Emergence: A Wikipedia Production

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Contents

1 Emergence 11.1 In philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.2 Strong and weak emergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.3 Objective or subjective quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 In religion, art and humanities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Emergent properties and processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Emergent structures in nature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4.1 Non-living, physical systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.4.2 Living, biological systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.5 In humanity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.5.1 Spontaneous order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.5.2 Computer AI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.5.3 Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.5.4 Emergent change processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.6 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.8 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.9 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.10 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2 Complexity 142.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2 Disorganized complexity vs. organized complexity . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3 Sources and factors of complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4 Varied meanings of complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.5 Study of complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.6 Complexity topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.6.1 Complex behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.6.2 Complex mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.6.3 Complex simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.6.4 Complex systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.6.5 Complexity in data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

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2.6.6 Complexity in molecular recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.7 Applications of complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.8 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.10 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.11 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3 Self-organization 203.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.1.1 Principles of self-organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.2 History of the idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2.1 Developing views . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.3.1 Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.3.2 Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.3.3 Biology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.3.4 Computer Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3.5 Cybernetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3.6 Human society . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.3.7 Psychology and education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.3.8 Traffic flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3.9 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.4 Criticism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.5 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.6 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.7 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.8 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.8.1 Dissertations and theses on self-organization . . . . . . . . . . . . . . . . . . . . . . . . . 33

4 Spontaneous order 344.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2.1 Markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.2.2 Game studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.2.3 Anarchism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.2.4 Sobornost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.2.5 Recent developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.3 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.5 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5 Complex system 37

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5.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.2 Types of complex systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.2.1 Nonlinear systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.2.2 Complex adaptive systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.3 Topics on complex systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.3.1 Features of complex systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.5 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395.6 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395.7 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

6 Integrative level 406.1 Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406.2 Philosophies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406.3 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

7 Chaos theory 427.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427.2 Chaotic dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

7.2.1 Sensitivity to initial conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437.2.2 Topological mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447.2.3 Density of periodic orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447.2.4 Strange attractors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447.2.5 Minimum complexity of a chaotic system . . . . . . . . . . . . . . . . . . . . . . . . . . 457.2.6 Jerk systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

7.3 Spontaneous order . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467.4 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467.5 Distinguishing random from chaotic data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487.6 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

7.6.1 Computer science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497.6.2 Biology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497.6.3 Other areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

7.7 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507.9 Scientific literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

7.9.1 Articles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537.9.2 Textbooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537.9.3 Semitechnical and popular works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

7.10 External links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

8 Emergence (disambiguation) 568.1 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

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8.2 Music . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568.3 Other . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568.4 See also . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

9 Emergence: The Connected Lives of Ants, Brains, Cities, and Software 579.1 Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579.2 Quote . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579.3 Achievements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579.4 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579.5 Text and image sources, contributors, and licenses . . . . . . . . . . . . . . . . . . . . . . . . . . 58

9.5.1 Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589.5.2 Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609.5.3 Content license . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Chapter 1

Emergence

For other uses, see Emergence (disambiguation).See also: Emergent (disambiguation), Spontaneous orderand Self-organizationIn philosophy, systems theory, science, and art, emer-

The formation of complex symmetrical and fractal patterns bySnowflakes is an example of emergence in a physical system.

gence is a process whereby larger entities, patterns, andregularities arise through interactions among smaller orsimpler entities that themselves do not exhibit such prop-erties.Emergence is central in theories of integrative levels andof complex systems. For instance, the phenomenon life asstudied in biology is commonly perceived as an emergentproperty of interacting molecules as studied in chemistry,whose phenomena reflect interactions among elementaryparticles, modeled in particle physics, that at such highermass—via substantial conglomeration—exhibit motionas modeled in gravitational physics. Neurobiological phe-nomena are often presumed to suffice as the underlying

A termite “cathedral” mound produced by a termite colony is aclassic example of emergence in nature.

basis of psychological phenomena, whereby economicphenomena are in turn presumed to principally emerge.In philosophy, emergence typically refers toemergentism. Almost all accounts of emergentisminclude a form of epistemic or ontological irreducibilityto the lower levels.[1]

1.1 In philosophy

Main article: Emergentism

In philosophy, emergence is often understood to be aclaim about the etiology of a system’s properties. Anemergent property of a system, in this context, is one thatis not a property of any component of that system, but

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is still a feature of the system as a whole. Nicolai Hart-mann, one of the first modern philosophers to write onemergence, termed this categorial novum (new category).

1.1.1 Definitions

This idea of emergence has been around since at least thetime of Aristotle.[2] John Stuart Mill[3] and Julian Hux-ley[4] are two of many scientists and philosophers whohave written on the concept.The term “emergent” was coined by philosopher G. H.Lewes, who wrote:

“Every resultant is either a sum or a differ-ence of the co-operant forces; their sum, whentheir directions are the same -- their differ-ence, when their directions are contrary. Fur-ther, every resultant is clearly traceable in itscomponents, because these are homogeneousand commensurable. It is otherwise with emer-gents, when, instead of adding measurable mo-tion to measurable motion, or things of onekind to other individuals of their kind, there isa co-operation of things of unlike kinds. Theemergent is unlike its components insofar asthese are incommensurable, and it cannot bereduced to their sum or their difference.”[5][6]

Economist Jeffrey Goldstein provided a current definitionof emergence in the journal Emergence.[7] Goldstein ini-tially defined emergence as: “the arising of novel and co-herent structures, patterns and properties during the pro-cess of self-organization in complex systems”.Goldstein’s definition can be further elaborated to de-scribe the qualities of this definition in more detail:

“The common characteristics are: (1) radi-cal novelty (features not previously observed insystems); (2) coherence or correlation (mean-ing integrated wholes that maintain themselvesover some period of time); (3) A global ormacro “level” (i.e. there is some property of“wholeness”); (4) it is the product of a dynam-ical process (it evolves); and (5) it is “osten-sive” (it can be perceived).” For good measure,Goldstein throws in supervenience.[8]

Systems scientist Peter Corning also says that living sys-tems cannot be reduced to underlying laws of physics:

Rules, or laws, have no causal efficacy; theydo not in fact “generate” anything. They servemerely to describe regularities and consistentrelationships in nature. These patterns may bevery illuminating and important, but the under-lying causal agencies must be separately speci-fied (though often they are not). But that aside,

the game of chess illustrates ... why any lawsor rules of emergence and evolution are insuffi-cient. Even in a chess game, you cannot use therules to predict “history” — i.e., the course ofany given game. Indeed, you cannot even re-liably predict the next move in a chess game.Why? Because the “system” involves morethan the rules of the game. It also includesthe players and their unfolding, moment-by-moment decisions among a very large numberof available options at each choice point. Thegame of chess is inescapably historical, eventhough it is also constrained and shaped by aset of rules, not to mention the laws of physics.Moreover, and this is a key point, the game ofchess is also shaped by teleonomic, cybernetic,feedback-driven influences. It is not simply aself-ordered process; it involves an organized,“purposeful” activity.[8]

1.1.2 Strong and weak emergence

Usage of the notion “emergence” may generally be sub-divided into two perspectives, that of “weak emergence”and “strong emergence”. In terms of physical systems,weak emergence is a type of emergence in which theemergent property is amenable to computer simulation.This is opposed to the older notion of strong emergence,in which the emergent property cannot be simulated by acomputer.Some common points between the two notions are thatemergence concerns new properties produced as the sys-tem grows, which is to say ones which are not shared withits components or prior states. Also, it is assumed thatthe properties are supervenient rather thanmetaphysicallyprimitive (Bedau 1997).Weak emergence describes new properties arising in sys-tems as a result of the interactions at an elemental level.However, it is stipulated that the properties can be deter-mined by observing or simulating the system, and not byany process of a priori analysis.Bedau notes that weak emergence is not a universal meta-physical solvent, as weak emergence leads to the conclu-sion that matter itself contains elements of awareness to it.However, Bedau concludes that adopting this view wouldprovide a precise notion that emergence is involved inconsciousness, and second, the notion of weak emergenceis metaphysically benign (Bedau 1997).Strong emergence describes the direct causal action ofa high-level system upon its components; qualities pro-duced this way are irreducible to the system’s constituentparts (Laughlin 2005). The whole is other than the sumof its parts. It follows that no simulation of the systemcan exist, for such a simulation would itself constitute areduction of the system to its constituent parts (Bedau1997).

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However, “the debate about whether or not the wholecan be predicted from the properties of the parts missesthe point. Wholes produce unique combined effects,but many of these effects may be co-determined by thecontext and the interactions between the whole and itsenvironment(s)" (Corning 2002). In accordance withhis Synergism Hypothesis (Corning 1983 2005), Corn-ing also stated, “It is the synergistic effects producedby wholes that are the very cause of the evolution ofcomplexity in nature.” Novelist Arthur Koestler used themetaphor of Janus (a symbol of the unity underlyingcomplements like open/shut, peace/war) to illustrate howthe two perspectives (strong vs. weak or holistic vs.reductionistic) should be treated as non-exclusive, andshould work together to address the issues of emergence(Koestler 1969). Further,

The ability to reduce everything to simplefundamental laws does not imply the ability tostart from those laws and reconstruct the uni-verse. The constructionist hypothesis breaksdown when confronted with the twin difficul-ties of scale and complexity. At each levelof complexity entirely new properties appear.Psychology is not applied biology, nor is biol-ogy applied chemistry. We can now see thatthe whole becomes not merely more, but verydifferent from the sum of its parts. (Anderson1972)

The plausibility of strong emergence is questioned bysome as contravening our usual understanding of physics.Mark A. Bedau observes:

Although strong emergence is logicallypossible, it is uncomfortably like magic. Howdoes an irreducible but supervenient downwardcausal power arise, since by definition it cannotbe due to the aggregation of themicro-level po-tentialities? Such causal powers would be quiteunlike anything within our scientific ken. Thisnot only indicates how they will discomfortreasonable forms of materialism. Their mys-teriousness will only heighten the traditionalworry that emergence entails illegitimately get-ting something from nothing.[9]

Meanwhile, others have worked towards developing ana-lytical evidence of strong emergence. In 2009, Gu et al.presented a class of physical systems that exhibits non-computable macroscopic properties.[10][11] More pre-cisely, if one could compute certain macroscopic prop-erties of these systems from the microscopic descriptionof these systems, then one would be able to solve compu-tational problems known to be undecidable in computerscience. They concluded that

Although macroscopic concepts are essen-tial for understanding our world, much of

fundamental physics has been devoted to thesearch for a `theory of everything', a set ofequations that perfectly describe the behaviorof all fundamental particles. The view that thisis the goal of science rests in part on the ratio-nale that such a theory would allow us to de-rive the behavior of all macroscopic concepts,at least in principle. The evidence we have pre-sented suggests that this view may be overlyoptimistic. A `theory of everything' is one ofmany components necessary for complete un-derstanding of the universe, but is not necessar-ily the only one. The development of macro-scopic laws from first principles may involvemore than just systematic logic, and could re-quire conjectures suggested by experiments,simulations or insight.[10]

Emergent structures are patterns that emerge via collec-tive actions of many individual entities. To explain suchpatterns, one might conclude, per Aristotle,[2] that emer-gent structures are other than the sum of their parts onthe assumption that the emergent order will not arise ifthe various parts simply interact independently of oneanother. However, there are those who disagree.[12] Ac-cording to this argument, the interaction of each part withits immediate surroundings causes a complex chain ofprocesses that can lead to order in some form. In fact,some systems in nature are observed to exhibit emer-gence based upon the interactions of autonomous parts,and some others exhibit emergence that at least at presentcannot be reduced in this way.

1.1.3 Objective or subjective quality

The properties of complexity and organization of anysystem are considered by Crutchfield to be subjectivequalities determined by the observer.

“Defining structure and detecting the emer-gence of complexity in nature are inherentlysubjective, though essential, scientific activ-ities. Despite the difficulties, these prob-lems can be analysed in terms of how model-building observers infer from measurementsthe computational capabilities embedded innon-linear processes. An observer’s notion ofwhat is ordered, what is random, and what iscomplex in its environment depends directly onits computational resources: the amount of rawmeasurement data, of memory, and of timeavailable for estimation and inference. Thediscovery of structure in an environment de-pends more critically and subtly, though, onhow those resources are organized. The de-scriptive power of the observer’s chosen (or im-plicit) computational model class, for example,

4 CHAPTER 1. EMERGENCE

can be an overwhelming determinant in findingregularity in data."(Crutchfield 1994)

On the other hand, Peter Corning argues “Must the syn-ergies be perceived/observed in order to qualify as emer-gent effects, as some theorists claim? Most emphaticallynot. The synergies associated with emergence are realandmeasurable, even if nobody is there to observe them.”(Corning 2002)

1.2 In religion, art and humanities

In religion, emergence grounds expressions of religiousnaturalism in which a sense of the sacred is perceived inthe workings of entirely naturalistic processes by whichmore complex forms arise or evolve from simpler forms.Examples are detailed in a 2006 essay titled 'The Sa-cred Emergence of Nature' by Ursula Goodenough andTerrence Deacon and a 2006 essay titled 'Beyond Reduc-tionism: Reinventing the Sacred' by Stuart Kauffman.An early argument (1904-5) for the emergence of socialformations, in part stemming from religion, can be foundin Max Weber's most famous work, The Protestant Ethicand the Spirit of Capitalism [13]

In art, emergence is used to explore the origins ofnovelty, creativity, and authorship. Some art/literarytheorists (Wheeler, 2006;[14] Alexander, 2011[15] haveproposed alternatives to postmodern understandings of“authorship” using the complexity sciences and emer-gence theory. They contend that artistic selfhood andmeaning are emergent, relatively objective phenomena.Michael J. Pearce has used emergence to describe theexperience of works of art in relation to contemporaryneuroscience.[16]) The concept of emergence has alsobeen applied to the theory of literature and art, his-tory, linguistics, cognitive sciences, etc. by the teach-ings of Jean-Marie Grassin at the University of Limoges(v. esp.: J. Fontanille, B. Westphal, J. Vion-Dury, éds.L'Émergence—Poétique de l'Émergence, en réponse auxtravaux de Jean-Marie Grassin, Bern, Berlin, etc., 2011;and: the article "Emergence" in the International Dictio-nary of Literary Terms (DITL).In international development, concepts of emergencehave been used within a theory of social change termedSEED-SCALE to show how standard principles inter-act to bring forward socio-economic development fittedto cultural values, community economics, and naturalenvironment (local solutions emerging from the largersocio-econo-biosphere). These principles can be imple-mented utilizing a sequence of standardized tasks thatself-assemble in individually specific ways utilizing recur-sive evaluative criteria.[17]

In postcolonial studies, the term “Emerging Literature”refers to a contemporary body of texts that is gaining mo-mentum in the global literary landscape (v. esp.: J.M.

Grassin, ed. Emerging Literatures, Bern, Berlin, etc. :Peter Lang, 1996). By opposition, “emergent literature”is rather a concept used in the theory of literature.

1.3 Emergent properties and pro-cesses

An emergent behavior or emergent property can appearwhen a number of simple entities (agents) operate in anenvironment, forming more complex behaviors as a col-lective. If emergence happens over disparate size scales,then the reason is usually a causal relation across differ-ent scales. In other words there is often a form of top-down feedback in systems with emergent properties.[18]The processes fromwhich emergent properties result mayoccur in either the observed or observing system, andcan commonly be identified by their patterns of accu-mulating change, most generally called 'growth'. Emer-gent behaviours can occur because of intricate causal re-lations across different scales and feedback, known asinterconnectivity. The emergent property itself may beeither very predictable or unpredictable and unprece-dented, and represent a new level of the system’s evo-lution. The complex behaviour or properties are not aproperty of any single such entity, nor can they easily bepredicted or deduced from behaviour in the lower-levelentities, and might in fact be irreducible to such behav-ior. The shape and behaviour of a flock of birds or schoolof fish are good examples of emergent properties.One reason why emergent behaviour is hard to predictis that the number of interactions between componentsof a system increases exponentially with the numberof components, thus potentially allowing for many newand subtle types of behaviour to emerge. Emergenceis often a product of particular patterns of interaction.Negative feedback introduces constraints that serve to fixstructures or behaviours. In contrast, positive feedbackpromotes change, allowing local variations to grow intoglobal patterns. Another way in which interactions leadsto emergent properties is dual-phase evolution. This oc-curs where interactions are applied intermittently, lead-ing to two phases: one in which patterns form or grow,the other in which they are refined or removed.On the other hand, merely having a large number of in-teractions is not enough by itself to guarantee emergentbehaviour; many of the interactions may be negligible orirrelevant, or may cancel each other out. In some cases,a large number of interactions can in fact work againstthe emergence of interesting behaviour, by creating a lotof “noise” to drown out any emerging “signal"; the emer-gent behaviour may need to be temporarily isolated fromother interactions before it reaches enough critical massto be self-supporting. Thus it is not just the sheer num-ber of connections between components which encour-ages emergence; it is also how these connections are or-

1.4. EMERGENT STRUCTURES IN NATURE 5

ganised. A hierarchical organisation is one example thatcan generate emergent behaviour (a bureaucracy may be-have in a way quite different from that of the individualhumans in that bureaucracy); but perhaps more interest-ingly, emergent behaviour can also arise from more de-centralized organisational structures, such as a market-place. In some cases, the system has to reach a combinedthreshold of diversity, organisation, and connectivity be-fore emergent behaviour appears.Unintended consequences and side effects are closely re-lated to emergent properties. Luc Steels writes: “A com-ponent has a particular functionality but this is not recog-nizable as a subfunction of the global functionality. In-stead a component implements a behaviour whose side ef-fect contributes to the global functionality [...] Each be-haviour has a side effect and the sum of the side effectsgives the desired functionality” (Steels 1990). In otherwords, the global or macroscopic functionality of a sys-tem with “emergent functionality” is the sum of all “sideeffects”, of all emergent properties and functionalities.Systems with emergent properties or emergent structuresmay appear to defy entropic principles and the second lawof thermodynamics, because they form and increase or-der despite the lack of command and central control. Thisis possible because open systems can extract informationand order out of the environment.Emergence helps to explain why the fallacy of division isa fallacy.

1.4 Emergent structures in nature

Main article: Patterns in natureEmergent structures can be found in many natural phe-

Ripple patterns in a sand dune created by wind or water is anexample of an emergent structure in nature.

nomena, from the physical to the biological domain.For example, the shape of weather phenomena such ashurricanes are emergent structures. The developmentand growth of complex, orderly crystals, as driven by therandom motion of water molecules within a conducive

Giant’s Causeway in Northern Ireland is an example of a complexemergent structure created by natural processes.

natural environment, is another example of an emergentprocess, where randomness can give rise to complex anddeeply attractive, orderly structures.

Water crystals forming on glass demonstrate an emergent, fractalnatural process occurring under appropriate conditions of tem-perature and humidity.

However, crystalline structure and hurricanes are said tohave a self-organizing phase.

Symphony of the Stones carved by the Goght River at Garni Gorgein Armenia is an example of an emergent natural structure.

It is useful to distinguish three forms of emergent struc-tures. A first-order emergent structure occurs as a resultof shape interactions (for example, hydrogen bonds in wa-ter molecules lead to surface tension). A second-order

6 CHAPTER 1. EMERGENCE

emergent structure involves shape interactions playedout sequentially over time (for example, changing atmo-spheric conditions as a snowflake falls to the ground buildupon and alter its form). Finally, a third-order emergentstructure is a consequence of shape, time, and heritableinstructions. For example, an organism’s genetic codesets boundary conditions on the interaction of biologicalsystems in space and time.

1.4.1 Non-living, physical systems

In physics, emergence is used to describe a property, law,or phenomenon which occurs at macroscopic scales (inspace or time) but not at microscopic scales, despite thefact that a macroscopic system can be viewed as a verylarge ensemble of microscopic systems.An emergent property need not bemore complicated thanthe underlying non-emergent properties which generateit. For instance, the laws of thermodynamics are remark-ably simple, even if the laws which govern the interac-tions between component particles are complex. Theterm emergence in physics is thus used not to signify com-plexity, but rather to distinguish which laws and conceptsapply to macroscopic scales, and which ones apply to mi-croscopic scales.Some examples include:

• Classical mechanics: The laws of classical mechan-ics can be said to emerge as a limiting case from therules of quantum mechanics applied to large enoughmasses. This is particularly strange since quantummechanics is generally thought of as more compli-cated than classical mechanics.

• Friction: Forces between elementary particles areconservative. However, friction emerges when con-sidering more complex structures of matter, whosesurfaces can convert mechanical energy into heatenergy when rubbed against each other. Similarconsiderations apply to other emergent concepts incontinuum mechanics such as viscosity, elasticity,tensile strength, etc.

• Patterned ground: the distinct, and often symmetri-cal geometric shapes formed by ground material inperiglacial regions.

• Statistical mechanics was initially derived using theconcept of a large enough ensemble that fluctuationsabout the most likely distribution can be all but ig-nored. However, small clusters do not exhibit sharpfirst order phase transitions such as melting, and atthe boundary it is not possible to completely catego-rize the cluster as a liquid or solid, since these con-cepts are (without extra definitions) only applicableto macroscopic systems. Describing a system usingstatistical mechanics methods is much simpler thanusing a low-level atomistic approach.

• Electrical networks: The bulk conductive responseof binary (RC) electrical networks with randomarrangements can be seen as emergent propertiesof such physical systems. Such arrangements canbe used as simple physical prototypes for derivingmathematical formulae for the emergent responsesof complex systems.[19]

• Weather.

