum in a social system such that the momentum becomes self-sustaining and creates further growth.
Social factors influencing critical mass may involve the size, interrelatedness and level of communication in a society or one of its subcultures. Another is social stigma, or the possibility of public advocacy due to such a factor. Critical mass may be closer to majority consensus in political circles, where the most effective position is more often that held by the majority of people in society. In this sense, small changes in public consensus can bring about swift changes in political consensus, due to the majority-dependent effectiveness of certain ideas as tools of political debate.
Critical mass is a concept used in a variety of contexts, including physics, group dynamics, politics, public opinion, and technology.
See also:
- Bandwagon effect
- Network effect
- One-third hypothesis
- Positive feedback
- Tipping point (sociology)
- Viral phenomenon
Viral phenomenonFrom Wikipedia, the free encyclopediaJump to: navigation, search
Viral phenomena are objects or patterns able to replicate themselves or convert other objects into copies of themselves when these objects are exposed to them.
The concept of something, other than a biological virus, being viral came into vogue just after the Internet became widely popular in the mid-to-late 1990s. An object, even a immaterial object, is considered to be viral when it has the ability to spread copies of itself or change other similar objects to become more like itself when those objects are simply exposed to the viral object. This has become a common way to describe how thoughts, information and trends move into and through a human population. Memes are possibly the best example of viral patterns. The 1992 novel Snow Crash explores the implications of an ancient memetic meta-virus and its modern day computer virus equivalent:
“ We are all susceptible to the pull of viral ideas. Like mass hysteria. Or a tune that gets into your head that you keep on humming all day until you spread it to someone else. Jokes. Urban legends. Crackpot religions. No matter how smart we get, there is always this deep irrational part that makes us potential hosts for self-replicating information. (see wikiquote) ”
Research on viral marketing techniques has begun to reveal some of the specific dynamics of the viral phenomenon. The viral spread of an Internet message involves a convergence of modalities, including blogs, social networking sites, and mass media coverage. It is common for the message to spread and obtain notoriety via Internet modalities some amount of time before such notoriety is reported by mass media sources.[1]
Examples of viral phenomena in addition to memes are:
- Viral marketing
- Viral Change (creating behavioural change in business through social networks)
- Viral video
- Chain letters
- Viral email
- Viral licenses (such as the GNU General Public License)
- Clothing fashion trends
Finally, psychology could at least theoretically be understood as an emergent property of neurobiological laws.
Hierarchy v. Network
Science and psychology of chaos
Attractor
Self organisation people