Temperature is sometimes used as an example of anemergent macroscopic behaviour. In classical dynam-ics, a snapshot of the instantaneous momenta of a largenumber of particles at equilibrium is sufficient to find theaverage kinetic energy per degree of freedom which isproportional to the temperature. For a small number ofparticles the instantaneous momenta at a given time arenot statistically sufficient to determine the temperatureof the system. However, using the ergodic hypothesis, thetemperature can still be obtained to arbitrary precision byfurther averaging the momenta over a long enough time.Convection in a liquid or gas is another example of emer-gent macroscopic behaviour that makes sense only whenconsidering differentials of temperature. Convectioncells, particularly Bénard cells, are an example of a self-organizing system (more specifically, a dissipative sys-tem) whose structure is determined both by the con-straints of the system and by random perturbations: thepossible realizations of the shape and size of the cells de-pends on the temperature gradient as well as the nature ofthe fluid and shape of the container, but which configura-tions are actually realized is due to random perturbations(thus these systems exhibit a form of symmetry break-ing).In some theories of particle physics, even such basicstructures as mass, space, and time are viewed as emer-gent phenomena, arising from more fundamental con-cepts such as the Higgs boson or strings. In some in-terpretations of quantum mechanics, the perception of adeterministic reality, in which all objects have a definiteposition, momentum, and so forth, is actually an emer-gent phenomenon, with the true state of matter being de-scribed instead by a wavefunction which need not have asingle position or momentum. Most of the laws of physicsthemselves as we experience them today appear to haveemerged during the course of timemaking emergence themost fundamental principle in the universe and raising thequestion of what might be the most fundamental law ofphysics from which all others emerged. Chemistry canin turn be viewed as an emergent property of the lawsof physics. Biology (including biological evolution) canbe viewed as an emergent property of the laws of chem-istry. Similarly, psychology could be understood as anemergent property of neurobiological laws. Finally, free-market theories understand economy as an emergent fea-ture of psychology.According to Laughlin (2005), for many particle systems,

1.4. EMERGENT STRUCTURES IN NATURE 7

nothing can be calculated exactly from the microscopicequations, and macroscopic systems are characterised bybroken symmetry: the symmetry present in the micro-scopic equations is not present in the macroscopic sys-tem, due to phase transitions. As a result, these macro-scopic systems are described in their own terminology,and have properties that do not depend on many micro-scopic details. This does not mean that the microscopicinteractions are irrelevant, but simply that you do not seethem anymore — you only see a renormalized effect ofthem. Laughlin is a pragmatic theoretical physicist: ifyou cannot, possibly ever, calculate the broken symmetrymacroscopic properties from the microscopic equations,then what is the point of talking about reducibility?

1.4.2 Living, biological systems

Emergence and evolution

See also: Abiogenesis

Life is a major source of complexity, and evolution is themajor process behind the varying forms of life. In thisview, evolution is the process describing the growth ofcomplexity in the natural world and in speaking of theemergence of complex living beings and life-forms, thisview refers therefore to processes of sudden changes inevolution.Life is thought to have emerged in the early RNA worldwhen RNA chains began to express the basic conditionsnecessary for natural selection to operate as conceived byDarwin: heritability, variation of type, and competitionfor limited resources. Fitness of an RNA replicator (itsper capita rate of increase) would likely be a function ofadaptive capacities that were intrinsic (in the sense thatthey were determined by the nucleotide sequence) and theavailability of resources.[20][21] The three primary adap-tive capacities may have been (1) the capacity to replicatewith moderate fidelity (giving rise to both heritability andvariation of type); (2) the capacity to avoid decay; and(3) the capacity to acquire and process resources.[20][21]These capacities would have been determined initiallyby the folded configurations of the RNA replicators (see“Ribozyme”) that, in turn, would be encoded in their indi-vidual nucleotide sequences. Competitive success amongdifferent replicators would have depended on the relativevalues of these adaptive capacities.Regarding causality in evolution Peter Corning observes:

“Synergistic effects of various kinds haveplayed a major causal role in the evolutionaryprocess generally and in the evolution of coop-eration and complexity in particular... Naturalselection is often portrayed as a “mechanism”,or is personified as a causal agency... In real-ity, the differential “selection” of a trait, or an

adaptation, is a consequence of the functionaleffects it produces in relation to the survivaland reproductive success of a given organismin a given environment. It is these functionaleffects that are ultimately responsible for thetrans-generational continuities and changes innature.” (Corning 2002)

Per his definition of emergence, Corning also addressesemergence and evolution:

"[In] evolutionary processes, causation isiterative; effects are also causes. And this isequally true of the synergistic effects producedby emergent systems. In other words, emer-gence itself... has been the underlying causeof the evolution of emergent phenomena inbiological evolution; it is the synergies pro-duced by organized systems that are the key.”(Corning 2002)

Swarming is a well-known behaviour in many ani-mal species from marching locusts to schooling fish toflocking birds. Emergent structures are a common strat-egy found in many animal groups: colonies of ants,mounds built by termites, swarms of bees, shoals/schoolsof fish, flocks of birds, and herds/packs of mammals.An example to consider in detail is an ant colony. Thequeen does not give direct orders and does not tell theants what to do. Instead, each ant reacts to stimuli in theform of chemical scent from larvae, other ants, intruders,food and buildup of waste, and leaves behind a chemi-cal trail, which, in turn, provides a stimulus to other ants.Here each ant is an autonomous unit that reacts dependingonly on its local environment and the genetically encodedrules for its variety of ant. Despite the lack of centralizeddecision making, ant colonies exhibit complex behaviorand have even been able to demonstrate the ability to solvegeometric problems. For example, colonies routinely findthe maximum distance from all colony entrances to dis-pose of dead bodies.[22]

Organization of life

A broader example of emergent properties in biology isviewed in the biological organisation of life, ranging fromthe subatomic level to the entire biosphere. For exam-ple, individual atoms can be combined to form moleculessuch as polypeptide chains, which in turn fold and re-fold to form proteins, which in turn create even morecomplex structures. These proteins, assuming their func-tional status from their spatial conformation, interact to-gether and with other molecules to achieve higher bio-logical functions and eventually create an organism. An-other example is how cascade phenotype reactions, as de-tailed in chaos theory, arise from individual genes mutat-ing respective positioning.[23] At the highest level, all the

8 CHAPTER 1. EMERGENCE

biological communities in the world form the biosphere,where its human participants form societies, and the com-plex interactions of meta-social systems such as the stockmarket.

1.5 In humanity

1.5.1 Spontaneous order

See also: Spontaneous order and Self-organization

Groups of human beings, left free to each regulate them-selves, tend to produce spontaneous order, rather than themeaningless chaos often feared. This has been observedin society at least since Chuang Tzu in ancient China. Aclassic traffic roundabout is a good example, with carsmoving in and out with such effective organization thatsome modern cities have begun replacing stoplights atproblem intersections with traffic circles , and getting bet-ter results. Open-source software andWiki projects forman even more compelling illustration.Emergent processes or behaviours can be seen in manyother places, such as cities, cabal and market-dominantminority phenomena in economics, organizational phe-nomena in computer simulations and cellular automata.Whenever you have a multitude of individuals interact-ing with one another, there often comes a moment whendisorder gives way to order and something new emerges:a pattern, a decision, a structure, or a change in direction(Miller 2010, 29).[24]

Economics

The stock market (or any market for that matter) is anexample of emergence on a grand scale. As a whole itprecisely regulates the relative security prices of com-panies across the world, yet it has no leader; when nocentral planning is in place, there is no one entity whichcontrols the workings of the entire market. Agents, orinvestors, have knowledge of only a limited number ofcompanies within their portfolio, andmust follow the reg-ulatory rules of the market and analyse the transactionsindividually or in large groupings. Trends and patternsemerge which are studied intensively by technical ana-lysts.

World Wide Web and the Internet

The World Wide Web is a popular example of a decen-tralized system exhibiting emergent properties. There isno central organization rationing the number of links, yetthe number of links pointing to each page follows a powerlaw in which a few pages are linked to many times andmost pages are seldom linked to. A related property of

the network of links in the World Wide Web is that al-most any pair of pages can be connected to each otherthrough a relatively short chain of links. Although rel-atively well known now, this property was initially un-expected in an unregulated network. It is shared withmany other types of networks called small-world net-works (Barabasi, Jeong, & Albert 1999, pp. 130–131).Internet traffic can also exhibit some seemingly emergentproperties. In the congestion control mechanism, TCPflows can become globally synchronized at bottlenecks,simultaneously increasing and then decreasing through-put in coordination. Congestion, widely regarded as anuisance, is possibly an emergent property of the spread-ing of bottlenecks across a network in high traffic flowswhich can be considered as a phase transition [see reviewof related research in (Smith 2008, pp. 1–31)].Another important example of emergence in web-basedsystems is social bookmarking (also called collabora-tive tagging). In social bookmarking systems, users as-sign tags to resources shared with other users, whichgives rise to a type of information organisation thatemerges from this crowdsourcing process. Recent re-search which analyzes empirically the complex dynam-ics of such systems[25] has shown that consensus on sta-ble distributions and a simple form of shared vocabular-ies does indeed emerge, even in the absence of a centralcontrolled vocabulary. Some believe that this could bebecause users who contribute tags all use the same lan-guage, and they share similar semantic structures under-lying the choice of words. The convergence in social tagsmay therefore be interpreted as the emergence of struc-tures as people who have similar semantic interpretationcollaboratively index online information, a process calledsemantic imitation.[26] [27]

Open-source software, or Wiki projects such asWikipedia and Wikivoyage are other impressive exam-ples of emergence. The “zeroeth law of Wikipedia”is often cited by its editors to highlight its apparentlysurprising and unpredictable quality: The problem withWikipedia is that it only works in practice. In theory, itcan never work.

Architecture and cities

Emergent structures appear at many different levels oforganization or as spontaneous order. Emergent self-organization appears frequently in cities where no plan-ning or zoning entity predetermines the layout of thecity. (Krugman 1996, pp. 9–29) The interdisciplinarystudy of emergent behaviors is not generally considereda homogeneous field, but divided across its application orproblem domains.Architects and Landscape Architects may not design allthe pathways of a complex of buildings. Instead theymight let usage patterns emerge and then place pavementwhere pathways have become worn in.

1.6. SEE ALSO 9

Traffic patterns in cities can be seen as an example of spontaneousorder

The on-course action and vehicle progression of the 2007Urban Challenge could possibly be regarded as an exam-ple of cybernetic emergence. Patterns of road use, inde-terministic obstacle clearance times, etc. will work to-gether to form a complex emergent pattern that can notbe deterministically planned in advance.The architectural school of Christopher Alexander takesa deeper approach to emergence attempting to rewrite theprocess of urban growth itself in order to affect form,establishing a new methodology of planning and designtied to traditional practices, an Emergent Urbanism. Ur-ban emergence has also been linked to theories of urbancomplexity (Batty 2005) and urban evolution (Marshall2009).Building ecology is a conceptual framework for under-standing architecture and the built environment as theinterface between the dynamically interdependent ele-ments of buildings, their occupants, and the larger envi-ronment. Rather than viewing buildings as inanimate orstatic objects, building ecologist Hal Levin views themas interfaces or intersecting domains of living and non-living systems.[28] The microbial ecology of the indoorenvironment is strongly dependent on the building mate-rials, occupants, contents, environmental context and theindoor and outdoor climate. The strong relationship be-tween atmospheric chemistry and indoor air quality andthe chemical reactions occurring indoors. The chemicalsmay be nutrients, neutral or biocides for the microbial or-ganisms. The microbes produce chemicals that affect thebuilding materials and occupant health and well being.Humans manipulate the ventilation, temperature and hu-midity to achieve comfort with the concomitant effectson the microbes that populate and evolve.[28][29][30]

Eric Bonabeau’s attempt to define emergent phenomenais through traffic: “traffic jams are actually very compli-cated and mysterious. On an individual level, each driveris trying to get somewhere and is following (or breaking)certain rules, some legal (the speed limit) and others so-cietal or personal (slow down to let another driver changeinto your lane). But a traffic jam is a separate and dis-tinct entity that emerges from those individual behaviors.

Gridlock on a highway, for example, can travel backwardfor no apparent reason, even as the cars are moving for-ward.” He has also likened emergent phenomena to theanalysis of market trends and employee behavior.[31]

Computational emergent phenomena have also beenutilized in architectural design processes, for exam-ple for formal explorations and experiments in digitalmateriality.[32]

1.5.2 Computer AI

Some artificially intelligent computer applications utilizeemergent behavior for animation. One example is Boids,which mimics the swarming behavior of birds.

1.5.3 Language

It has been argued that the structure and regularityof language grammar, or at least language change, isan emergent phenomenon (Hopper 1998). While eachspeaker merely tries to reach his or her own communica-tive goals, he or she uses language in a particular way. Ifenough speakers behave in that way, language is changed(Keller 1994). In a wider sense, the norms of a language,i.e. the linguistic conventions of its speech society, canbe seen as a system emerging from long-time participa-tion in communicative problem-solving in various socialcircumstances. (Määttä 2000)

1.5.4 Emergent change processes

Within the field of group facilitation and organization de-velopment, there have been a number of new group pro-cesses that are designed to maximize emergence and self-organization, by offering a minimal set of effective initialconditions. Examples of these processes include SEED-SCALE, Appreciative Inquiry, Future Search, the WorldCafe or Knowledge Cafe, Open Space Technology, andothers. (Holman, 2010)

1.6 See also• Abstraction

• Agent-based model

• Anthropic principle

• Big History

• Connectionism

• Consilience

• Constructal theory

• Dynamical system

10 CHAPTER 1. EMERGENCE

• Deus ex machina

• Dual-phase evolution

• Emergenesis

• Emergent algorithm

• Emergent evolution

• Emergent gameplay

• Emergent organization

• Epiphenomenon

• Externality

• Free will

• Generative sciences

• Innovation butterfly

• Interconnectedness

• Irreducible complexity

• Langton’s ant

• Law of Complexity-Consciousness

• Mass action (sociology)

• Neural networks

• Organic Wholes of G.E. Moore

• Polytely

• Society of Mind theory

• Structuralism

• Swarm intelligence

• System of systems

• Teleology

• Synergetics (Fuller)

• Synergetics (Haken)

1.7 References[1] O'Connor, Timothy and Wong, Hong Yu (February 28,

2012). Edward N. Zalta,, ed. “Emergent Properties”. TheStanford Encyclopedia of Philosophy (Spring 2012 Edi-tion).

[2] Aristotle,Metaphysics, Book Η 1045a 8–10: "... the total-ity is not, as it were, a mere heap, but the whole is some-thing besides the parts ...”, i.e., the whole is other than thesum of the parts.

[3] “The chemical combination of two substances produces,as is well known, a third substance with properties differ-ent from those of either of the two substances separately,or of both of them taken together” (Mill 1843)

[4] Julian Huxley: “now and again there is a sudden rapidpassage to a totally new and more comprehensive type oforder or organization, with quite new emergent proper-ties, and involving quite newmethods of further evolution”(Huxley & Huxley 1947)

[5] (Lewes 1875, p. 412)

[6] (Blitz 1992)

[7] (Goldstein 1999)

[8] Corning, Peter A. (2002), “The Re-Emergence of “Emer-gence": A Venerable Concept in Search of a Theory”(PDF), Complexity 7 (6): 18–30, doi:10.1002/cplx.10043

[9] (Bedau 1997)

[10] Gu, Mile, et al. "More really is different.” Physica D:Nonlinear Phenomena 238.9 (2009): 835-839.

[11] Binder, P-M. “Computation: The edge of reductionism.”Nature 459.7245 (2009): 332-334.

[12] Steven Weinberg. “A Designer Universe?". Retrieved2008-07-14. A version of the original quote from addressat the Conference on Cosmic Design, American Associ-ation for the Advancement of Science, Washington, D.C.in April 1999

[13] McKinnon, AM. (2010). 'Elective affinities of the Protes-tant ethic: Weber and the chemistry of capitalism'. Soci-ological Theory, vol 28, no. 1, pp. 108-126.

[14] Wheeler, Wendy (2006). The Whole Creature: Complex-ity, Biosemiotics and the Evolution of Culture. London:Lawrence & Wishart. p. 192. ISBN 1-905007-30-2.

[15] Alexander, Victoria N. (2011). The Biologist’s Mistress:Rethinking Self-Organization in Art, Literature, and Na-ture. Litchfield Park, AZ: Emergent Publications. ISBN0-9842165-5-3.

[16] Pearce, Michael J. (2015). Art in the Age of Emergence.Manchester, England: Cambridge Scholars Publishing.ISBN 1443870579.

[17] Daniel C. Taylor, Carl E. Taylor, Jesse O. Taylor, ‘’Em-powerment on an Unstable Planet: From Seeds of HumanEnergy to a Scale of Global Change’’ (New York: OxfordUniversity Press, 2012)

[18] See, e.g., Korotayev, A.; Malkov, A.; Khaltourina, D.(2006), Introduction to Social Macrodynamics: Com-pact Macromodels of the World System Growth, Moscow:URSS, ISBN 5-484-00414-4

[19] “The origin of power-law emergent scaling in large binarynetworks” D. P. Almond, C. J. Budd, M. A. Freitag, G.W. Hunt, N. J. McCullen and N. D. Smith. Physica A:Statistical Mechanics and its Applications, Volume 392,Issue 4, 15 February 2013

1.9. FURTHER READING 11

[20] Bernstein H, Byerly HC, Hopf FA, Michod RA, Vemu-lapalli GK. (1983) The Darwinian Dynamic. QuarterlyReview of Biology 58, 185-207. http://www.jstor.org/discover/10.2307/2828805?uid=3739568&uid=2&uid=4&uid=3739256&sid=21102790068637

[21] Michod RE. (2000) Darwinian Dynamics: EvolutionaryTransitions in Fitness and Individuality. Princeton Uni-versity Press, Princeton, New Jersey ISBN 0691050112ISBN 978-0691050119

[22] Steven Johnson. 2001. Emergence: The Connected Livesof Ants, Brains, Cities, and Software

[23] Campbell, Neil A., and Jane B. Reece. Biology. 6th ed.San Francisco: Benjamin Cummings, 2002.

[24] Miller, Peter. 2010. The Smart Swarm: How understand-ing flocks, schools, and colonies can make us better atcommunicating, decisionmaking, and getting things done.New York: Avery.

[25] Valentin Robu, Harry Halpin, Hana Shepherd Emergenceof consensus and shared vocabularies in collaborative tag-ging systems, ACM Transactions on the Web (TWEB),Vol. 3(4), article 14, ACM Press, September 2009.

[26] Fu, Wai-Tat; Kannampallil, Thomas George; Kang,Ruogu (August 2009), “A Semantic Imitation Model ofSocial Tagging”, Proceedings of the IEEE conference onSocial Computing: 66–72, doi:10.1109/CSE.2009.382,ISBN 978-1-4244-5334-4

[27] Fu, Wai-Tat; Kannampallil, Thomas; Kang, Ruogu; He,Jibo (2010), “Semantic Imitation in Social Tagging”,ACMTransactions on Computer-Human Interaction (TOCHI) 17(3): 1, doi:10.1145/1806923.1806926

[28] http://www.microbe.net/fact-sheet-building-ecology/

[29] http://www.microbe.net

[30] http://buildingecology.com

[31] Bonabeau E. Predicting the Unpredictable. Harvard Busi-ness Review [serial online]. March 2002;80(3):109-116.Available from: Business Source Complete, Ipswich, MA.Accessed February 1, 2012.

[32] Roudavski, Stanislav and Gwyllim Jahn (2012). 'Emer-gent Materiality though an Embedded Multi-Agent Sys-tem', in 15th Generative Art Conference, ed. by CelestinoSoddu (Lucca, Italy: Domus Argenia), pp. 348-363

1.8 Bibliography

• Anderson, P.W. (1972), “More is Different:Broken Symmetry and the Nature of the Hi-erarchical Structure of Science”, Science 177(4047): 393–396, Bibcode:1972Sci...177..393A,doi:10.1126/science.177.4047.393, PMID17796623

• Bedau, Mark A. (1997),Weak Emergence (PDF)

• Corning, Peter A. (1983), The Synergism Hypothe-sis: A Theory of Progressive Evolution, New York:McGraw-Hill

• Koestler, Arthur (1969), A. Koestler & J. R.Smythies, ed., Beyond Reductionism: New Perspec-tives in the Life Sciences, London: Hutchinson

• Laughlin, Robert (2005), A Different Universe:Reinventing Physics from the Bottom Down, BasicBooks, ISBN 0-465-03828-X

1.9 Further reading• Alexander, V. N. (2011). The Biologist’s Mistress:

Rethinking Self-Organization in Art, Literature andNature. Litchfield Park AZ: Emergent Publications.

• Anderson, P.W. (1972), “More is Different:Broken Symmetry and the Nature of the Hierar-chical Structure of Science” (PDF), Science 177(4047): 393–396, Bibcode:1972Sci...177..393A,doi:10.1126/science.177.4047.393, PMID17796623

• Barabási, Albert-László; Jeong, Hawoong; Albert,Réka (1999), “The Diameter of the World WideWeb”, Nature 401 (6749): 130–131, arXiv:cond-mat/9907038, Bibcode:1999Natur.401..130A,doi:10.1038/43601

• Bar-Yam, Yaneer (2004), “A MathematicalTheory of Strong Emergence using MultiscaleVariety” (PDF), Complexity 9 (6): 15–24,doi:10.1002/cplx.20029

• Bateson, Gregory (1972), Steps to an Ecology ofMind, Ballantine Books, ISBN 0-226-03905-6

• Batty, Michael (2005), Cities and Complexity, MITPress, ISBN 0-262-52479-1

• Bedau, Mark A. (1997).“Weak Emergence”.

• Blitz, David. (1992). Emergent Evolution: Quali-tative Novelty and the Levels of Reality. Dordrecht:Kluwer Academic.

• Bunge, Mario Augusto (2003), Emergence and Con-vergence: Qualitiative Novelty and the Unity ofKnowledge, Toronto: University of Toronto Press

• Chalmers, David J. (2002). “Strong and WeakEmergence” http://consc.net/papers/emergence.pdf Republished in P. Clayton and P. Davies, eds.(2006) The Re-Emergence of Emergence. Oxford:Oxford University Press.

• Philip Clayton (2005). Mind and Emergence: FromQuantum to Consciousness Oxford: OUP, ISBN978-0-19-927252-5

12 CHAPTER 1. EMERGENCE

• Philip Clayton&Paul Davies (eds.) (2006). The Re-Emergence of Emergence: The Emergentist Hypothe-sis from Science to Religion Oxford: Oxford Univer-sity Press.

• Corning, Peter A. (2005). “Holistic Darwinism:Synergy, Cybernetics and the Bioeconomics of Evo-lution.” Chicago: University of Chicago Press.

• Crutchfield, James P. (1994), “Special issue onthe Proceedings of the Oji International Sem-inar: Complex Systems — from Complex Dy-namics to Artificial Reality" (PDF), Physica D,Bibcode:1994PhyD...75...11C, doi:10.1016/0167-2789(94)90273-9 |contribution= ignored (help)

• Felipe Cucker and Stephen Smale (2007), TheJapanese Journal of Mathematics, The Mathematicsof Emergence

• Delsemme, Armand (1998), Our Cosmic Origins:From the Big Bang to the Emergence of Life and In-telligence, Cambridge University Press

• De Wolf, Tom; Holvoet, Tom (2005), “EmergenceVersus Self-Organisation: Different Concepts butPromising When Combined”, Engineering Self Or-ganising Systems: Methodologies and Applications,Lecture Notes in Computer Science: 3464, pp. 1–15

• Fromm, Jochen (2004), The Emergence of Complex-ity, Kassel University Press, ISBN 3-89958-069-9*Fromm, Jochen (2005a), Types and Forms of Emer-gence, arXiv, arXiv:nlin.AO/0506028

• Fromm, Jochen (2005b), Ten Questions about Emer-gence, arXiv, arXiv:nlin.AO/0509049

• Goodwin, Brian (2001), How the Leopard ChangedIts Spots: The Evolution of Complexity, PrincetonUniversity Press

• Goldstein, Jeffrey (1999), “Emergence as aConstruct: History and Issues” (PDF), Emer-gence: Complexity and Organization 1 (1): 49–72,doi:10.1207/s15327000em0101_4

• Haag, James W. (2008). Emergent Freedom: Nat-uralizing Free Will Goettingen: Vandenhoeck &Ruprecht, ISBN 978-3-525-56988-7

• Hayek, Friedrich (1973), Law, Legislation and Lib-erty, ISBN 0-226-32086-3

• Hofstadter, Douglas R. (1979),Gödel, Escher, Bach:an Eternal Golden Braid, Harvester Press

• Holland, John H. (1998), Emergence from Chaosto Order, Oxford University Press, ISBN 0-7382-0142-1

• Holman, Peggy. (2010). Engaging Emergence:Turning upheaval into opportunity. San Francisco:Barrett-Koehler. ISBN 978-1-60509-521-9

• Hopfield, John J. (1982), “Neural networks andphysical systems with emergent collective compu-tational abilities”, Proc. Natl. Acad. Sci. USA 79(8): 2554–2558, Bibcode:1982PNAS...79.2554H,doi:10.1073/pnas.79.8.2554, PMC 346238, PMID6953413

• Hopper, P. 1998. Emergent Grammar. In:Tomasello, M. eds. 1998. The new psychologyof language: Cognitive and functional approachesto language structure. Mahwah, NJ: Earlbaum, pp.155–176.

• Huxley, Julian S.; Huxley, Thomas Henry (1947),Evolution and Ethics: 1893-1943, London, 1947:The Pilot Press, p. 120

• Johnson, Steven Berlin (2001), Emergence: TheConnected Lives of Ants, Brains, Cities, and Soft-ware, Scribner’s, ISBN 0-684-86876-8

• Kauffman, Stuart (1993), The Origins of Order: Self-Organization and Selection in Evolution, OxfordUni-versity Press, ISBN 0-19-507951-5

• Keller, Rudi (1994), On Language Change: TheInvisible Hand in Language, London/New York:Routledge, ISBN 0-415-07671-4

• Kauffman, Stuart (1995), At Home in the Universe,New York: Oxford University Press

• Kelly, Kevin (1994), Out of Control: The New Biol-ogy of Machines, Social Systems, and the EconomicWorld, Perseus Books, ISBN 0-201-48340-8

• Koestler, Arthur (1969), A. Koestler & J. R.Smythies, ed., Beyond Reductionism: New Perspec-tives in the Life Sciences, London: Hutchinson

• Korotayev, A.; Malkov, A.; Khaltourina, D. (2006),Introduction to Social Macrodynamics: CompactMacromodels of the World System Growth, Moscow:URSS, ISBN 5-484-00414-4

• Krugman, Paul (1996), The Self-organizing Econ-omy, Oxford: Blackwell, ISBN 1-55786-698-8,ISBN 0-87609-177-X

• Laughlin, Robert (2005), A Different Universe:Reinventing Physics from the Bottom Down, BasicBooks, ISBN 0-465-03828-X

• Leland, W.E.; Willinger, M.S.; Taqqu, M.S.;Wilson, D.V. (1994), “On the self-similar na-ture of Ethernet traffic (extended version)",IEEE/ACM Transactions on Networking 2: 1–15,doi:10.1109/90.282603

• Lewes, G. H. (1875), Problems of Life and Mind(First Series) 2, London: Trübner, ISBN 1-4255-5578-0

1.10. EXTERNAL LINKS 13

• Lewin, Roger (2000), Complexity - Life at the Edgeof Chaos (second ed.), University of Chicago Press,ISBN 0-226-47654-5, ISBN 0-226-47655-3

• Ignazio Licata & Ammar Sakaji (eds) (2008).Physics of Emergence and Organization, ISBN 978-981-277-994-6, World Scientific and Imperial Col-lege Press.

• Marshall, Stephen (2009), Cities Design and Evo-lution, Routledge, ISBN 978-0-415-42329-8, ISBN0-415-42329-5

• Mill, John Stuart (1843), “On the Composition ofCauses”,A System of Logic, Ratiocinative and Induc-tive (1872 ed.), London: John W. Parker and Son,p. 371

• Morowitz, Harold J. (2002), The Emergence of Ev-erything: How the World Became Complex, OxfordUniversity Press, ISBN 0-19-513513-X

• Ryan, Alex J. (2006), “Emergence is Coupled toScope, not Level”, Complexity (arXiv), (to be sub-mitted), arXiv:nlin.AO/0609011

• Schelling, Thomas C. (1978), Micromotives andMacrobehaviour, W. W. Norton

• Jackie (Jianhong) Shen (2008), Cucker–SmaleFlocking Emergence under Hierarchical LeadershipIn: SIAM J. Applied Math., 68:3,

• Smith, John Maynard; Szathmáry, Eörs (1997), TheMajor Transitions in Evolution, Oxford UniversityPress, ISBN 0-19-850294-X

• Smith, Reginald D. (2008), The Dynamics of In-ternet Traffic: Self-Similarity, Self-Organization,and Complex Phenomena 0807, arXiv, p. 3374,arXiv:0807.3374, Bibcode:2008arXiv0807.3374S

• Solé, Ricard and Goodwin, Brian (2000) Signs oflife: how complexity pervades biology, Basic Books,New York.

• Steels, Luc (1990), “Towards a Theory of EmergentFunctionality”, in Jean-Arcady Meyer; Stewart W.Wilson, From Animals to Animats (Proceedings ofthe First International Conference on Simulation ofAdaptive behaviour), Cambridge, MA & London,England: Bradford Books (MIT Press), pp. 451–461

• Wan, Poe Yu-ze (2011), “Emergence a la SystemsTheory: Epistemological Totalausschluss or Onto-logical Novelty?", Philosophy of the Social Sciences,41(2), pp. 178–210

• Wan, Poe Yu-ze (2011), Reframing the Social:Emergentist Systemism and Social Theory, AshgatePublishing

• Weinstock, Michael (2010), The Architecture ofEmergence - the evolution of form in Nature andCivilisation, John Wiley and Sons, ISBN 0-470-06633-4

• Wolfram, Stephen (2002), A New Kind of Science,ISBN 1-57955-008-8

• Young, Louise B. (2002), The Unfinished Universe,ISBN 0-19-508039-4

1.10 External links• Emergence entry in the Internet Encyclopedia of Phi-

losophy

• Emergent Properties entry in the Stanford Encyclo-pedia of Philosophy

• Emergence at PhilPapers

• Emergence at the Indiana Philosophy OntologyProject

• The Emergent Universe: An interactive introduc-tion to emergent phenomena, from ant colonies toAlzheimer’s.

• Exploring Emergence: An introduction to emer-gence using CA and Conway’s Game of Life fromthe MIT Media Lab

• ISCE group: Institute for the Study of Coherenceand Emergence.

• Towards modeling of emergence: lecture slidesfrom Helsinki University of Technology

• Biomimetic Architecture - Emergence applied tobuilding and construction

• Studies in Emergent Order: Studies in Emergent Or-der (SIEO) is an open-access journal

• Emergence

Chapter 2

Complexity

For other uses, see Complexity (disambiguation).

There is no absolute definition of what complexity means;the only consensus among researchers is that there isno agreement about the specific definition of complex-ity. However, a characterization of what is complex ispossible.[1] Complexity is generally used to character-ize something with many parts where those parts interactwith each other in multiple ways. The study of these com-plex linkages at various scales is the main goal of complexsystems theory.In science,[2] there are as of 2010 a number of approachesto characterizing complexity; this article reflects many ofthese. Neil Johnson states that “even among scientists,there is no unique definition of complexity - and the sci-entific notion has traditionally been conveyed using par-ticular examples...” Ultimately he adopts the definitionof 'complexity science' as “the study of the phenomenawhich emerge from a collection of interacting objects.”[3]

2.1 Overview

Definitions of complexity often depend on the conceptof a "system"—a set of parts or elements that have re-lationships among them differentiated from relationshipswith other elements outside the relational regime. Manydefinitions tend to postulate or assume that complexityexpresses a condition of numerous elements in a systemand numerous forms of relationships among the elements.However, what one sees as complex and what one sees assimple is relative and changes with time.WarrenWeaver posited in 1948 two forms of complexity:disorganized complexity, and organized complexity.[4]Phenomena of 'disorganized complexity' are treated us-ing probability theory and statistical mechanics, while 'or-ganized complexity' deals with phenomena that escapesuch approaches and confront “dealing simultaneouslywith a sizable number of factors which are interrelatedinto an organic whole”.[4] Weaver’s 1948 paper has influ-enced subsequent thinking about complexity.[5]

The approaches that embody concepts of systems, multi-ple elements, multiple relational regimes, and state spaces

might be summarized as implying that complexity arisesfrom the number of distinguishable relational regimes(and their associated state spaces) in a defined system.Some definitions relate to the algorithmic basis for theexpression of a complex phenomenon or model or math-ematical expression, as later set out herein.

2.2 Disorganized complexity vs.organized complexity

One of the problems in addressing complexity issues hasbeen formalizing the intuitive conceptual distinction be-tween the large number of variances in relationships ex-tant in random collections, and the sometimes large, butsmaller, number of relationships between elements in sys-tems where constraints (related to correlation of other-wise independent elements) simultaneously reduce thevariations from element independence and create distin-guishable regimes of more-uniform, or correlated, rela-tionships, or interactions.Weaver perceived and addressed this problem, in at leasta preliminary way, in drawing a distinction between “dis-organized complexity” and “organized complexity”.In Weaver’s view, disorganized complexity results fromthe particular system having a very large number of parts,say millions of parts, or many more. Though the interac-tions of the parts in a “disorganized complexity” situationcan be seen as largely random, the properties of the sys-tem as a whole can be understood by using probabilityand statistical methods.A prime example of disorganized complexity is a gas ina container, with the gas molecules as the parts. Somewould suggest that a system of disorganized complexitymay be compared with the (relative) simplicity of plan-etary orbits — the latter can be predicted by applyingNewton’s laws of motion. Of course, most real-world sys-tems, including planetary orbits, eventually become the-oretically unpredictable even using Newtonian dynamics;as discovered by modern chaos theory.[6]

Organized complexity, in Weaver’s view, resides in noth-ing else than the non-random, or correlated, interaction

14

2.4. VARIED MEANINGS OF COMPLEXITY 15

between the parts. These correlated relationships create adifferentiated structure that can, as a system, interact withother systems. The coordinated system manifests proper-ties not carried or dictated by individual parts. The orga-nized aspect of this form of complexity vis a vis to othersystems than the subject system can be said to “emerge,”without any “guiding hand”.The number of parts does not have to be very large for aparticular system to have emergent properties. A systemof organized complexity may be understood in its prop-erties (behavior among the properties) through modelingand simulation, particularly modeling and simulation withcomputers. An example of organized complexity is a cityneighborhood as a living mechanism, with the neighbor-hood people among the system’s parts.[7]

2.3 Sources and factors of com-plexity

There are generally rules which can be invoked to explainthe origin of complexity in a given system.The source of disorganized complexity is the large num-ber of parts in the system of interest, and the lack of cor-relation between elements in the system.In the case of self-organizing living systems, usefully or-ganized complexity comes from beneficially mutated or-ganisms being selected to survive by their environmentfor their differential reproductive ability or at least suc-cess over inanimate matter or less organized complexorganisms. See e.g. Robert Ulanowicz's treatment ofecosystems.[8]

Complexity of an object or system is a relative prop-erty. For instance, for many functions (problems), sucha computational complexity as time of computation issmaller when multitape Turing machines are used thanwhen Turing machines with one tape are used. RandomAccess Machines allow one to even more decrease timecomplexity (Greenlaw and Hoover 1998: 226), while in-ductive Turing machines can decrease even the complex-ity class of a function, language or set (Burgin 2005).This shows that tools of activity can be an important fac-tor of complexity.

2.4 Varied meanings of complexity

In several scientific fields, “complexity” has a precisemeaning:

• In computational complexity theory, the amounts ofresources required for the execution of algorithms isstudied. The most popular types of computationalcomplexity are the time complexity of a problemequal to the number of steps that it takes to solve an

instance of the problem as a function of the size ofthe input (usually measured in bits), using the mostefficient algorithm, and the space complexity of aproblem equal to the volume of the memory usedby the algorithm (e.g., cells of the tape) that it takesto solve an instance of the problem as a functionof the size of the input (usually measured in bits),using the most efficient algorithm. This allows toclassify computational problems by complexity class(such as P, NP ... ). An axiomatic approach tocomputational complexity was developed byManuelBlum. It allows one to deduce many properties ofconcrete computational complexity measures, suchas time complexity or space complexity, from prop-erties of axiomatically defined measures.

• In algorithmic information theory, the Kolmogorovcomplexity (also called descriptive complexity, algo-rithmic complexity or algorithmic entropy) of a stringis the length of the shortest binary program thatoutputs that string. Minimum message length isa practical application of this approach. Differentkinds of Kolmogorov complexity are studied: theuniform complexity, prefix complexity, monotonecomplexity, time-bounded Kolmogorov complex-ity, and space-bounded Kolmogorov complexity.An axiomatic approach to Kolmogorov complexitybased on Blum axioms (Blum 1967) was introducedby Mark Burgin in the paper presented for publi-cation by Andrey Kolmogorov (Burgin 1982). Theaxiomatic approach encompasses other approachesto Kolmogorov complexity. It is possible to treatdifferent kinds of Kolmogorov complexity as par-ticular cases of axiomatically defined generalizedKolmogorov complexity. Instead, of proving sim-ilar theorems, such as the basic invariance theorem,for each particular measure, it is possible to easilydeduce all such results from one corresponding the-orem proved in the axiomatic setting. This is a gen-eral advantage of the axiomatic approach in math-ematics. The axiomatic approach to Kolmogorovcomplexity was further developed in the book (Bur-gin 2005) and applied to software metrics (Burginand Debnath, 2003; Debnath and Burgin, 2003).

• In information processing, complexity is a measureof the total number of properties transmitted by anobject and detected by an observer. Such a collec-tion of properties is often referred to as a state.

• In physical systems, complexity is a measure of theprobability of the state vector of the system. Thisshould not be confused with entropy; it is a distinctmathematical measure, one in which two distinctstates are never conflated and considered equal, asis done for the notion of entropy in statistical me-chanics.

• In mathematics, Krohn–Rhodes complexity is an

16 CHAPTER 2. COMPLEXITY

important topic in the study of finite semigroups andautomata.

• In Network theory complexity is the product of rich-ness in the connections between components of asystem.

• In software engineering, programming complexityis a measure of the interactions of the various ele-ments of the software. This differs from the com-putational complexity described above in that it is ameasure of the design of the software.

• In abstract sense - Abstract Complexity, is based onvisual structures perception [9] It is complexity ofbinary string defined as a square of features numberdivided by number of elements (0’s and 1’s). Fea-tures comprise here all distinctive arrangements of0’s and 1’s. Though the features number have to bealways approximated the definition is precise andmeet intuitive criterion.

Other fields introduce less precisely defined notions ofcomplexity:

• A complex adaptive system has some or all of thefollowing attributes:[3]

• The number of parts (and types of parts) in thesystem and the number of relations betweenthe parts is non-trivial – however, there is nogeneral rule to separate “trivial” from “non-trivial";

• The system has memory or includes feedback;• The system can adapt itself according to itshistory or feedback;

• The relations between the system and its envi-ronment are non-trivial or non-linear;

• The system can be influenced by, or can adaptitself to, its environment; and

• The system is highly sensitive to initial condi-tions.

2.5 Study of complexity

Complexity has always been a part of our environment,and therefore many scientific fields have dealt with com-plex systems and phenomena. From one perspective, thatwhich is somehow complex-—displaying variation with-out being random – is most worthy of interest given therewards found in the depths of exploration.The use of the term complex is often confused with theterm complicated. In today’s systems, this is the differ-ence between myriad connecting “stovepipes” and effec-tive “integrated” solutions.[10] This means that complex

is the opposite of independent, while complicated is theopposite of simple.While this has led some fields to come up with spe-cific definitions of complexity, there is a more recentmovement to regroup observations from different fields tostudy complexity in itself, whether it appears in anthills,human brains, or stock markets. One such interdisci-plinary group of fields is relational order theories.

2.6 Complexity topics

2.6.1 Complex behaviour

The behavior of a complex system is often said to be dueto emergence and self-organization. Chaos theory has in-vestigated the sensitivity of systems to variations in initialconditions as one cause of complex behaviour.

2.6.2 Complex mechanisms

Recent developments around artificial life, evolutionarycomputation and genetic algorithms have led to an in-creasing emphasis on complexity and complex adaptivesystems.

2.6.3 Complex simulations

In social science, the study on the emergence of macro-properties from the micro-properties, also known asmacro-micro view in sociology. The topic is commonlyrecognized as social complexity that is often related tothe use of computer simulation in social science, i.e.:computational sociology.

2.6.4 Complex systems

Main article: Complex system

Systems theory has long been concerned with the studyof complex systems (in recent times, complexity theoryand complex systems have also been used as names ofthe field). These systems are present in the research ofa variety disciplines, including biology, economics, andtechnology. Recently, complexity has become a natu-ral domain of interest of real world socio-cognitive sys-tems and emerging systemics research. Complex systemstend to be high-dimensional, non-linear, and difficult tomodel. In specific circumstances, they may exhibit low-dimensional behaviour.

2.7. APPLICATIONS OF COMPLEXITY 17

2.6.5 Complexity in data

In information theory, algorithmic information theory isconcerned with the complexity of strings of data.Complex strings are harder to compress. While intuitiontells us that this may depend on the codec used to com-press a string (a codec could be theoretically created inany arbitrary language, including one in which the verysmall command “X” could cause the computer to out-put a very complicated string like “18995316”), any twoTuring-complete languages can be implemented in eachother, meaning that the length of two encodings in dif-ferent languages will vary by at most the length of the“translation” language—which will end up being negligi-ble for sufficiently large data strings.These algorithmic measures of complexity tend to assignhigh values to random noise. However, those studyingcomplex systems would not consider randomness as com-plexity.Information entropy is also sometimes used in informa-tion theory as indicative of complexity.Recent work in machine learning has examined the com-plexity of the data as it affects the performance ofsupervised classification algorithms. Ho and Basu presenta set of complexity measures for binary classificationproblems.[11] The complexity measures broadly cover 1)the overlaps in feature values from differing classes, 2)the separability of the classes, and 3) measures of geom-etry, topology, and density of manifolds. Instance hard-ness is another approach seeks to characterize the datacomplexity with the goal of determining how hard a dataset is to classify correctly and is not limited to binaryproblems.[12] Instance hardness is a bottom-up approachthat first seeks to identify instances that are likely to bemisclassified (or, in other words, which instances are themost complex). The characteristics of the instances thatare likely to be misclassified are then measured based onthe output from a set of hardness measures. The hard-ness measures are based on several supervised learningtechniques such as measuring the number of disagree-ing neighbors or the likelihood of the assigned class labelgiven the input features. The information provided by thecomplexity measures has been examined for use in metalearning to determine for which data sets filtering (or re-moving suspected noisy instances from the training set)is the most beneficial[13] and could be expanded to otherareas.

2.6.6 Complexity in molecular recognition

A recent study based on molecular simulations andcompliance constants describes molecular recognitionas a phenomenon of organisation.[14] Even for smallmolecules like carbohydrates, the recognition process cannot be predicted or designed even assuming that each in-dividual hydrogen bond's strength is exactly known.

2.7 Applications of complexity

Computational complexity theory is the study of the com-plexity of problems—that is, the difficulty of solvingthem. Problems can be classified by complexity classaccording to the time it takes for an algorithm—usuallya computer program—to solve them as a function ofthe problem size. Some problems are difficult to solve,while others are easy. For example, some difficult prob-lems need algorithms that take an exponential amount oftime in terms of the size of the problem to solve. Takethe travelling salesman problem, for example. It can besolved in time O(n22n) (where n is the size of the net-work to visit—let’s say the number of cities the travellingsalesman must visit exactly once). As the size of the net-work of cities grows, the time needed to find the routegrows (more than) exponentially.Even though a problem may be computationally solvablein principle, in actual practice it may not be that sim-ple. These problems might require large amounts of timeor an inordinate amount of space. Computational com-plexity may be approached from many different aspects.Computational complexity can be investigated on the ba-sis of time, memory or other resources used to solve theproblem. Time and space are two of the most importantand popular considerations when problems of complexityare analyzed.There exist a certain class of problems that although theyare solvable in principle they require so much time orspace that it is not practical to attempt to solve them.These problems are called intractable.There is another form of complexity called hierarchicalcomplexity. It is orthogonal to the forms of complexitydiscussed so far, which are called horizontal complexityBejan and Lorente showed that complexity is modest (notmaximum, not increasing), and is a feature of the natu-ral phenomenon of design generation in nature, which ispredicted by the Constructal law.[15]

Bejan and Lorente also showed that all the optimality(max,min) statements have limited ad-hoc applicability,and are unified under the Constructal law of design andevolution in nature.[16][17]

2.8 See also

• Chaos theory

• Command and Control Research Program

• Complex systems

• Complexity theory (disambiguation page)

• Constructal law

• Cyclomatic complexity

18 CHAPTER 2. COMPLEXITY

• Digital morphogenesis

• Dual-phase evolution

• Emergence

• Evolution of complexity

• Game complexity

• Holism in science

• Interconnectedness

• Law of Complexity/Consciousness

• Model of Hierarchical Complexity

• Names of large numbers

• Network science

• Network theory

• Novelty theory

• Occam’s razor

• Process architecture

• Programming Complexity

• Sociology and complexity science

• Systems theory

• Thorngate’s postulate of commensurate complexity

• Variety (cybernetics)

• Volatility, uncertainty, complexity and ambiguity

2.9 References[1] Antunes, Ricardo; Gonzalez, Vicente (3 March 2015).

“A Production Model for Construction: A Theo-retical Framework”. Buildings 5 (1): 209–228.doi:10.3390/buildings5010209. Retrieved 17 March2015.

[2] J. M. Zayed, N. Nouvel, U. Rauwald, O. A. Scherman.Chemical Complexity – supramolecular self-assembly ofsynthetic and biological building blocks in water. Chem-ical Society Reviews, 2010, 39, 2806–2816 http://pubs.rsc.org/en/Content/ArticleLanding/2010/CS/b922348g

[3] Johnson, Neil F. (2009). “Chapter 1: Two’s company,three is complexity”. Simply complexity: A clear guide tocomplexity theory (PDF). Oneworld Publications. p. 3.ISBN 978-1780740492.

[4] Weaver, Warren (1948). “Science and Complexity”(PDF). American Scientist 36 (4): 536–44. PMID18882675. Retrieved 2007-11-21.

[5] Johnson, Steven (2001). Emergence: the connected livesof ants, brains, cities, and software. New York: Scribner.p. 46. ISBN 0-684-86875-X.

[6] “Sir James Lighthill and Modern Fluid Me-chanics”, by Lokenath Debnath, The Univer-sity of Texas-Pan American, US, Imperial Col-lege Press: ISBN 978-1-84816-113-9: ISBN 1-84816-113-1, Singapore, page 31. Online at http://cs5594.userapi.com/u11728334/docs/25eb2e1350a5/Lokenath_Debnath_Sir_James_Lighthill_and_mode.pdf

[7] Jacobs, Jane (1961). The Death and Life of Great Ameri-can Cities. New York: Random House.

[8] Ulanowicz, Robert, “Ecology, the Ascendant Perspec-tive”, Columbia, 1997

[9] Mariusz Stanowski (2011) Abstract Complexity Defini-tion, Complicity 2, p.78-83

[10] Lissack, Michael R.; Johan Roos (2000). The Next Com-mon Sense, The e-Manager’s Guide to Mastering Complex-ity. Intercultural Press. ISBN 978-1-85788-235-3.

[11] Ho, T.K.; Basu, M. (2002). "Complexity Measures of Su-pervised Classification Problems". IEEE Transactions onPattern Analysis and Machine Intelligence 24 (3), pp 289-300.

[12] Smith, M.R.; Martinez, T.; Giraud-Carrier, C. (2014)."An Instance Level Analysis of Data Complexity". Ma-chine Learning, 95(2): 225-256.

[13] Saez, J.; Luengo, J.; Herrera, F. (2013). "PredictingNoise Filtering Efficacy with Data Complexity Measuresfor Nearest Neighbor Classification". Pattern Recognition46 (1) pp 355-364.

[14] Phys. Chem. Chem. Phys., 2011, 13, 10136–10146

[15] Bejan A., Lorente S., The Constructal Law of Designand Evolution in Nature. Philosophical Transactions ofthe Royal Society B, Biological Science, Vol. 365, 2010,pp. 1335–1347.

[16] Lorente S., Bejan A. (2010). Few Large and Many Small:Hierarchy in Movement on Earth, International Journalof Design of Nature and Ecodynamics, Vol. 5, No. 3, pp.254–267.

[17] Kim S., Lorente S., Bejan A., Milter W., Morse J. (2008)The Emergence of Vascular Design in Three Dimensions,Journal of Applied Physics, Vol. 103, 123511.

2.10 Further reading• Chu, Dominique (2011). Complexity: Against Sys-

tems. Theory in Biosciences (Springer). PMID21287293.

• Waldrop, M. Mitchell (1992). Complexity: TheEmerging Science at the Edge of Order and Chaos.New York: Simon & Schuster. ISBN 978-0-671-76789-1.

• Czerwinski, Tom; David Alberts (1997).Complexity, Global Politics, and National Se-curity (PDF). National Defense University. ISBN978-1-57906-046-6.

2.11. EXTERNAL LINKS 19

• Solé, R. V.; B. C. Goodwin (2002). Signs of Life:How Complexity Pervades Biology. Basic Books.ISBN 978-0-465-01928-1.

• Heylighen, Francis (2008). “Complexity and Self-Organization” (PDF). In Bates, Marcia J.; Maack,Mary Niles. Encyclopedia of Library and Informa-tion Sciences. CRC. ISBN 978-0-8493-9712-7.

• Burgin, M. (1982) Generalized Kolmogorov com-plexity and duality in theory of computations, No-tices of the Russian Academy of Sciences, v.25, No.3, pp. 19–23

• Meyers, R.A., (2009) “Encyclopedia of Complexityand Systems Science”, ISBN 978-0-387-75888-6

• Mitchell, M. (2009). Complexity: A Guided Tour.Oxford University Press, Oxford, UK.

• Gershenson, C., Ed. (2008). Complexity: 5 Ques-tions. Automatic Peess / VIP.

2.11 External links• Complexity Measures – an article about the abun-dance of not-that-useful complexity measures.

• Exploring Complexity in Science and Technology– Introductory complex system course by MelanieMitchell

• Quantifying Complexity Theory – classification ofcomplex systems

• Santa Fe Institute focusing on the study of complex-ity science: Lecture Videos

• UC Four Campus Complexity Videoconferences –Human Sciences and Complexity

Chapter 3

Self-organization

Self-organization in micron-sized Nb3O7(OH) cubes during ahydrothermal treatment at 200 °C. Initially amorphous cubesgradually transform into ordered 3D meshes of crystallinenanowires as summarized in the model below.[1]

Self-organization is a process where some form of over-all order or coordination arises out of the local interac-tions between smaller component parts of an initially dis-ordered system. The process of self-organization can bespontaneous, and it is not necessarily controlled by anyauxiliary agent outside of the system. It is often triggeredby random fluctuations that are amplified by positivefeedback. The resulting organization is wholly decentral-ized or distributed over all the components of the system.As such, the organization is typically robust and able tosurvive and, even, self-repair substantial damage or per-turbations. Chaos theory discusses self-organization interms of islands of predictability in a sea of chaotic un-predictability. Self-organization occurs in a variety ofphysical, chemical, biological, robotic, social, and cog-nitive systems. Examples of its realization can be foundin crystallization, thermal convection of fluids, chemicaloscillation, animal swarming, and neural networks.

3.1 Overview

Self-organization is realized[2] in the physics of non-equilibrium processes, and in chemical reactions, whereit is often described as self-assembly. The concept ofself-organization is central to the description of bio-logical systems, from the subcellular to the ecosystemlevel. There are also cited examples of self-organizing be-haviour found in the literature of many other disciplines,

both in the natural sciences and the social sciences suchas economics or anthropology. Self-organization has alsobeen observed in mathematical systems such as cellularautomata. Sometimes the notion of self-organization isconflated with that of the related concept of emergence.[3]Properly defined, however, theremay be instances of self-organization without emergence and emergence withoutself-organization.Self-organization usually relies on three basicingredients:[4]

1. Strong dynamical non-linearity, often though notnecessarily involving positive and negative feedback

2. Balance of exploitation and exploration

3. Multiple interactions

3.1.1 Principles of self-organization

The original principle of self-organization was for-mulated in 1947 by the cybernetician William RossAshby.[5][6] It states that any deterministic dynamic sys-tem will automatically evolve towards a state of equilib-rium that can be described in terms of an attractor in abasin of surrounding states. Once there, the further evo-lution of the system is constrained to remain in the at-tractor. This constraint on the system as a whole impliesa form of mutual dependency or coordination betweenits constituent components or “subsystems”. In Ashby’sterms, each subsystem has adapted to the environmentformed by all other subsystems.The principle of “order from noise” was formulated bythe cybernetician Heinz von Foerster in 1960.[7] It notesthat self-organization is facilitated by random perturba-tions (“noise”) that let the system explore a variety ofstates in its state space. This increases the chance thatthe system would arrive into the basin of a “strong” or“deep” attractor, from which it would then quickly enterthe attractor itself. A similar principle was formulatedby the thermodynamicist Ilya Prigogine as “order throughfluctuations”[8] or “order out of chaos”.[9] It is applied inthe method of simulated annealing that is used in problemsolving and machine learning

20

3.2. HISTORY OF THE IDEA 21

3.2 History of the idea

The idea that the dynamics of a system can lead to anincrease of the system’s organization has a long history.One of the earliest statements of this idea was by thephilosopher Descartes, in the fifth part of his DiscourseonMethod, where he presents it hypothetically. Descartesfurther elaborated on the idea at great length in his unpub-lished work The World.The ancient atomists believed that a designing intelli-gence is unnecessary to effect natural order, arguing thatgiven enough time and space and matter, organization isultimately inevitable, although there is no preferred ten-dency for this to happen. What Descartes introduced wasthe idea that the ordinary laws of nature tend to produceorganization (For related history, see Aram Vartanian,Diderot and Descartes).The economic concept of the "invisible hand" due toAdam Smith can be understood as an attempt to describethe influence of themarket as a spontaneous order on peo-ple’s actions.Beginning with the 18th century, natural scientists soughtto understand the “universal laws of form” in order to ex-plain the observed forms of living organisms. Becauseof its association with Lamarckism, their ideas fell intodisrepute until the early 20th century, when pioneerssuch as D'ArcyWentworth Thompson revived them. Themodern understanding is that there are indeed universallaws, arising from fundamental physics and chemistry,that govern growth and form in biological systems.Sadi Carnot and Rudolf Clausius discovered the SecondLaw of Thermodynamics in the 19th century. It statesthat total entropy, sometimes understood as disorder, willalways increase over time in an isolated system. Thismeans that a system cannot spontaneously increase its or-der, without an external relationship that decreases orderelsewhere in the system (e.g. through consuming the low-entropy energy of a battery and diffusing high-entropyheat).Originally, the term “self-organizing” was used byImmanuel Kant in his Critique of Judgment, where he ar-gued that teleology is a meaningful concept only if thereexists such an entity whose parts or “organs” are simulta-neously ends and means. Such a system of organs mustbe able to behave as if it has a mind of its own, that is, itis capable of governing itself.The term “self-organizing” was introduced to contem-porary science in 1947 by the psychiatrist and engineerW. Ross Ashby.[5] It was taken up by the cyberneticiansHeinz von Foerster, Gordon Pask, Stafford Beer, and vonFoerster organized a conference on “The Principles ofSelf-Organization” at the University of Illinois’ AllertonPark in June, 1960 which led to a series of conferences onSelf-Organizing Systems.[10] Norbert Wiener also tookup the idea in the second edition of his Cybernetics: or

Control and Communication in the Animal and the Ma-chine (1961).Self-organization as a word and concept was used bythose associated with general systems theory in the 1960s,but did not become commonplace in the scientific litera-ture until its adoption by physicists and researchers in thefield of complex systems in the 1970s and 1980s.[11] Af-ter Ilya Prigogine's 1977 Nobel Prize, the thermodynamicconcept of self-organization received some attention of thepublic, and scientific researchers started to migrate fromthe cybernetic view to the thermodynamic view.[12]

3.2.1 Developing views

Other views of self-organization in physical systems in-terpret it as a strictly accumulative construction process,commonly displaying an “S” curve history of develop-ment. As discussed somewhat differently by differentresearchers, local complex systems for exploiting en-ergy gradients evolve from seeds of organization, througha succession of natural starting and ending phases forinverting their directions of development. The accu-mulation of working processes which their exploratoryparts construct as they exploit their gradient becomes the“learning”, “organization” or “design” of the system as aphysical artifact, such for an ecology or economy. Forexample, A. Bejan’s books and papers describe his ap-proach as “Constructal Theory”.[13] P. F. Henshaw’s workon decoding net-energy system construction processestermed “Natural Systems Theory”, uses various analyticalmethods to quantify and map them such as System En-ergy Assessment[14] for taking true quantitative measuresof whole complex energy using systems, and for anticipat-ing their successions, such asModels Learning Change[15]to permit adapting models to their emerging inverted de-signs. G. Y. Georgiev’s work is utilizing the principle ofleast (stationary) action in Physics, to define organizationof a complex system as the state of the constraints de-termining the total action of the elements in a system.Organization is then defined numerically as the recipro-cal of the average action per one element and one edgecrossing, if the system is described as a network. The el-ementary quantum of action, Planck’s constant, is usedto make the measure dimensionless and to define it as in-versely proportional to the number of quanta of action ex-pended by the elements for one edge crossing. The mech-anism of self-organization is the interaction between theelements and the constrains, which leads to constraintminimization. This is consistent with the Gauss’ princi-ple of least constraint. More elements minimize the con-straints faster, another aspect of the mechanism, whichis through quantity accumulation. As a result, the pathsof the elements are straightened, which is consistent withHertz’s principle of least curvature. The state of a systemwith least average sum of actions of its elements is de-fined as its attractor. In open systems, where there is con-stant inflow and outflow of energy and elements, this final

22 CHAPTER 3. SELF-ORGANIZATION

state is never reached, but the system always tends towardit.[12] This method can help describe, quantify, manage,design and predict future behavior of complex systems, toachieve the highest rates of self-organization to improvetheir quality, which is the numerical value of their orga-nization. It can be applied to complex systems in physics,chemistry, biology, ecology, economics, cities, networktheory and others, where they are present.[12][16][17]

3.3 Examples

The following list summarizes and classifies the instancesof self-organization found in different disciplines. As thelist grows, it becomes increasingly difficult to determinewhether these phenomena are all fundamentally the sameprocess, or the same label applied to several different pro-cesses. Self-organization, despite its intuitive simplicityas a concept, has proven notoriously difficult to define andpin down formally or mathematically, and it is entirelypossible that any precise definition might not include allthe phenomena to which the label has been applied.The farther a phenomenon is removed from physics, themore controversial the idea of self-organization as un-derstood by physicists becomes. Also, even when self-organization is clearly present, attempts at explainingit through physics or statistics are usually criticized asreductionistic.Similarly, when ideas about self-organization originatein, say, biology or social science, the farther one tries totake the concept into chemistry, physics or mathemat-ics, the more resistance is encountered, usually on thegrounds that it implies direction in fundamental physi-cal processes. However the tendency of hot bodies to getcold (see Thermodynamics) and by Le Chatelier’s Prin-ciple—the statistical mechanics extension of Newton’sThird Law—to oppose this tendency should be noted.

3.3.1 Physics

Convection cells in a gravity field

There are several broad classes of physical processes thatcan be described as self-organization. Such examplesfrom physics include:

• structural (order-disorder, first-order) phase transi-tions, and spontaneous symmetry breaking such as

• spontaneous magnetization, crystallization(see crystal growth, and liquid crystal) in theclassical domain and

• the laser, superconductivity and Bose–Einsteincondensation, in the quantum domain (butwith macroscopic manifestations)

• second-order phase transition, associated with"critical points" at which the system exhibits scale-invariant structures. Examples of these include:

• critical opalescence of fluids at the criticalpoint

• percolation in random media

• structure formation in thermodynamic systemsaway from equilibrium. The theory of dissipa-tive structures of Prigogine and Hermann Haken’sSynergetics were developed to unify the understand-ing of these phenomena, which include lasers, turbu-lence and convective instabilities (e.g., Bénard cells)in fluid dynamics,

• structure formation in astrophysics and cos-mology (including star formation, planetarysystems formation, galaxy formation)

• self-similar expansion• Diffusion-limited aggregation• percolation• reaction-diffusion systems, such as Belousov–Zhabotinsky reaction

• self-organizing dynamical systems: complex sys-tems made up of small, simple units connected toeach other usually exhibit self-organization

• Self-organized criticality (SOC)

• In tribology, friction coupled with other simultane-ous effects, such as heat transfer, wear, and materialdiffusion. can lead to self-organized patterns at thefrictional interface, ranging from stick-slip patternsto in-situ formed tribofilms and surface roughnessadjustment of two materials in contact.

• In spin foam system and loop quantum gravity thatwas proposed by Lee Smolin. The main idea is thatthe evolution of space in time should be robust ingeneral. Any fine-tuning of cosmological param-eters weaken the independency of the fundamen-tal theory. Philosophically, it can be assumed that

3.3. EXAMPLES 23

in the early time, there has not been any agent totune the cosmological parameters. Smolin and hiscolleagues in a series of works show that, based onthe loop quantization of spacetime, in the very earlytime, a simple evolutionary model (similar to thesand pile model) behaves as a power law distribu-tion on both the size and area of avalanche.

• Although, this model, which is restricted onlyon the frozen spin networks, exhibits a non-stationary expansion of the universe. How-ever, it is the first serious attempt toward thefinal ambitious goal of determining the cos-mic expansion and inflation based on a self-organized criticality theory in which the pa-rameters are not tuned, but instead are deter-mined from within the complex system.[18]

• A laser can also be characterized as a self orga-nized system to the extent that normal states of ther-mal equilibrium characterized by electromagneticenergy absorption are stimulated out of equilibriumin a reverse of the absorption process. “If the mattercan be forced out of thermal equilibrium to a suffi-cient degree, so that the upper state has a higher pop-ulation than the lower state (population inversion),then more stimulated emission than absorption oc-curs, leading to coherent growth (amplification orgain) of the electromagnetic wave at the transitionfrequency.”[19]

3.3.2 Chemistry

The DNA structure at left (schematic shown) will self-assembleinto the structure visualized by atomic force microscopy at right.Image from Strong.[20]

Self-organization in chemistry includes:

1. molecular self-assembly

2. reaction-diffusion systems and oscillating chemicalreactions

3. autocatalytic networks (see: autocatalytic set)

4. liquid crystals

5. colloidal crystals

6. self-assembled monolayers

7. micelles

8. microphase separation of block copolymers

9. Langmuir-Blodgett films

3.3.3 Biology

Birds flocking, an example of self-organization in biology

Main article: Biological organisation

According to Scott Camazine.. [et al.]:The following is an incomplete list of the diverse phe-nomena which have been described as self-organizing inbiology.

1. spontaneous folding of proteins and other biomacro-molecules

2. formation of lipid bilayer membranes

3. homeostasis (the self-maintaining nature of systemsfrom the cell to the whole organism)

4. pattern formation and morphogenesis, or how theliving organism develops and grows. See alsoembryology.

5. the coordination of human movement, e.g. seminalstudies of bimanual coordination by Kelso

6. the creation of structures by social animals, suchas social insects (bees, ants, termites), and manymammals

7. flocking behaviour (such as the formation of flocksby birds, schools of fish, etc.)

8. the origin of life itself from self-organizing chem-ical systems, in the theories of hypercycles andautocatalytic networks

24 CHAPTER 3. SELF-ORGANIZATION

9. the organization of Earth’s biosphere in a way that isbroadly conducive to life (according to the contro-versial Gaia hypothesis)

3.3.4 Computer Science

Gosper’s Glider Gun creating "gliders" in the cellular automatonConway’s Game of Life.[22]

As mentioned above, phenomena from mathematics andcomputer science such as cellular automata, randomgraphs, and some instances of evolutionary computationand artificial life exhibit features of self-organization.In swarm robotics, self-organization is used to produceemergent behavior. In particular the theory of ran-dom graphs has been used as a justification for self-organization as a general principle of complex systems.In the field of multi-agent systems, understanding howto engineer systems that are capable of presenting self-organized behavior is a very active research area.

Algorithms

Many optimization algorithms can be considered as aself-organization system because the aim of the optimiza-tion is to find the optimal solution to a problem. If thesolution is considered as a state of the iterative system,the optimal solution is essentially the selected, convergedstate or structure of the system, driven by the algorithmbased on the system landscape.[23][24] In fact, one canview all optimization algorithms as a self-organizationsystem.

Networks

Self-organization is an important component for a suc-cessful ability to establish networking whenever needed.Such mechanisms are also referred to as Self-organizingnetworks. Intensified work in the latter half of the firstdecade of the 21st century was mainly due to interestfrom the wireless communications industry. It is drivenby the plug and play paradigm, and that wireless networks

need to be relatively simpler to manage than they used tobe.Only certain kinds of networks are self-organizing. Thebest known examples are small-world networks and scale-free networks. These emerge from bottom-up interac-tions, and appear to be limitless in size. In contrast, thereare top-down hierarchical networks, which are not self-organizing. These are typical of organizations, and havesevere size limits.In many natural systems, self-organization results fromrepeated phase shifts in their underlying network of con-nections. Such phase shifts alter the balance between in-ternal processes (e.g. selection and variation). They giverise to the phenomenon of dual-phase evolution.

3.3.5 Cybernetics

Wiener regarded the automatic serial identification of ablack box and its subsequent reproduction as sufficientto meet the condition of self-organization.[25] The im-portance of phase locking or the “attraction of frequen-cies”, as he called it, is discussed in the 2nd edition of his"Cybernetics".[26] Drexler sees self-replication as a keystep in nano and universal assembly.By contrast, the four concurrently connected galvanome-ters of W. Ross Ashby's Homeostat hunt, when per-turbed, to converge on one of many possible stablestates.[27] Ashby used his state counting measure ofvariety[28] to describe stable states and produced the"Good Regulator"[29] theorem which requires internalmodels for self-organized endurance and stability (e.g.Nyquist stability criterion).Warren McCulloch proposed “Redundancy of PotentialCommand”[30] as characteristic of the organization of thebrain and human nervous system and the necessary con-dition for self-organization.Heinz von Foerster proposed Redundancy, R = 1 −H/H ₐₓ, where H is entropy.[31][32] In essence this statesthat unused potential communication bandwidth is a mea-sure of self-organization.In the 1970s Stafford Beer considered this condition asnecessary for autonomy which identifies self-organizationin persisting and living systems. Using Variety analy-ses he applied his neurophysiologically derived recursiveViable System Model to management. It consists of fiveparts: the monitoring of performance of the survival pro-cesses (1), their management by recursive application ofregulation (2), homeostatic operational control (3) anddevelopment (4) which produce maintenance of identity(5) under environmental perturbation. Focus is priori-tized by an alerting “algedonic loop” feedback: a sen-sitivity to both pain and pleasure produced from under-performance or over-performance relative to a standardcapability.[33]

3.3. EXAMPLES 25

In the 1990s Gordon Pask pointed out von Foerster’sH and Hmax were not independent and interacted viacountably infinite recursive concurrent spin processes[34](he favoured the Bohm interpretation) which he calledconcepts (liberally defined in any medium, “productiveand, incidentally reproductive”). His strict definition ofconcept “a procedure to bring about a relation”[35] per-mitted his theorem “Like concepts repel, unlike con-cepts attract”[36] to state a general spin based Principleof Self-organization. His edict, an exclusion princi-ple, “There are No Doppelgangers"[37][34] means no twoconcepts can be the same (all interactions occur withdifferent perspectives making time incommensurable foractors). This means, after sufficient duration as differ-ences assert, all concepts will attract and coalesce as pinknoise and entropy increases (and see Big Crunch, self-organized criticality). The theory is applicable to all or-ganizationally closed or homeostatic processes that pro-duce enduring and coherent products (where spins have afixed average phase relationship and also in the sense ofRescher Coherence Theory of Truth with the proviso thatthe sets and their members exert repulsive forces at theirboundaries) through interactions: evolving, learning andadapting.Pask’s Interactions of Actors “hard carapace” model is re-flected in some of the ideas of emergence and coherence.It requires a knot emergence topology that produces ra-diation during interaction with a unit cell that has a pris-matic tensegrity structure. Laughlin's contribution toemergence reflects some of these constraints.

3.3.6 Human society

Social self-organization in international drug routes

The self-organizing behaviour of social animals and theself-organization of simple mathematical structures bothsuggest that self-organization should be expected in hu-man society. Tell-tale signs of self-organization areusually statistical properties shared with self-organizingphysical systems (see Zipf’s law, power law, Paretoprinciple). Examples such as critical mass, herd be-haviour, groupthink and others, abound in sociology,economics, behavioral finance and anthropology.[38] Thetheory of human social self-organization is also known asspontaneous order theory.

In social theory the concept of self-referentiality hasbeen introduced as a sociological application of self-organization theory byNiklas Luhmann (1984). For Luh-mann the elements of a social system are self-producingcommunications, i.e. a communication produces furthercommunications and hence a social system can reproduceitself as long as there is dynamic communication. ForLuhmann human beings are sensors in the environmentof the system. Luhmann developed an evolutionary the-ory of Society and its subsytems, using functional analy-ses and systems theory.[39]

Self-organization in human and computer networks cangive rise to a decentralized, distributed, self-healing sys-tem, protecting the security of the actors in the networkby limiting the scope of knowledge of the entire systemheld by each individual actor. The Underground Rail-road is a good example of this sort of network. Thenetworks that arise from drug trafficking exhibit similarself-organizing properties. The Sphere College Projectseeks to apply self-organization to adult education. Paral-lel examples exist in the world of privacy-preserving com-puter networks such as Tor. In each case, the network asa whole exhibits distinctive synergistic behavior throughthe combination of the behaviors of individual actors inthe network. Usually the growth of such networks is fu-eled by an ideology or sociological force that is adheredto or shared by all participants in the network.[12]

Economics

In economics, a market economy is sometimes said tobe self-organizing. Paul Krugman has written on therole that market self-organization plays in the businesscycle in his book “The Self Organizing Economy”.[40]Friedrich Hayek coined the term catallaxy[41] to describea “self-organizing system of voluntary co-operation”, inregards to the spontaneous order of the free marketeconomy. Neo-classical economists hold that impos-ing central planning usually makes the self-organizedeconomic system less efficient. On the other end ofthe spectrum, economists consider that market failuresare so significant that self-organization produces badresults and that the state should direct production andpricing. Most economists adopt an intermediate posi-tion and recommend a mixture of market economy andcommand economy characteristics (sometimes called amixed economy). When applied to economics, the con-cept of self-organization can quickly become ideologi-cally imbued.[12][42]

Collective intelligence

Non-thermodynamic concepts of entropy and self-organization have been explored by many theorists. CliffJoslyn and colleagues and their so-called "global brain"projects. Marvin Minsky's "Society of Mind" and the no-central editor in charge policy of the open sourced inter-

26 CHAPTER 3. SELF-ORGANIZATION

Visualization of links between pages on a wiki. This is an exam-ple of collective intelligence through collaborative editing.

net encyclopedia, called Wikipedia, are examples of ap-plications of these principles – see collective intelligence.Donella Meadows, who codified twelve leverage pointsthat a self-organizing system could exploit to organize it-self, was one of a school of theorists who saw humancreativity as part of a general process of adapting hu-man lifeways to the planet and taking humans out of con-flict with natural processes. See Gaia philosophy, deepecology, ecology movement and Green movement forsimilar self-organizing ideals. (The connections betweenself-organisation and Gaia theory and the environmentalmovement are explored in A. Marshall, 2002, The Unityof Nature, Imperial College Press: London).

3.3.7 Psychology and education

Self-organised learning

Enabling others to “learn how to learn”[43] is usuallymisconstrued as instructing them[44] how to successfullysubmit to being taught. Whilst fully accepting that wecan always learn from others, particularly those withmore and/or different experience than ourselves; self-organised learning (SOL) repudiates any idea[45] that thisreduces to accepting that “the expert knows best” or thatthere is ever “the one best method.” It offers an alternativedefinition of learning as “the construction of personallysignificant, relevant and viable meaning.”This more democratic 'bottom up' approach to learning isto be frequently tested experientially[46] by the learner(s)as being more “meaningful, constructive and creativelyeffective for me or us.”Since human learning may be achieved by one person,[47]or groups of learners working together;[48] SOL is not

Cybernetic algorithm

Systems algorithm

only a more rewarding and effective way of living one’spersonal life; it is also applicable in any group of peopleliving, playing and/or working together.As many young children, pupils, students and lifelonglearners eventually become ruefully aware, this ‘testingout of what I have learned’ needs to be carried out in eachlearner(s) whole process of living, and so it extends wellbeyond the confines of specific learning environments(home, school, university, etc.), and eventually beyondthe reaches of the controllers of these environments (par-ents, teachers, employers, etc.)[49]

SOL needs to be tested, and intermittently revised,through the ongoing personal experience[50] of thelearner(s) themselves in their ever-expanding outer andinner lives.Whilst internal life may cease to expand, the external en-vironment does not. If a learner allows themselves to be-come progressively more other-organised, they becomeless able to recognise and respond to varying needs forchange. Unfortunately this is often the current reportedexperience of many during, and hence after their parent-ing, schooling and/or higher education.But, this SOL way of understanding the learning pro-cess need not be restricted by either consciousness orlanguage.[51] Nor is it restricted to humans, since anal-

3.3. EXAMPLES 27

ogous directional self-organizing (learning?) processesare reported variously within the life sciences and evenwithin the less-living sciences, for example, of physicsand chemistry: (as is clearly articulated in other sectionsof this 'Self-organization' Section).Since SOL is as yet only very superficially recognisedwithin psychology and education, it is useful to place itmore firmly within the human public mind-pool[52] ofachievement, knowledge, experience and understanding.SOL can also be placed within a hierarchy of scientificexplanatory concepts, for example:

1. Cause and Effect (requires “other things beingequal”)

2. Cybernetics[35] (incorporates item 1 in this list) withgreater complexity, providing internal feedback andfeed-forward controls: but still implying a sealedboundary. (i.e. other things being equal)

3. Systems Theory[53] (incorporates item 2 in this list,and opens the boundaries)

4. Self-organized System (incorporates item 3 in thislist) and attributes this property to the interaction,patterning and coordination among the sub-systemsof the system in question; in response to flow acrossits boundaries

5. Self-Organised Learning (SOL)[54] (incorporatesitem 4 in this list) but also requires that the partseach systematically respond, change and develop inthe light of their experience, whilst self-organizingin the developing experiential interest of the whole).SOL not only involves self-organization of the firstorder, i.e. what is mostly experienced as learn-ing from experience without much conscious aware-ness of the process. At a second level of SOL con-sciousness enables us, (possibly uniquely among liv-ing beings) to reflect upon and thus self-organise thevery process of self-organisation itself, (See 'Cy-bernetic algorithm' figure). It also enables organi-sations small and large to self-organise themselves,(see 'System algorithm' figure).Once this approach to human learning is acknowl-edged, then we can re-set science into its placewithin the total human mind-pool. A mind-pool ofhuman know-how and feel-how as an ever expand-ing and hopefully self-organizing resource.

6. Learning Conversation (incorporates item 5 in thislist) and yet is at the same time its major tool.The Learning Conversation is a two-way process be-tween SOLers, even within one person (conversingwith oneself). Whilst not necessarily requiring lan-guage i.e. dialogue; it does require that the each par-ticipant really attempts to represent their meaningto the other(s), and that they all attempt to createpersonally significant, relevant and viable meaning

in themselves in response to the others representa-tions. So art, drama, music, computer programs,maths problems, ???, etc., can all create different, iflimited, forms of Learning Conversation which re-ally only become fully functional when at least twohumans really attempt to fully communicate, and ef-fectively share their understanding. That is achieveshared meaning in an event that approximates towhat Maslow called a creative encounter[55]

7. Conversational Science[56] (will require item 6 inthis list, the main method of SOL) among all seekersafter significant, relevant and viable shared mean-ing. Science and many other human activities stillneedmajor paradigm shifts if we are to achieve Self-Organised Living. It also requires equal stakeholder-ship for each converser. Thus SOL can be seen asnecessary but not sufficient for science to contributepositively to the benefit of the society, within whichit may have only spasmodically been conversing suc-cessfully (SOL wise). Until, perhaps, both scienceand society as a whole will become Self-OrganisedLearners (SOLers) continually learning from theirown shared experience and using what they learn inthe shared interest of all concerned.

3.3.8 Traffic flow

The self-organizing behaviour of drivers in traffic flowdetermines almost all traffic spatiotemporal phenomenaobserved in real traffic data like traffic breakdown at ahighway bottleneck, highway capacity, the emergence ofmoving traffic jams, etc. Self-organization in traffic flowis extremely complex spatiotemporal dynamic process.For this reason, only in 1996–2002 spatiotemporal self-organization effects in traffic have been understood inreal measured traffic data and explained by Boris Kerner'sthree-phase traffic theory.

3.3.9 Methodology

In many complex systems in nature, there are global phe-nomena that are the irreducible result of local interactionsbetween components whose individual study would notallow us to see the global properties of the whole com-bined system. Thus, a growing number of researchersthink that many properties of language are not directlyencoded by any of the components involved, but are theself-organized outcomes of the interactions of the com-ponents.Building mathematical models in the context of researchinto language origins and the evolution of languages isenjoying growing popularity in the scientific community,because it is a crucial tool for studying the phenomenaof language in relation to the complex interactions of itscomponents. These systems are put to two main types ofuse: 1) they serve to evaluate the internal coherence of

28 CHAPTER 3. SELF-ORGANIZATION

verbally expressed theories already proposed by clarify-ing all their hypotheses and verifying that they do indeedlead to the proposed conclusions ; 2) they serve to ex-plore and generate new theories, which themselves oftenappear when one simply tries to build an artificial systemreproducing the verbal behavior of humans.As it were, the construction of operational models to testproposed hypotheses in linguistics is gaining much con-temporary attention. An operational model is one whichdefines the set of its assumptions explicitly and aboveall shows how to calculate their consequences, that is, toprove that they lead to a certain set of conclusions.

In the emergence of language

The emergence of language in the human species hasbeen described in a game-theoretic framework based on amodel of senders and receivers of information. The evo-lution of certain properties of language such as inferencefollow from this sort of framework (with the param-eters stating that information transmitted can be par-tial or redundant, and the underlying assumption thatthe sender and receiver each want to take the actionin his/her best interest). Likewise, models have shownthat compositionality, a central component of humanlanguage, emerges dynamically during linguistic evolu-tion, and need not be introduced by biological evolution.Tomasello (1999) argues that through one evolutionarystep, the ability to sustain culture, the groundwork forthe evolution of human language was laid. The abil-ity to ratchet cultural advances cumulatively allowed forthe complex development of human cognition unseen inother animals.

In language acquisition

Within a species’ ontogeny, the acquisition of languagehas also been shown to self-organize. Through the abil-ity to see others as intentional agents (theory of mind),and actions such as 'joint attention,' human children havethe scaffolding they need to learn the language of thosearound them.

In articulatory phonology

Articulatory phonology takes the approach that speechproduction consists of a coordinated series of gestures,called 'constellations,' which are themselves dynamicalsystems. In this theory, linguistic contrast comes from thedistinction between such gestural units, which can be de-scribed on a low-dimensional level in the abstract. How-ever, these structures are necessarily context-dependentin real-time production. Thus the context-dependenceemerges naturally from the dynamical systems them-selves. This statement is controversial, however, as it sug-gests a universal phonetics which is not evident across

languages.[57] Cross-linguistic patterns show that whatcan be treated as the same gestural units produce differentcontextualised patterns in different languages.[58] Artic-ulatory Phonology fails to attend to the acoustic outputof the gestures themselves (meaning that many typologi-cal patterns remain unexplained).[59] Freedom among lis-teners in the weighting of perceptual cues in the acousticsignal has a more fundamental role to play in the emer-gence of structure.[60] The realization of the perceptualcontrasts by means of articulatory movements means thatarticulatory considerations do play a role,[61] but these arepurely secondary.

In diachrony and synchrony

Several mathematical models of language change rely onself-organizing or dynamical systems. Abrams and Stro-gatz (2003) produced a model of language change thatfocused on "language death" – the process by which aspeech community merges into the surrounding speechcommunities. Nakamura et al. (2008) proposed a variantof this model that incorporates spatial dynamics into lan-guage contact transactions in order to describe the emer-gence of creoles. Both of these models proceed from theassumption that language change, like any self-organizingsystem, is a large-scale act or entity (in this case the cre-ation or death of a language, or changes in its boundaries)that emerges from many actions on a micro-level. Themicrolevel in this example is the everyday production andcomprehension of language by speakers in areas of lan-guage contact.

3.4 Criticism

Heinz Pagels, in a balanced, but ultimately negative 1985book review of Ilya Prigogine and Isabelle Stengers'OrderOut of Chaos in Physics Today, appeals to authority:[62]

In theology, Thomas Aquinas (1225–1274) in his SummaTheologica assumes a teleological created universe in re-jecting the idea that something can be a self-sufficientcause of its own organization:[63]

(“The body of the Article” consists of the quinque viae.)

3.5 See also• Ant mill

• Autowave

• Biology concepts: Bow tie (biology) – evolution –morphogenesis – homeostasis – Gaia Hypothesis

• Causality

• Chemistry concepts: reaction-diffusion –autocatalysis

3.6. REFERENCES 29

• Complex systems concepts: emergence –evolutionary computation – artificial life –self-organized criticality – "edge of chaos" –spontaneous order – metastability – Chaos theory –Butterfly effect

• Computer science concepts: swarm intelligence

• Constructal law

• Dual-phase evolution

• Self-organized criticality control

• Free energy principle

• Free will

• Information theory

• Language – Operator grammar

• Mathematics concepts: fractal – random graph –power law – small world phenomenon – cellular au-tomata

• Organization of the artist

• Philosophical concepts: tectology – Religious natu-ralism

• Physics concepts: thermodynamics – non-equilibrium thermodynamics – constructal theory –statistical mechanics – phase transition – dissipativestructures – turbulence

• Social concepts: participatory organization

• Spontaneous order

• Stigmergy

• Systems theory concepts: cybernetics – autopoiesis– polytely

• Santiago theory of cognition

• Thermodynamics concepts: Second Law of Ther-modynamics – Heat death of the Universe

3.6 References[1] Betzler, S. B.; Wisnet, A.; Breitbach, B.; Mitterbauer,

C.; Weickert, J.; Schmidt-Mende, L.; Scheu, C. (2014).“Template-free synthesis of novel, highly-ordered 3D hi-erarchical Nb3O7(OH) superstructures with semiconduc-tive and photoactive properties”. Journal of MaterialsChemistry A 2 (30): 12005. doi:10.1039/C4TA02202E.

[2] Glansdorff, P., Prigogine, I. (1971). ThermodynamicTheory of Structure, Stability and Fluctuations, Wiley-Interscience, London. ISBN 0-471-30280-5

[3] Bernard Feltz et al (2006). Self-organization and Emer-gence in Life Sciences. ISBN 9781402039164. p. 1.

[4] Bonabeau, Eric; Dorigo, Marco and Theraulaz, Guy(1999). Swarm intelligence: from natural to artificial sys-tems. ISBN 0195131592. pp. 9–11.

[5] Ashby, W. R. (1947). “Principles of the Self-OrganizingDynamic System”. The Journal of General Psychology37 (2): 125–8. doi:10.1080/00221309.1947.9918144.PMID 20270223.

[6] Ashby, W. R. (1962). “Principles of the self-organizingsystem”, pp. 255–278 in Principles of Self-Organization.Heinz von Foerster and George W. Zopf, Jr. (eds.) U.S.Office of Naval Research.

[7] Von Foerster, H. (1960). [Retrieved from http://e1020.pbworks.com/f/fulltext.pdf “On self-organizing systemsand their environments"], pp. 31–50 in Self-organizingsystems. M.C. Yovits and S. Cameron (eds.), PergamonPress, London

[8] Nicolis, G. and Prigogine, I. (1977). Self-organization innonequilibrium systems: From dissipative structures to or-der through fluctuations. Wiley, New York.

[9] Prigogine, I. and Stengers, I. (1984). Order out of chaos:Man’s new dialogue with nature. Bantam Books.

[10] Asaro, P. (2007). “Heinz von Foerster and the Bio-Computing Movements of the 1960s” in Albert Müllerand Karl H. Müller (eds.) An Unfinished Revolution?Heinz von Foerster and the Biological Computer Lab-oratory BCL 1958–1976. Vienna, Austria: EditionEchoraum.

[11] As an indication of the increasing importance of this con-cept, when queried with the keyword self-organ*, Disser-tation Abstracts finds nothing before 1954, and only fourentries before 1970. There were 17 in the years 1971–1980; 126 in 1981–1990; and 593 in 1991–2000.

[12] Biel, R.; Mu-Jeong Kho (November 2009). “The Issue ofEnergy within a Dialectical Approach to the RegulationistProblematique” (PDF). Recherches & Régulation Work-ing Papers, RR Série ID 2009-1, Association Recherche& Régulation (http://theorie-regulation.org): 1–21. Re-trieved 2013-11-09.

[13] Bejan, A.; Lorente, S. (2006). “Constructal the-ory of generation of configuration in nature andengineering”. Journal of Applied Physics 100(4): 041301. Bibcode:2006JAP...100d1301B.doi:10.1063/1.2221896.

[14] Henshaw, King; Zarnikau (2011). “System Energy As-sessment (SEA), Defining a Standard Measure of EROIfor Energy Businesses as Whole Systems”. Sustainability3 (10): 1908–1943. doi:10.3390/su3101908.

[15] Henshaw, P. F. (2010). “Models Learning Change”. Cos-mos and History 6 (1).

[16] Georgiev, Georgi Yordanov (2012) “A quantitative mea-sure, mechanism and attractor for self-organization in net-worked complex systems”, pp. 90–95 in Lecture Notes inComputer Science (LNCS 7166), F. A. Kuipers and P. E.Heegaard (Eds.): IFIP International Federation for Infor-mation Processing, Proceedings of the Sixth International

30 CHAPTER 3. SELF-ORGANIZATION

Workshop on Self-Organizing Systems (IWSOS 2012),Springer-Verlag (2012).

[17] Georgiev, Georgi Yordanov; Georgiev, Iskren Yor-danov (2002). “The least action and the metric ofan organized system”. Open Systems and Informa-tion Dynamics 9 (4): 371–380. arXiv:1004.3518.Bibcode:2010arXiv1004.3518G.

[18] Ansari M. H. (2004) Self-organized theory in quantumgravity. arxiv.org

[19] Zeiger, H. J. and Kelley, P. L. (1991) “Lasers”, pp.614–619 in The Encyclopedia of Physics, Second Edition,edited by Lerner, R. and Trigg, G., VCH Publishers.

[20] Strong, M. (2004). “Protein Nanomachines”. PLoSBiol. 2 (3): e73–e74. doi:10.1371/journal.pbio.0020073.PMC 368168. PMID 15024422.

[21] Camazine, Deneubourg, Franks, Sneyd, Theraulaz,Bonabeau, Self-Organization in Biological Systems,Princeton University Press, 2003. ISBN 0-691-11624-5--ISBN 0-691-01211-3 (pbk.) p. 8

[22] Dennett, Daniel (1995), Darwin’s Dangerous Idea, Pen-guin Books, London, ISBN 978-0-14-016734-4

[23] Yang, X. S.; Deb, S.; Loomes, M.; Karamanoglu, M.(2013). “A framework for self-tuning optimization al-gorithm”. Neural Computing and Applications 23 (7–8):2051. doi:10.1007/s00521-013-1498-4.

[24] X. S. Yang (2014) Nature-Inspired Optimization Algo-rithms, Elsevier.

[25] Wiener, Norbert (1962) “The mathematics of self-organising systems”. Recent developments in informationand decision processes, Macmillan, N. Y. and Chapter XinCybernetics, or control and communication in the animaland the machine, The MIT Press.

[26] Cybernetics, or control and communication in the ani-mal and the machine, The MIT Press, Cambridge, Mas-sachusetts and Wiley, NY, 1948. 2nd Edition 1962“Chapter X “Brain Waves and Self-Organizing Sys-tems"pp 201–202.

[27] Ashby, William Ross (1952) Design for a Brain, Chapter5 Chapman & Hall

[28] Ashby, William Ross (1956) An Introduction to Cybernet-ics, Part Two Chapman & Hall

[29] Conant, R. C.; Ashby, W. R. (1970). “Every good regu-lator of a system must be a model of that system” (PDF).Int. J. Systems Sci. 1 (2): 89–97.

[30] Embodiments of Mind MIT Press (1965)"

[31] von Foerster, Heinz; Pask, Gordon (1961). “A PredictiveModel for Self-Organizing Systems, Part I”. Cybernetica3: 258–300.

[32] von Foerster, Heinz; Pask, Gordon (1961). “A PredictiveModel for Self-Organizing Systems, Part II”. Cybernetica4: 20–55.

[33] “Brain of the Firm”Alan Lane (1972) see also Viable Sys-temModel also in “Beyond Dispute " Wiley Stafford Beer1994 “Redundancy of Potential Command” pp. 157–158.

[34] Pask, Gordon (1996). “Heinz von Foerster’s Self-Organisation, the Progenitor of Conversation and Interac-tion Theories” (PDF). Systems Research 13 (3): 349–362.

[35] Pask, G. (1973). Conversation, Cognition and Learning.A Cybernetic Theory and Methodology. Elsevier

[36] Green, N. (2001). “On Gordon Pask”. Kybernetes 30(5/6): 673. doi:10.1108/03684920110391913.

[37] Pask, Gordon (1993) Interactions of Actors (IA), Theoryand Some Applications.

[38] Interactive models for self organization and biological sys-tems Center for Models of Life, Niels Bohr Institute, Den-mark

[39] Luhmann, Niklas (1995) Social Systems. Stanford, Cali-fornia: Stanford University Press. ISBN 0804726256. p.410.

[40] Krugman, P. (1995)The Self Organizing Economy. Black-well Publishers. ISBN 1557866996

[41] Hayek, F. (1976) Law, Legislation and Liberty, Volume 2:The Mirage of Social Justice. University of Chicago Press.

[42] Marshall, A. (2002) The Unity of Nature, Chapter 5. Im-perial College Press. ISBN 1860943306.

[43] Rogers.C. (1969). Freedom to Learn. Merrill

[44] Feynman, R. P. (1987) Elementary Particles and the Lawsof Physics. The Dyrac 1997 Memorial Lecture. Cam-bridge University Press. ISBN 9780521658621.

[45] Illich. I. (1971) A Celebration of Awareness. PenguinBooks.

[46] Harri-Augstein E. S. (2000) The University of Learning intransformation

[47] Schumacher, E. F. (1997) This I Believe and Other Essays(Resurgence Book). ISBN 1870098668.

[48] Revans R. W. (1982) The Origins and Growth of ActionLearning Chartwell-Bratt, Bromley

[49] Thomas L.F. and Harri-Augstein S. (1993) “On Becom-ing a Learning Organisation” in Report of a 7 year Ac-tion Research Project with the Royal Mail Business. CSHLMonograph

[50] Rogers C.R. (1971) On Becoming a Person. Constable,London

[51] Prigogyne I. & Sengers I. (1985) Order out of ChaosFlamingo Paperbacks. London

[52] Capra F (1989) Uncommon Wisdom Flamingo Paper-backs. London

[53] Bohm D. (1994) Thought as a System. Routledge.

3.7. FURTHER READING 31

[54] Harri-Augstein E. S. and Thomas L. F. (1991)LearningConversations: The SOL way to personal and organiza-tional growth. Routledge

[55] Maslow, A. H. (1964). Religions, values, and peak-experiences, Columbus: Ohio State University Press.

[56] Conversational Science Thomas L.F. and Harri-AugsteinE.S. (1985)

[57] Sole, M-J. (1992). “Phonetic and phonological processes:nasalization”. Language & Speech 35: 29–43.

[58] Ladefoged, Peter (2003) “Commentary: some thoughtson syllables – an old-fashioned interlude”, pp. 269–276 inPapers in laboratory Phonology VI. Local, John, RichardOgden&Ros Temple (eds.). Cambridge University Press.

[59] see papers in Phonetica 49, 1992, special issue on Articu-latory Phonology

[60] Ohala, John J. (1996). “Speech perception ishearing sounds, not tongues”. Journal of theAcoustical Society of America 99 (3): 1718–1725.Bibcode:1996ASAJ...99.1718O. doi:10.1121/1.414696.PMID 8819861.

[61] Lindblom, B. (1999). Emergent phonology (PDF). Pro-ceedings of the Twenty-fifth Annual Meeting of theBerkeley Linguistics Society, University of California,Berkeley.

[62] Pagels, H. R. (January 1, 1985). “Is the irreversibility wesee a fundamental property of nature?" (PDF). Physics To-day: 97–99.

[63] Article 3. Whether God exists? newadvent.org

3.7 Further reading

• W. Ross Ashby (1966), Design for a Brain, Chap-man & Hall, 2nd edition.

• Amoroso, Richard (2005) The Fundamental Limitand Origin of Complexity in Biological Systems .

• Per Bak (1996), How Nature Works: The Science ofSelf-Organized Criticality, Copernicus Books.

• Philip Ball (1999), The Self-Made Tapestry: PatternFormation in Nature, Oxford University Press.

• Stafford Beer, Self-organization as autonomy: Brainof the Firm 2nd editionWiley 1981 and Beyond Dis-puteWiley 1994.

• A. Bejan (2000), Shape and Structure, from En-gineering to Nature, Cambridge University Press,Cambridge, UK, 324 pp.

• Mark Buchanan (2002), Nexus: Small Worlds andthe Groundbreaking Theory of Networks W. W.Norton & Company.

• Scott Camazine, Jean-Louis Deneubourg, NigelR. Franks, James Sneyd, Guy Theraulaz, & EricBonabeau (2001) Self-Organization in BiologicalSystems, Princeton Univ Press.

• Falko Dressler (2007), Self-Organization in Sensorand Actor Networks, Wiley & Sons.

• Manfred Eigen and Peter Schuster (1979), The Hy-percycle: A principle of natural self-organization,Springer.

• Myrna Estep (2003),ATheory of Immediate Aware-ness: Self-Organization and Adaptation in NaturalIntelligence, Kluwer Academic Publishers.

• Myrna L. Estep (2006), Self-Organizing Natural In-telligence: Issues of Knowing, Meaning, and Com-plexity, Springer-Verlag.

• J. Doyne Farmer et al. (editors) (1986), “Evolu-tion, Games, and Learning: Models for Adaptationin Machines and Nature”, in: Physica D, Vol 22.

• Carlos Gershenson and Francis Heylighen (2003).“When Can we Call a System Self-organizing?" InBanzhaf, W, T. Christaller, P. Dittrich, J. T. Kim,and J. Ziegler, Advances in Artificial Life, 7th Eu-ropean Conference, ECAL 2003, Dortmund, Ger-many, pp. 606–614. LNAI 2801. Springer.

• Hermann Haken (1983) Synergetics: An Introduc-tion. Nonequilibrium Phase Transition and Self-Organization in Physics, Chemistry, and Biology,Third Revised and Enlarged Edition, Springer-Verlag.

• F.A. Hayek Law, Legislation and Liberty, RKP, UK.

• Francis Heylighen (2001): “The Science of Self-organization and Adaptivity”.

• Henrik Jeldtoft Jensen (1998), Self-Organized Crit-icality: Emergent Complex Behaviour in Physicaland Biological Systems, Cambridge Lecture Notesin Physics 10, Cambridge University Press.

• Steven Berlin Johnson (2001), Emergence: The Con-nected Lives of Ants, Brains, Cities, and Software.

• Stuart Kauffman (1995), At Home in the Universe,Oxford University Press.

• Stuart Kauffman (1993), Origins of Order: Self-Organization and Selection in EvolutionOxford Uni-versity Press.

• J. A. Scott Kelso (1995), Dynamic Patterns: Theself-organization of brain and behavior, The MITPress, Cambridge, Massachusetts.

• J. A. Scott Kelso & David A Engstrom (2006), "TheComplementary Nature", The MIT Press, Cam-bridge, Massachusetts.

32 CHAPTER 3. SELF-ORGANIZATION

• Alex Kentsis (2004), Self-organization of biologicalsystems: Protein folding and supramolecular assem-bly, Ph.D. Thesis, New York University.

• E.V.Krishnamurthy(2009)", Multiset of Agents ina Network for Simulation of Complex Systems”,in “Recent advances in Nonlinear Dynamics andsynchronization, ,(NDS-1) -Theory and applica-tions, Springer Verlag, New York,2009. Eds.K.Kyamakya et al.

• Paul Krugman (1996), The Self-Organizing Econ-omy, Cambridge, Massachusetts, and Oxford:Blackwell Publishers.

• ElizabethMcMillan (2004) “Complexity, Organiza-tions and Change”.

• Marshall, A (2002) The Unity of Nature, ImperialCollege Press: London (esp. chapter 5)

• Müller, J.-A., Lemke, F. (2000), Self-OrganizingData Mining.

• Gregoire Nicolis and Ilya Prigogine (1977) Self-Organization in Non-Equilibrium Systems, Wiley.

• Heinz Pagels (1988), The Dreams of Reason: TheComputer and the Rise of the Sciences of Complexity,Simon & Schuster.

• Gordon Pask (1961), The cybernetics of evolution-ary processes and of self organizing systems, 3rd. In-ternational Congress on Cybernetics, Namur, Asso-ciation Internationale de Cybernetique.

• Christian Prehofer ea. (2005), “Self-Organizationin Communication Networks: Principles and De-sign Paradigms”, in: IEEE Communications Maga-zine, July 2005.

• Mitchell Resnick (1994), Turtles, Termites andTraffic Jams: Explorations in Massively Parallel Mi-croworlds, Complex Adaptive Systems series, MITPress.

• Lee Smolin (1997), The Life of the Cosmos OxfordUniversity Press.

• Ricard V. Solé and Brian C. Goodwin (2001), Signsof Life: How Complexity Pervades Biology, BasicBooks.

• Ricard V. Solé and Jordi Bascompte (2006), Self-organization in Complex Ecosystems, Princeton U.Press

• Steven Strogatz (2004), Sync: The Emerging Scienceof Spontaneous Order, Theia.

• D'Arcy Thompson (1917), On Growth and Form,Cambridge University Press, 1992 Dover Publica-tions edition.

• Tom De Wolf, Tom Holvoet (2005), EmergenceVersus Self-Organisation: Different Concepts butPromising When Combined, In Engineering Self Or-ganising Systems: Methodologies and Applications,Lecture Notes in Computer Science, volume 3464,pp 1–15.

• K. Yee (2003), “Ownership and Trade from Evolu-tionary Games”, International Review of Law andEconomics, 23.2, 183–197.

• Louise B. Young (2002), The Unfinished Universe

• Mikhail Prokopenko (ed.) (2008), Advances in Ap-plied Self-organizing Systems, Springer.

• Alfred Hübler (2009), “Digital wires,” Complexity,14.5,7–9,

• Rüdiger H. Jung (2010), Self-organization In: Hel-mut K. Anheier, Stefan Toepler, Regina List (ed-itors): International Encyclopedia of Civil Society.Springer Science + Business Media LLC, NewYork2010, ISBN 978-0-387-93996-4, p. 1364–1370.

3.8 External links

• Self-organization at Scholarpedia, curated byHermann Haken.

• Max Planck Institute for Dynamics and Self-Organization, Göttingen

• PDF file on self-organized common law with refer-ences

• An entry on self-organization at the Principia Cyber-netica site

• The Science of Self-organization and Adaptivity, areview paper by Francis Heylighen

• The Self-Organizing Systems (SOS) FAQ byChris Lucas, from the USENET newsgroupcomp.theory.self-org.sys

• David Griffeath, Primordial Soup Kitchen (graphics,papers)

• nlin.AO, nonlinear preprint archive, (electronicpreprints in adaptation and self-organizing systems)

• Structure and Dynamics of Organic Nanostructures

• Metal organic coordination networks of oligopy-ridines and Cu on graphite

• Selforganization in complex networks The ComplexSystems Lab, Barcelona

• Computational Mechanics Group at the Santa Fe In-stitute

3.8. EXTERNAL LINKS 33

• “Organisation must grow” (1939) W. Ross Ashbyjournal page 759, from The W. Ross Ashby Digi-tal Archive

• Cosma Shalizi’s notebook on self-organization from2003-06-20, used under the GFDL with permissionfrom author.

• Connectivism:SelfOrganization

• UCLA Human Complex Systems Program

• “Interactions of Actors (IA), Theory and Some Ap-plications” 1993 Gordon Pask’s theory of learning,evolution and self-organization (in draft).

• The Cybernetics Society

• Scott Camazine’s webpage on self-organization inbiological systems

• Mikhail Prokopenko’s page on Information-drivenSelf-organisation (IDSO)

• Lakeside Labs Self-Organizing Networked SystemsA platform for science and technology, Klagenfurt,Austria.

• Watch 32 discordant metronomes synch up all bythemselves theatlantic.com

3.8.1 Dissertations and theses on self-organization

• Gershenson, Carlos. (2007). “Design and control ofSelf-organizing Systems” (PhD thesis).

• de Boer, Bart. (1999). Self-Organisation in VowelSystems Vrije Universiteit Brussel AI-lab (PhD the-sis).

Chapter 4

Spontaneous order

See also: Emergence and Self-organization

Spontaneous order, also named "self-organization", isthe spontaneous emergence of order out of seemingchaos. It is a process found in physical, biological, andsocial networks, as well as economics, though the term“self-organization” is more often used for physical andbiological processes, while “spontaneous order” is typi-cally used to describe the emergence of various kinds ofsocial orders from a combination of self-interested in-dividuals who are not intentionally trying to create or-der through planning. The evolution of life on Earth,language, crystal structure, the Internet and a free marketeconomy have all been proposed as examples of systemswhich evolved through spontaneous order.[1] Naturalistsoften point to the inherent “watch-like” precision of un-cultivated ecosystems and to the universe itself as ulti-mate examples of this phenomenon.Spontaneous orders are to be distinguished from organi-zations. Spontaneous orders are distinguished by beingscale-free networks, while organizations are hierarchicalnetworks. Further, organizations can be and often are apart of spontaneous social orders, but the reverse is nottrue. Further, while organizations are created and con-trolled by humans, spontaneous orders are created, con-trolled, and controllable by no one. In economics and thesocial sciences, spontaneous order is defined as “the resultof human actions, not of human design.”Spontaneous order is also used as a synonym for anyemergent behavior of which self-interested spontaneousorder is just an instance.

4.1 History

According to Murray Rothbard, Zhuangzi (369–286BCE) was the first to work out the idea of spontaneousorder. The philosopher rejected the authoritarianism ofConfucianism, writing that there “has been such a thing asletting mankind alone; there has never been such a thingas governing mankind [with success].” He articulated anearly form of spontaneous order, asserting that “good or-der results spontaneously when things are let alone”, a

concept later “developed particularly by Proudhon in thenineteenth” century.[2]

The thinkers of the Scottish Enlightenment were the firstto seriously develop and inquire into the idea of the mar-ket as a spontaneous order. In 1767, the sociologist andhistorian Adam Ferguson described the phenomenon ofspontaneous order in society as the “result of human ac-tion, but not the execution of any human design”.[3][4]

The Austrian School of Economics, led by Carl Menger,Ludwig von Mises and Friedrich Hayek, would later re-fine the concept and make it a centerpiece in its social andeconomic thought.

4.2 Examples

4.2.1 Markets

Many economic classical liberals, such as Hayek, haveargued that market economies are a spontaneous order,“a more efficient allocation of societal resources than anydesign could achieve.”[5] They claim this spontaneous or-der (referred to as the extended order in Hayek’s "The Fa-tal Conceit") is superior to any order a human mind candesign due to the specifics of the information required.[6]Centralized statistical data cannot convey this informa-tion because the statistics are created by abstracting awayfrom the particulars of the situation.[7]

In a market economy, price is the aggregation of informa-tion acquired when people are free to use their individualknowledge. Price then allows everyone dealing in a com-modity or its substitutes to make decisions based on moreinformation than he or she could personally acquire, in-formation not statistically conveyable to a centralized au-thority. Interference from a central authority which af-fects price will have consequences they could not foreseebecause they do not know all of the particulars involved.This is illustrated in the concept of the invisible hand pro-posed by Adam Smith in The Wealth of Nations.[1] Thusin this view by acting on information with greater detailand accuracy than possible for any centralized authority,a more efficient economy is created to the benefit of awhole society.

34

4.3. SEE ALSO 35

Lawrence Reed, president of the Foundation for Eco-nomic Education, describes spontaneous order as follows:

Spontaneous order is what happens whenyou leave people alone—when entrepreneurs...see the desires of people... and then provide forthem.

They respond to market signals, to prices.Prices tell them what’s needed and how ur-gently and where. And it’s infinitely better andmore productive than relying on a handful ofelites in some distant bureaucracy.[8]

4.2.2 Game studies

The concept of spontaneous order is closely related withmodern game studies. As early as in the 1940s, historianJohanHuizinga wrote that “inmyth and ritual the great in-stinctive forces of civilized life have their origin: law andorder, commerce and profit, craft and art, poetry, wisdomand science. All are rooted in the primeval soil of play.”Following on this in his book The Fatal Conceit, Hayeknotably wrote that “a game is indeed a clear instance of aprocess wherein obedience to common rules by elementspursuing different and even conflicting purposes resultsin overall order.”

4.2.3 Anarchism

Anarchists argue that the state is in fact an artificial cre-ation of the ruling elite, and that true spontaneous orderwould arise if it was eliminated. Construed by some butnot all as the ushering in of organization by anarchist law.In the anarchist view, such spontaneous order would in-volve the voluntary cooperation of individuals. Accord-ing to the Oxford Dictionary of Sociology, “the work ofmany symbolic interactionists is largely compatible withthe anarchist vision, since it harbours a view of society asspontaneous order.”[9]

4.2.4 Sobornost

The concept of spontaneous order can also be seen in theworks of the Russian Slavophile movements and specifi-cally in the works of FyodorDostoyevsky. The concept ofan organic social manifestation as a concept in Russia ex-pressed under the idea of sobornost. Sobornost was alsoused by Leo Tolstoy as an underpinning to the ideology ofChristian anarchism. The concept was used to describethe uniting force behind the peasant or serf Obshchina inpre-Soviet Russia.[10]

4.2.5 Recent developments

Perhaps the most famous theorist of social spontaneousorders is Friedrich Hayek. In addition to arguing theeconomy is a spontaneous order, which he termed acatallaxy, he argued that common law[11] and the brain[12]are also types of spontaneous orders. In “The Republicof Science,”[13] Michael Polanyi also argued that scienceis a spontaneous order, a theory further developed by BillButos and Thomas McQuade in a variety of papers. GusDiZerega has argued that democracy is the spontaneousorder form of government,[14] David Emmanuel Ander-sson has argued that religion in places like the UnitedStates is a spontaneous order,[15] and Troy Camplin ar-gues that artistic and literary production are spontaneousorders.[16] Paul Krugman too has contributed to sponta-neous order theory in his book The Self-Organizing Econ-omy,[17] in which he claims that cities are self-organizingsystems.

4.3 See also• Anonymous

• Deregulation

• Extended order

• Free price system

• "I, Pencil" by Leonard Read

• Invisible hand

• Mutual aid

• Natural law

• Natural order

• Organised order

• Revolutionary spontaneity

• Stigmergy

• Tragedy of the commons

4.4 References[1] Norman Barry, The Tradition of Spontaneous Order,

Literature of Liberty: A Review of Contemporary LiberalThought, Library of Economics and Liberty, 1982, ac-cessed 2010-12-12

[2] Rothbard, Murray. Concepts of the Role of Intellectuals inSocial Change Toward Laissez Faire, The Journal of Lib-ertarian Studies, Vol IX No. 2 (Fall 1990)

[3] Adam Ferguson on The History of Economic ThoughtWebsite

36 CHAPTER 4. SPONTANEOUS ORDER

[4] Ferguson, Adam (1767). An Essay on the History of CivilSociety. The Online Library of Liberty: T. Cadell, Lon-don. p. 205.

[5] Hayek cited. Petsoulas, Christian. Hayek’s Liberalismand Its Origins: His Idea of Spontaneous Order and theScottish Enlightenment. Routledge. 2001. p. 2

[6] Hayek, F.A. The Fatal Conceit: The Errors of Socialism.The University of Chicago Press. 1991. Page 6.

[7] Hayek cited. Boaz, David. The Libertarian Reader. TheFree Press. 1997. p. 220

[8] Stossel, John (2011-02-10) Spontaneous Order, Reason

[9] Marshall, Gordon; et al. (1998) [1994]. Oxford Dictio-nary of Sociology (2 ed.). Oxford: Oxford UniversityPress. pp. 19–20. ISBN 0-19-280081-7.

[10] Faith and Order: The Reconciliation of Law and Re-ligion By Harold Joseph pg 388 Berman Wm. B.Eerdmans Publishing Religion and law ISBN 0-8028-4852-4 http://books.google.com/books?id=j1208xA7F_0C&lpg=PA388&ots=p0N6U4zWbf&pg=PA388

[11] The Constitution of Liberty; Law, Legislation and Liberty

[12] The Sensory Order

[13] http://fiesta.bren.ucsb.edu/~{}gsd/595e/docs/41.%20Polanyi_Republic_of_Science.pdf

[14] Persuasion, Power, and Polity

[15] http://www.amazon.com/Persuasion-Power-Polity-Democratic-Self-Organization/dp/1572732571/ref=sr_1_4?ie=UTF8&s=books&qid=1302773406&sr=1-4

[16] http://studiesinemergentorder.org/current-issue/sieo3-195/

[17] The Self-Organizing Economy

4.5 External links• The Tradition of Spontaneous Order, by NormanBarry, Library of Economics and Liberty

Chapter 5

Complex system

This article largely discusses complex systems as asubject of mathematics and the attempts to emulatephysical complex systems with emergent properties. Forother scientific and professional disciplines addressingcomplexity in their fields see the complex systems articleand references.

A complex system is a system that exhibits some (andpossibly all) of the following characteristics:[1]

• feedback loops;

• some degree of spontaneous order;

• robustness of the order;

• emergent organization;

• numerosity;[2]

• hierarchical organization.[3]

Examples of complex systems are Earth’s global climate,the human brain, social organization, an ecosystem, a liv-ing cell, and ultimately the entire universe.

5.1 History

Although it is arguable that humans have been studyingcomplex systems for thousands of years, the modern sci-entific study of complex systems is relatively young incomparison to conventional fields of science with sim-ple system assumptions, such as physics and chemistry.The history of the scientific study of these systems fol-lows several different research trends.In the area of mathematics, arguably the largest con-tribution to the study of complex systems was the dis-covery of chaos in deterministic systems, a feature ofcertain dynamical systems that is strongly related tononlinearity.[4] The study of neural networks was also in-tegral in advancing themathematics needed to study com-plex systems.

The notion of self-organizing systems is tied up to workin nonequilibrium thermodynamics, including that pio-neered by chemist and Nobel laureate Ilya Prigogine inhis study of dissipative structures.

5.2 Types of complex systems

5.2.1 Nonlinear systems

The behaviour of non-linear systems is not subject to theprinciple of superposition while that of linear systems issubject to superposition. Thus, a complex nonlinear sys-tem is one whose behaviour cannot be expressed as a sumof the behaviour of its parts (or of their multiples).[5]

Chaotic systems

For a dynamical system to be classified as chaotic, it musthave the following properties:[6]

Assign z to z2 minus the conjugate of z, plus the original valueof the pixel for each pixel, then count how many cycles it tookwhen the absolute value of z exceeds two; inversion (borders areinner set), so that you can see that it threatens to fail that thirdcondition, even if it meets condition two.

1. it must be sensitive to initial conditions,

2. it must be topologically mixing, and

37

38 CHAPTER 5. COMPLEX SYSTEM

3. its periodic orbits must be dense.

Sensitivity to initial conditions means that each pointin such a system is arbitrarily closely approximated byother points with significantly different future trajecto-ries. Thus, an arbitrarily small perturbation of the cur-rent trajectory may lead to significantly different futurebehavior.

5.2.2 Complex adaptive systems

Complex adaptive systems (CAS) are special cases ofcomplex systems. They are complex in that they are di-verse and made up of multiple interconnected elementsand adaptive in that they have the capacity to change andlearn from experience. Examples of complex adaptivesystems include the stock market, social insect and antcolonies, the biosphere and the ecosystem, the brain andthe immune system, the cell and the developing embryo,manufacturing businesses and any human social group-based endeavor in a cultural and social system such aspolitical parties or communities. This includes somelarge-scale online systems, such as collaborative taggingor social bookmarking systems.

5.3 Topics on complex systems

5.3.1 Features of complex systems

Complex systems may have the following features:

Cascading Failures Due to the strong coupling be-tween components in complex systems, a failure inone or more components can lead to cascading fail-ures which may have catastrophic consequences onthe functioning of the system.[7]

Complex systems may be open Complex systems areusually open systems — that is, they exist in athermodynamic gradient and dissipate energy. Inother words, complex systems are frequently farfrom energetic equilibrium: but despite this flux,there may be pattern stability, see synergetics.

Complex systems may have a memory The history ofa complex system may be important. Because com-plex systems are dynamical systems they changeover time, and prior states may have an influence onpresent states. More formally, complex systems of-ten exhibit hysteresis.

Complex systems may be nested The components of acomplex system may themselves be complex sys-tems. For example, an economy is made up oforganisations, which are made up of people, which

are made up of cells - all of which are complex sys-tems.

Dynamic network of multiplicity As well as couplingrules, the dynamic network of a complex sys-tem is important. Small-world or scale-freenetworks[8][9][10] which have many local interactionsand a smaller number of inter-area connections areoften employed. Natural complex systems often ex-hibit such topologies. In the human cortex for ex-ample, we see dense local connectivity and a fewvery long axon projections between regions insidethe cortex and to other brain regions.

May produce emergent phenomena Complex systemsmay exhibit behaviors that are emergent, which isto say that while the results may be sufficiently de-termined by the activity of the systems’ basic con-stituents, they may have properties that can only bestudied at a higher level. For example, the termitesin a mound have physiology, biochemistry and bio-logical development that are at one level of analy-sis, but their social behavior and mound building isa property that emerges from the collection of ter-mites and needs to be analysed at a different level.

Relationships are non-linear In practical terms, thismeans a small perturbation may cause a large effect(see butterfly effect), a proportional effect, or evenno effect at all. In linear systems, effect is alwaysdirectly proportional to cause. See nonlinearity.

Relationships contain feedback loops Both negative(damping) and positive (amplifying) feedback arealways found in complex systems. The effects of anelement’s behaviour are fed back to in such a waythat the element itself is altered.

5.4 See also

• Biological organisation

• Complex (disambiguation)

• Complexity (disambiguation)

• Dissipative system

• Fractal

• Innovation butterfly

• Practopoiesis

• System equivalence

5.7. EXTERNAL LINKS 39

5.5 References[1] Ladyman, James; Lambert, James; Wiesner, Karoline

(2013). “What is a Complex System?". European Journalfor Philosophy of Science 3: 33–67.

[2] Anderson, P. W. (1972). “More is differ-ent: Broken symmerty and the nature of thehierarchical structure of science.”. Science177: 393–396. Bibcode:1972Sci...177..393A.doi:10.1126/science.177.4047.393.

[3] Simon, Herbert A. (1991). “The architecture of complex-ity”. Springer US.

[4] History of Complex Systems

[5] EPSRC description of Non-linear systems retrieved 11Aug 2015

[6] Hasselblatt, Boris; Anatole Katok (2003). A First Coursein Dynamics: With a Panorama of Recent Developments.Cambridge University Press. ISBN 0-521-58750-6.

[7] S. V. Buldyrev, R. Parshani, G. Paul, H. E. Stanley,S. Havlin (2010). “Catastrophic cascade of failures ininterdependent networks”. Nature 464 (7291): 08932.arXiv:0907.1182. Bibcode:2010Natur.464.1025B.doi:10.1038/nature08932. PMID 20393559.

[8] A. L. Barab´asi, R. Albert (2002). “Statisticalmechanics of complex networks”. Rev.Mod. Phys 74: 47–94. arXiv:cond-mat/0106096. Bibcode:2002RvMP...74...47A.doi:10.1103/RevModPhys.74.47.

[9] M. Newman (2010). Networks: An Introduction. OxfordUniversity Press. ISBN 978-0-19-920665-0.

[10] Reuven Cohen, Shlomo Havlin (2010). Complex Net-works: Structure, Robustness and Function. CambridgeUniversity Press. ISBN 978-0-521-84156-6.

5.6 Further reading• Paolo Sibani & Henrik Jeldtoft Jensen (2013).

Stochastic Dynamics of Complex Systems, ISBN 978-1-84816-993-7, World Scientific and Imperial Col-lege Press.

• Chu, Dominique (2011). Complexity: Against Sys-tems. Theory in Biosciences, Springer Verlag.

• Rocha, Luis M. (1999). "Complex Systems Mod-eling: Using Metaphors From Nature in Simulationand Scientific Models". BITS: Computer and Com-munications News. Computing, Information, andCommunications Division. Los Alamos NationalLaboratory. November 1999

• Ignazio Licata & Ammar Sakaji (eds) (2008).Physics of Emergence and Organization, ISBN 978-981-277-994-6, World Scientific and Imperial Col-lege Press.

• Alfred Hübler, Cory Stephenson, Dave Lyon, RyanSwindeman (2011). Fabrication and programmingof large physically evolving networks Complexity,16(5), pp. 7–8

• De Toni, Alberto and Comello, Luca (2011). Jour-ney into Complexity. Udine: Lulu. ISBN 978-1-4452-6078-5.

5.7 External links• Introduction to complex systems-short course byShlomo Havlin

• Complex systems in scholarpedia.

• (European) Complex Systems Society

• (Australian) Complex systems research network.

• Complex Systems Modeling based on Luis M.Rocha, 1999.

• CRM Complex systems research group

• The Center for Complex Systems Research, Univ.of Illinois at Urbana-Champaign

• FuturICT - Exploring and Managing our Future

Chapter 6

Integrative level

An integrative level, or level of organization, is a setof phenomena emerging on pre-existing phenomena oflower level. Typical examples include life emerging onnon-living substances, and consciousness emerging onnervous systems.

6.1 Levels

The main levels usually acknowledged are those ofmatter, life, mind, and society. These are called stratain Nicolai Hartmann's ontology. They can be further an-alyzed into more specific layers, such as those of parti-cles, atoms, molecules, and rocks forming the materialstratum, or those of cells, organisms, populations, andecosystems forming the life stratum.The sequence of levels is often described as one of in-creasing complexity, although it is not clear whether thisis always true: for example, parasitism emerges on pre-existing organisms, although parasites are often simplerthan their originating forms.

6.2 Philosophies

Integrative levels are discussed variously in the work ofmany philosophers, although few have dealt with thisnotion in a systematic way; among them are SamuelAlexander, Alfred North Whitehead, Conwy Lloyd Mor-gan, George Conger, John G. Bennett, Ervin Laszlo,Joseph Needham, James K. Feibleman, Nicolai Hart-mann, James GrierMiller, KenWilber, and Roberto Poli.Ideas connected to levels can be found in the works ofboth materialist philosophers, like Friedrich Engels, andanti-materialist ones, like Henri Bergson. A recent theoryutilizing concepts from physics and neurophysiology pro-poses that God can be conceptualized within the theoryof integrative levels.[1]

Integrative levels, or the disciplines focusing on them,form the main classes of several knowledge organizationsystems, including Roget’s Thesaurus, the Bliss biblio-graphic classification, the Colon classification, and theInformation Coding Classification. Their use as the basis

of a general classification of phenomena has been espe-cially studied by Douglas Foskett for the ClassificationResearch Group, and by the Integrative Levels Classifi-cation project.

6.3 References[1] Nikoletseas, Michael M. (2014). Deus Absconditus - The

Hidden God. ISBN 978-1495336225.

• Alexander S., Space, time and deity, London, 1920

• Blitz D., Emergent evolution: qualitative novelty andthe levels of reality, Kluwer, 1992

• Conger G.P., The doctrine of levels, Journal of phi-losophy, 22: 1925, 12, p. 309-321

• Feibleman James K., Theory of integrative levels,British journal for the philosophy of science, 5:1954, 17, p. 59-66

• Foskett D.J., The theory of integrative levels and itsrelevance to the design of information systems, Aslibproceedings, 30: 1978, 6, p. 202-208

• Hartmann N., Die Aufbau der realen Welt: Grun-driss der allgemeinen Kategorienlehre, De Gruyter,1940

• Hartmann N., New ways of ontology, GreenwoodPress, 1952

• Morgan C.L., Emergent evolution, Williams andNorgate, London 1923

• Needham J., Integrative levels: a revaluation of theidea of progress, in Time: the refreshing river: es-says and addresses, 1932-1942, Allen and Unwin,London 1943, p. 233-272

• Novikoff A.B., The concept of integrative levels andbiology, Science, 101: 1945, p. 209-215

• Pettersson M., Complexity and evolution, Cam-bridge University Press, 1996

40

6.3. REFERENCES 41

• Poli R., Levels, Axiomathes, 9: 1998, 1-2. p. 197-211

• Poli R., The basic problem of the theory of levels ofreality, Axiomathes, 12: 2001, 3-4, p. 261-283

Chapter 7

Chaos theory

For other uses, see Chaos Theory (disambiguation).Chaos theory is the field of study in mathematics that

A plot of Lorenz attractor for values r = 28, σ = 10, b = 8/3

A double rod pendulum animation showing chaotic behavior.Starting the pendulum from a slightly different initial conditionwould result in a completely different trajectory. The doublerod pendulum is one of the simplest dynamical systems that haschaotic solutions.

studies the behavior of dynamical systems that are highly

sensitive to initial conditions—a response popularly re-ferred to as the butterfly effect.[1] Small differences ininitial conditions (such as those due to rounding errors innumerical computation) yield widely diverging outcomesfor such dynamical systems, rendering long-term predic-tion impossible in general.[2] This happens even thoughthese systems are deterministic, meaning that their futurebehavior is fully determined by their initial conditions,with no random elements involved.[3] In other words, thedeterministic nature of these systems does not make thempredictable.[4][5] This behavior is known as determinis-tic chaos, or simply chaos. The theory was summarizedby Edward Lorenz as:[6]

Chaos: When the present determines thefuture, but the approximate present does notapproximately determine the future.

Chaotic behavior exists in many natural systems, suchas weather and climate.[7][8] This behavior can be stud-ied through analysis of a chaotic mathematical model, orthrough analytical techniques such as recurrence plots andPoincaré maps. Chaos theory has applications in severaldisciplines, including meteorology, sociology, physics,engineering, economics, biology, and philosophy.

7.1 Introduction

Chaos theory concerns deterministic systems whose be-havior can in principle be predicted. Chaotic systems arepredictable for a while and then 'appear' to become ran-dom. The amount of time for which the behavior of achaotic system can be effectively predicted depends onthree things: Howmuch uncertainty we are willing to tol-erate in the forecast, how accurately we are able to mea-sure its current state, and a time scale depending on thedynamics of the system, called the Lyapunov time. Someexamples of Lyapunov times are: chaotic electrical cir-cuits, about 1 millisecond; weather systems, a few days(unproven); the solar system, 50 million years. In chaoticsystems, the uncertainty in a forecast increases exponen-tially with elapsed time. Hence, doubling the forecasttime more than squares the proportional uncertainty in

42

7.2. CHAOTIC DYNAMICS 43

the forecast. This means, in practice, a meaningful pre-diction cannot be made over an interval of more thantwo or three times the Lyapunov time. When meaning-ful predictions cannot be made, the system appears to berandom.[9]

7.2 Chaotic dynamics

The map defined by x → 4 x (1 – x) and y → (x + y) mod 1displays sensitivity to initial x positions. Here, two series of x andy values diverge markedly over time from a tiny initial difference.Note, however, that the y coordinate is effectively only definedmodulo one, so the square region is actually depicting a cylinder,and the two points are closer than they look

In common usage, “chaos”means “a state of disorder”.[10]However, in chaos theory, the term is defined more pre-cisely. Although no universally accepted mathematicaldefinition of chaos exists, a commonly used definitionoriginally formulated by Robert L. Devaney says that, fora dynamical system to be classified as chaotic, it musthave these properties:[11]

1. it must be sensitive to initial conditions

2. it must be topologically mixing

3. it must have dense periodic orbits

7.2.1 Sensitivity to initial conditions

Main article: Butterfly effect

Sensitivity to initial conditions means that each pointin a chaotic system is arbitrarily closely approximated byother points with significantly different future paths, or

trajectories. Thus, an arbitrarily small change, or pertur-bation, of the current trajectory may lead to significantlydifferent future behavior.In some cases, the last two properties in the abovehave been shown to actually imply sensitivity to initialconditions,[12][13] and if attention is restricted to intervals,the second property implies the other two[14] (an alterna-tive, and in general weaker, definition of chaos uses onlythe first two properties in the above list).[15] The mostpractically significant property, sensitivity to initial con-ditions, is redundant in the definition, since it is impliedby two (or for intervals, one) purely topological proper-ties, which are therefore of greater interest to mathemati-cians.Sensitivity to initial conditions is popularly known as the"butterfly effect", so-called because of the title of a papergiven by Edward Lorenz in 1972 to the American Asso-ciation for the Advancement of Science in Washington,D.C., entitled Predictability: Does the Flap of a Butter-fly’s Wings in Brazil set off a Tornado in Texas?. The flap-ping wing represents a small change in the initial condi-tion of the system, which causes a chain of events leadingto large-scale phenomena. Had the butterfly not flappedits wings, the trajectory of the system might have beenvastly different.A consequence of sensitivity to initial conditions is thatif we start with only a finite amount of information aboutthe system (as is usually the case in practice), then beyonda certain time the system will no longer be predictable.This is most familiar in the case of weather, which is gen-erally predictable only about a week ahead.[16] Of course,this does not mean that we cannot say anything aboutevents far in the future; some restrictions on the systemare present. With weather, we know that the temperaturewill never reach 100 °C or fall to −130 °C on earth, butwe are not able to say exactly what day we will have thehottest temperature of the year.In more mathematical terms, the Lyapunov exponentmeasures the sensitivity to initial conditions. Given twostarting trajectories in the phase space that are infinitesi-mally close, with initial separation δZ0 end up divergingat a rate given by

|δZ(t)| ≈ eλt|δZ0|

where t is the time and λ is the Lyapunov exponent. Therate of separation depends on the orientation of the ini-tial separation vector, so a whole spectrum of Lyapunovexponents exist. The number of Lyapunov exponents isequal to the number of dimensions of the phase space,though it is common to just refer to the largest one. Forexample, themaximal Lyapunov exponent (MLE) is mostoften used because it determines the overall predictabil-ity of the system. A positive MLE is usually taken as anindication that the system is chaotic.Also, other properties relate to sensitivity of initial con-

44 CHAPTER 7. CHAOS THEORY

ditions, such as measure-theoretical mixing (as discussedin ergodic theory) and properties of a K-system.[5]

7.2.2 Topological mixing

The map defined by x→4 x (1 – x) and y→ (x + y)mod 1 alsodisplays topological mixing. Here, the blue region is transformedby the dynamics first to the purple region, then to the pink andred regions, and eventually to a cloud of vertical lines scatteredacross the space.

Topological mixing (or topological transitivity) meansthat the system will evolve over time so that any given re-gion or open set of its phase space will eventually overlapwith any other given region. This mathematical conceptof “mixing” corresponds to the standard intuition, and themixing of colored dyes or fluids is an example of a chaoticsystem.Topological mixing is often omitted from popular ac-counts of chaos, which equate chaos with only sensitiv-ity to initial conditions. However, sensitive dependenceon initial conditions alone does not give chaos. For ex-ample, consider the simple dynamical system producedby repeatedly doubling an initial value. This system hassensitive dependence on initial conditions everywhere,since any pair of nearby points will eventually becomewidely separated. However, this example has no topolog-ical mixing, and therefore has no chaos. Indeed, it hasextremely simple behavior: all points except 0 will tendto positive or negative infinity.

7.2.3 Density of periodic orbits

For a chaotic system to have a dense periodic orbit meansthat every point in the space is approached arbitrar-ily closely by periodic orbits.[17] The one-dimensionallogistic map defined by x → 4 x (1 – x) is one of thesimplest systems with density of periodic orbits. For

example, 5−√5

8 → 5+√5

8 → 5−√5

8 (or approximately0.3454915 → 0.9045085 → 0.3454915) is an (unsta-ble) orbit of period 2, and similar orbits exist for peri-ods 4, 8, 16, etc. (indeed, for all the periods specified bySharkovskii’s theorem).[18]

Sharkovskii’s theorem is the basis of the Li and Yorke[19](1975) proof that any one-dimensional system that ex-hibits a regular cycle of period three will also display reg-ular cycles of every other length, as well as completelychaotic orbits.

7.2.4 Strange attractors

The Lorenz attractor displays chaotic behavior. These two plotsdemonstrate sensitive dependence on initial conditions within theregion of phase space occupied by the attractor.

Some dynamical systems, like the one-dimensionallogistic map defined by x → 4 x (1 – x), are chaotic ev-erywhere, but in many cases chaotic behavior is foundonly in a subset of phase space. The cases of most in-terest arise when the chaotic behavior takes place on anattractor, since then a large set of initial conditions willlead to orbits that converge to this chaotic region.An easy way to visualize a chaotic attractor is to start witha point in the basin of attraction of the attractor, and thensimply plot its subsequent orbit. Because of the topologi-cal transitivity condition, this is likely to produce a pictureof the entire final attractor, and indeed both orbits shownin the figure on the right give a picture of the generalshape of the Lorenz attractor. This attractor results froma simple three-dimensional model of the Lorenz weathersystem. The Lorenz attractor is perhaps one of the best-known chaotic system diagrams, probably because it wasnot only one of the first, but it is also one of the mostcomplex and as such gives rise to a very interesting pat-tern, that with a little imagination, looks like the wings ofa butterfly.Unlike fixed-point attractors and limit cycles, the attrac-tors that arise from chaotic systems, known as strange at-tractors, have great detail and complexity. Strange attrac-tors occur in both continuous dynamical systems (such as

7.2. CHAOTIC DYNAMICS 45

the Lorenz system) and in some discrete systems (such asthe Hénon map). Other discrete dynamical systems havea repelling structure called a Julia set which forms at theboundary between basins of attraction of fixed points –Julia sets can be thought of as strange repellers. Bothstrange attractors and Julia sets typically have a fractalstructure, and the fractal dimension can be calculated forthem.

7.2.5 Minimum complexity of a chaoticsystem

Bifurcation diagram of the logistic map x → r x (1 – x). Eachvertical slice shows the attractor for a specific value of r. Thediagram displays period-doubling as r increases, eventually pro-ducing chaos.

Discrete chaotic systems, such as the logistic map, canexhibit strange attractors whatever their dimensionality.In contrast, for continuous dynamical systems, thePoincaré–Bendixson theorem shows that a strange attrac-tor can only arise in three or more dimensions. Finite-dimensional linear systems are never chaotic; for a dy-namical system to display chaotic behavior, it has to beeither nonlinear or infinite-dimensional.The Poincaré–Bendixson theorem states that a two-dimensional differential equation has very regular behav-ior. The Lorenz attractor discussed above is generated bya system of three differential equations such as:

dxdt = σy − σx,

dydt = ρx− xz − y,

dzdt = xy − βz.

where x , y , and z make up the system state, t is time,and σ , ρ , β are the system parameters. Five of the termson the right hand side are linear, while two are quadratic;a total of seven terms. Another well-known chaotic at-tractor is generated by the Rossler equations which haveonly one nonlinear term out of seven. Sprott [20] found

a three-dimensional system with just five terms, that hadonly one nonlinear term, which exhibits chaos for certainparameter values. Zhang and Heidel [21][22] showed that,at least for dissipative and conservative quadratic systems,three-dimensional quadratic systems with only three orfour terms on the right-hand side cannot exhibit chaoticbehavior. The reason is, simply put, that solutions to suchsystems are asymptotic to a two-dimensional surface andtherefore solutions are well behaved.While the Poincaré–Bendixson theorem shows that a con-tinuous dynamical system on the Euclidean plane can-not be chaotic, two-dimensional continuous systems withnon-Euclidean geometry can exhibit chaotic behavior.[23]Perhaps surprisingly, chaos may occur also in linear sys-tems, provided they are infinite dimensional.[24] A theoryof linear chaos is being developed in a branch of mathe-matical analysis known as functional analysis.

7.2.6 Jerk systems

In physics, jerk is the third derivative of position, and assuch, in mathematics differential equations of the form

J(...x, x, x, x

)= 0

are sometimes called Jerk equations. It has been shown,that a jerk equation, which is equivalent to a system ofthree first order, ordinary, non-linear differential equa-tions is in a certain sense the minimal setting for solu-tions showing chaotic behaviour. This motivates math-ematical interest in jerk systems. Systems involving afourth or higher derivative are called accordingly hyper-jerk systems.[25]

A jerk system’s behavior is described by a jerk equation,and for certain jerk equations, simple electronic circuitsmay be designed which model the solutions to this equa-tion. These circuits are known as jerk circuits.One of the most interesting properties of jerk circuits isthe possibility of chaotic behavior. In fact, certain well-known chaotic systems, such as the Lorenz attractor andthe Rössler map, are conventionally described as a systemof three first-order differential equations, but which maybe combined into a single (although rather complicated)jerk equation. Nonlinear jerk systems are in a sense min-imally complex systems to show chaotic behaviour, thereis no chaotic system involving only two first-order, or-dinary differential equations (the system resulting in anequation of second order only).An example of a jerk equation with nonlinearity in themagnitude of x is:

d3xdt3 +A

d2xdt2 +

dxdt − |x|+ 1 = 0.

46 CHAPTER 7. CHAOS THEORY

Here, A is an adjustable parameter. This equation hasa chaotic solution for A=3/5 and can be implementedwith the following jerk circuit; the required nonlinearityis brought about by the two diodes:

In the above circuit, all resistors are of equal value, exceptRA = R/A = 5R/3 , and all capacitors are of equalsize. The dominant frequency will be 1/2πRC . Theoutput of op amp 0 will correspond to the x variable, theoutput of 1 will correspond to the first derivative of x andthe output of 2 will correspond to the second derivative.

7.3 Spontaneous order

Under the right conditions, chaos will spontaneouslyevolve into a lockstep pattern. In the Kuramoto model,four conditions suffice to produce synchronization in achaotic system. Examples include the coupled oscillationof Christiaan Huygens' pendulums, fireflies, neurons, theLondon Millenium Bridge resonance, and large arrays ofJosephson junctions.[26]

7.4 History

An early proponent of chaos theory was Henri Poincaré.In the 1880s, while studying the three-body problem,he found that there can be orbits that are nonperiodic,and yet not forever increasing nor approaching a fixedpoint.[27][28] In 1898 Jacques Hadamard published an in-fluential study of the chaoticmotion of a free particle glid-ing frictionlessly on a surface of constant negative cur-vature, called "Hadamard’s billiards".[29] Hadamard wasable to show that all trajectories are unstable, in that allparticle trajectories diverge exponentially from one an-other, with a positive Lyapunov exponent.Chaos theory got its start in the field of ergodic theory.Later studies, also on the topic of nonlinear differentialequations, were carried out by George David Birkhoff,[30]Andrey Nikolaevich Kolmogorov,[31][32][33] Mary LucyCartwright and John Edensor Littlewood,[34] and StephenSmale.[35] Except for Smale, these studies were all di-rectly inspired by physics: the three-body problem in the

Barnsley fern created using the chaos game. Natural forms(ferns, clouds, mountains, etc.) may be recreated through anIterated function system (IFS).

case of Birkhoff, turbulence and astronomical problemsin the case of Kolmogorov, and radio engineering in thecase of Cartwright and Littlewood. Although chaoticplanetary motion had not been observed, experimental-ists had encountered turbulence in fluid motion and non-periodic oscillation in radio circuits without the benefit ofa theory to explain what they were seeing.Despite initial insights in the first half of the twentiethcentury, chaos theory became formalized as such only af-ter mid-century, when it first became evident to some sci-entists that linear theory, the prevailing system theory atthat time, simply could not explain the observed behaviorof certain experiments like that of the logistic map. Whathad been attributed to measure imprecision and simple"noise" was considered by chaos theorists as a full com-ponent of the studied systems.The main catalyst for the development of chaos theorywas the electronic computer. Much of the mathematicsof chaos theory involves the repeated iteration of simplemathematical formulas, which would be impractical todo by hand. Electronic computers made these repeatedcalculations practical, while figures and images made itpossible to visualize these systems. As a graduate stu-dent in Chihiro Hayashi's laboratory at Kyoto University,Yoshisuke Ueda was experimenting with analog comput-ers and noticed, on Nov. 27, 1961, what he called “ran-domly transitional phenomena”. Yet his advisor did notagree with his conclusions at the time, and did not allowhim to report his findings until 1970.[36][37]

An early pioneer of the theory was Edward Lorenz whoseinterest in chaos came about accidentally through hiswork on weather prediction in 1961.[7] Lorenz was us-ing a simple digital computer, a Royal McBee LGP-30,to run his weather simulation. He wanted to see a se-quence of data again and to save time he started the sim-

7.4. HISTORY 47

Turbulence in the tip vortex from an airplane wing. Studies ofthe critical point beyond which a system creates turbulence wereimportant for chaos theory, analyzed for example by the Sovietphysicist Lev Landau, who developed the Landau-Hopf theoryof turbulence. David Ruelle and Floris Takens later predicted,against Landau, that fluid turbulence could develop through astrange attractor, a main concept of chaos theory.

ulation in the middle of its course. He was able to dothis by entering a printout of the data corresponding toconditions in the middle of his simulation which he hadcalculated last time. To his surprise the weather that themachine began to predict was completely different fromthe weather calculated before. Lorenz tracked this downto the computer printout. The computer worked with 6-digit precision, but the printout rounded variables off toa 3-digit number, so a value like 0.506127 was printedas 0.506. This difference is tiny and the consensus atthe time would have been that it should have had prac-tically no effect. However, Lorenz had discovered thatsmall changes in initial conditions produced large changesin the long-term outcome.[38] Lorenz’s discovery, whichgave its name to Lorenz attractors, showed that even de-tailed atmospheric modelling cannot, in general, makeprecise long-term weather predictions.In 1963, Benoit Mandelbrot found recurring patterns atevery scale in data on cotton prices.[39] Beforehand hehad studied information theory and concluded noise waspatterned like a Cantor set: on any scale the proportion ofnoise-containing periods to error-free periods was a con-stant – thus errors were inevitable andmust be planned forby incorporating redundancy.[40] Mandelbrot describedboth the “Noah effect” (in which sudden discontinuouschanges can occur) and the “Joseph effect” (in which per-sistence of a value can occur for a while, yet suddenlychange afterwards).[41][42] This challenged the idea thatchanges in price were normally distributed. In 1967,he published "How long is the coast of Britain? Sta-tistical self-similarity and fractional dimension", show-ing that a coastline’s length varies with the scale of themeasuring instrument, resembles itself at all scales, andis infinite in length for an infinitesimally small measur-

ing device.[43] Arguing that a ball of twine appears to bea point when viewed from far away (0-dimensional), aball when viewed from fairly near (3-dimensional), or acurved strand (1-dimensional), he argued that the dimen-sions of an object are relative to the observer and may befractional. An object whose irregularity is constant overdifferent scales (“self-similarity”) is a fractal (examplesinclude the Menger sponge, the Sierpiński gasket, andthe Koch curve or “snowflake”, which is infinitely longyet encloses a finite space and has a fractal dimension ofcirca 1.2619). In 1982 Mandelbrot published The Frac-tal Geometry of Nature, which became a classic of chaostheory. Biological systems such as the branching of thecirculatory and bronchial systems proved to fit a fractalmodel.[44]

In December 1977, the New York Academy of Sciencesorganized the first symposium on Chaos, attended byDavid Ruelle, Robert May, James A. Yorke (coiner ofthe term “chaos” as used in mathematics), Robert Shaw,and the meteorologist Edward Lorenz. The followingyear, independently Pierre Coullet and Charles Tresserwith the article “Iterations d'endomorphismes et groupede renormalisation” and Mitchell Feigenbaum with thearticle “Quantitative Universality for a Class of Non-linear Transformations” described logistic maps.[45][46]They notably discovered the universality in chaos, per-mitting the application of chaos theory to many differentphenomena.In 1979, Albert J. Libchaber, during a symposium orga-nized in Aspen by Pierre Hohenberg, presented his exper-imental observation of the bifurcation cascade that leadsto chaos and turbulence in Rayleigh–Bénard convectionsystems. He was awarded the Wolf Prize in Physics in1986 along with Mitchell J. Feigenbaum for their inspir-ing achievements.[47]

In 1986, the New York Academy of Sciences co-organized with the National Institute of Mental Healthand the Office of Naval Research the first importantconference on chaos in biology and medicine. There,Bernardo Huberman presented a mathematical model ofthe eye tracking disorder among schizophrenics.[48] Thisled to a renewal of physiology in the 1980s through theapplication of chaos theory, for example, in the study ofpathological cardiac cycles.In 1987, Per Bak, Chao Tang and Kurt Wiesenfeld pub-lished a paper in Physical Review Letters[49] describing forthe first time self-organized criticality (SOC), consideredto be one of the mechanisms by which complexity arisesin nature.Alongside largely lab-based approaches such as the Bak–Tang–Wiesenfeld sandpile, many other investigationshave focused on large-scale natural or social systems thatare known (or suspected) to display scale-invariant be-havior. Although these approaches were not always wel-comed (at least initially) by specialists in the subjectsexamined, SOC has nevertheless become established as

48 CHAPTER 7. CHAOS THEORY

a strong candidate for explaining a number of naturalphenomena, including earthquakes (which, long beforeSOC was discovered, were known as a source of scale-invariant behavior such as the Gutenberg–Richter law de-scribing the statistical distribution of earthquake sizes,and the Omori law[50] describing the frequency of af-tershocks), solar flares, fluctuations in economic systemssuch as financial markets (references to SOC are com-mon in econophysics), landscape formation, forest fires,landslides, epidemics, and biological evolution (whereSOC has been invoked, for example, as the dynami-cal mechanism behind the theory of "punctuated equi-libria" put forward by Niles Eldredge and Stephen JayGould). Given the implications of a scale-free distribu-tion of event sizes, some researchers have suggested thatanother phenomenon that should be considered an exam-ple of SOC is the occurrence of wars. These investiga-tions of SOC have included both attempts at modelling(either developing new models or adapting existing onesto the specifics of a given natural system), and extensivedata analysis to determine the existence and/or character-istics of natural scaling laws.In the same year, James Gleick published Chaos: Mak-ing a New Science, which became a best-seller and intro-duced the general principles of chaos theory as well asits history to the broad public, though his history under-emphasized important Soviet contributions.[51] Initiallythe domain of a few, isolated individuals, chaos theoryprogressively emerged as a transdisciplinary and institu-tional discipline, mainly under the name of nonlinear sys-tems analysis. Alluding to Thomas Kuhn's concept of aparadigm shift exposed in The Structure of Scientific Rev-olutions (1962), many “chaologists” (as some describedthemselves) claimed that this new theory was an exampleof such a shift, a thesis upheld by Gleick.The availability of cheaper, more powerful comput-ers broadens the applicability of chaos theory. Cur-rently, chaos theory continues to be a very activearea of research,[52] involving many different disci-plines (mathematics, topology, physics, social systems,population modeling, biology, meteorology, astrophysics,information theory, computational neuroscience, etc.).

7.5 Distinguishing random fromchaotic data

It can be difficult to tell from data whether a physical orother observed process is random or chaotic, because inpractice no time series consists of a pure “signal”. Therewill always be some form of corrupting noise, even ifit is present as round-off or truncation error. Thus anyreal time series, even if mostly deterministic, will containsome (pseudo-)randomness.[53][54]

All methods for distinguishing deterministic andstochastic processes rely on the fact that a deterministic

system always evolves in the same way from a givenstarting point.[53][55] Thus, given a time series to test fordeterminism, one can

1. pick a test state;

2. search the time series for a similar or nearby state;and

3. compare their respective time evolutions.

Define the error as the difference between the time evolu-tion of the test state and the time evolution of the nearbystate. A deterministic system will have an error that ei-ther remains small (stable, regular solution) or increasesexponentially with time (chaos). A stochastic system willhave a randomly distributed error.[56]

Essentially, all measures of determinism taken from timeseries rely upon finding the closest states to a given teststate (e.g., correlation dimension, Lyapunov exponents,etc.). To define the state of a system, one typically re-lies on phase space embedding methods such as Poincaréplots.[57] Typically one chooses an embedding dimensionand investigates the propagation of the error between twonearby states. If the error looks random, one increases thedimension. If the dimension can be increased to obtaina deterministically looking error, then analysis is done.Though it may sound simple, one complication is that asthe dimension increases, the search for a nearby state re-quires a lot more computation time and a lot of data (theamount of data required increases exponentially with em-bedding dimension) to find a suitably close candidate. Ifthe embedding dimension (number of measures per state)is chosen too small (less than the “true” value), determin-istic data can appear to be random, but in theory thereis no problem choosing the dimension too large – themethod will work.When a nonlinear deterministic system is attended byexternal fluctuations, its trajectories present serious andpermanent distortions. Furthermore, the noise is ampli-fied due to the inherent nonlinearity and reveals totallynew dynamical properties. Statistical tests attemptingto separate noise from the deterministic skeleton or in-versely isolate the deterministic part risk failure. Thingsbecome worse when the deterministic component is anonlinear feedback system.[58] In presence of interactionsbetween nonlinear deterministic components and noise,the resulting nonlinear series can display dynamics thattraditional tests for nonlinearity are sometimes not ableto capture.[59]

The question of how to distinguish deterministic chaoticsystems from stochastic systems has also been discussedin philosophy. It has been shown that they might beobservationally equivalent.[60]

7.6. APPLICATIONS 49

A conus textile shell, similar in appearance to Rule 30, a cellularautomaton with chaotic behaviour.[61]

7.6 Applications

Chaos theory was born from observing weather pat-terns, but it has become applicable to a variety ofother situations. Some areas benefiting from chaostheory today are geology, mathematics, microbiology,biology, computer science, economics,[62][63][64]engineering,[65] finance,[66][67] algorithmic trad-ing,[68][69][70] meteorology, philosophy, physics, politics,population dynamics,[71] psychology, and robotics. Afew categories are listed below with examples, but thisis by no means a comprehensive list as new applicationsare appearing.

7.6.1 Computer science

Chaos theory is not new to computer science and hasbeen used for many years in cryptography. One typeof encryption, secret key or symmetric key, relies ondiffusion and confusion, which is modeled well by chaostheory.[72] Another type of computing, DNA comput-ing, when paired with chaos theory, offers a more ef-ficient way to encrypt images and other information.[73]Robotics is another area that has recently benefited fromchaos theory. Instead of robots acting in a trial-and-errortype of refinement to interact with their environment,chaos theory has been used to build a predictivemodel.[74]Chaotic dynamics have been exhibited by passive walkingbiped robots.[75]

7.6.2 Biology

For over a hundred years, biologists have been keepingtrack of populations of different species with populationmodels. Most models are continuous, but recently sci-entists have been able to implement chaotic models incertain populations.[76] For example, a study on modelsof Canadian lynx showed there was chaotic behavior inthe population growth.[77] Chaos can also be found in

ecological systems, such as hydrology. While a chaoticmodel for hydrology has its shortcomings, there is stillmuch to be learned from looking at the data through thelens of chaos theory.[78] Another biological application isfound in cardiotocography. Fetal surveillance is a deli-cate balance of obtaining accurate information while be-ing as noninvasive as possible. Better models of warn-ing signs of fetal hypoxia can be obtained through chaoticmodeling.[79]

7.6.3 Other areas

In chemistry, predicting gas solubility is essential to man-ufacturing polymers, but models using particle swarm op-timization (PSO) tend to converge to the wrong points.An improved version of PSO has been created by in-troducing chaos, which keeps the simulations from get-ting stuck.[80] In celestial mechanics, especially when ob-serving asteroids, applying chaos theory leads to bet-ter predictions about when these objects will come inrange of Earth and other planets.[81] In quantum physicsand electrical engineering, the study of large arraysof Josephson junctions benefitted greatly from chaostheory.[82] Closer to home, coal mines have always beendangerous places where frequent natural gas leaks causemany deaths. Until recently, there was no reliable way topredict when they would occur. But these gas leaks havechaotic tendencies that, when properly modeled, can bepredicted fairly accurately.[83]

Chaos theory can be applied outside of the natural sci-ences. By adapting a model of career counseling to in-clude a chaotic interpretation of the relationship betweenemployees and the job market, better suggestions canbe made to people struggling with career decisions.[84]Modern organizations are increasingly seen as open com-plex adaptive systems, with fundamental natural non-linear structures, subject to internal and external forceswhich may be sources of chaos. The chaos metaphor—used in verbal theories—grounded onmathematical mod-els and psychological aspects of human behavior provideshelpful insights to describing the complexity of smallwork groups, that go beyond the metaphor itself.[85]

It is possible that economic models can also be improvedthrough an application of chaos theory, but predicting thehealth of an economic system and what factors influenceit most is an extremely complex task.[86] Economic and fi-nancial systems are fundamentally different from those inthe physical and natural sciences since the former are in-herently stochastic in nature, as they result from the inter-actions of people, and thus pure deterministic models areunlikely to provide accurate representations of the data.The empirical literature that tests for chaos in economicsand finance presents very mixed results, in part due toconfusion between specific tests for chaos and more gen-eral tests for non-linear relationships.[87]

Traffic forecasting is another area that greatly benefits

50 CHAPTER 7. CHAOS THEORY

The red cars and blue cars take turns to move; the red ones onlymove upwards, and the blue ones move rightwards. Every time,all the cars of the same colour try to move one step if there isno car in front of it. Here, the model has self-organized in asomewhat geometric pattern where there are some traffic jamsand some areas where cars can move at top speed.

from applications of chaos theory. Better predictionsof when traffic will occur would allow measures to betaken for it to be dispersed before the traffic starts, ratherthan after. Combining chaos theory principles with a fewother methods has led to a more accurate short-term pre-diction model (see the plot of the BML traffic model atright).[88]

Chaos theory also finds applications in psychology. Forexample, in modeling group behavior in which heteroge-neous members may behave as if sharing to different de-grees what inWilfred Bion's theory is a basic assumption,the group dynamics is the result of the individual dynam-ics of the members: each individual reproduces the groupdynamics in a different scale, and the chaotic behavior ofthe group is reflected in each member.[89]

7.7 See also

7.8 References

[1] Boeing (2015). “Chaos Theory and the Logistic Map”.Retrieved 2015-07-16.

[2] Kellert, Stephen H. (1993). In the Wake of Chaos: Un-predictable Order in Dynamical Systems. University ofChicago Press. p. 32. ISBN 0-226-42976-8.

[3] Kellert 1993, p. 56

[4] Kellert 1993, p. 62

[5] Werndl, Charlotte (2009). “What are the New Impli-cations of Chaos for Unpredictability?". The BritishJournal for the Philosophy of Science 60 (1): 195–220.doi:10.1093/bjps/axn053.

[6] Danforth, Christopher M. (April 2013). “Chaos in anAtmosphere Hanging on a Wall”. Mathematics of PlanetEarth 2013. Retrieved 4 April 2013.

[7] Lorenz, Edward N. (1963). “Deterministic non-periodicflow”. Journal of the Atmospheric Sciences 20 (2): 130–141. Bibcode:1963JAtS...20..130L. doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.

[8] Ivancevic, Vladimir G.; Tijana T. Ivancevic (2008).Complex nonlinearity: chaos, phase transitions, topologychange, and path integrals. Springer. ISBN 978-3-540-79356-4.

[9] Sync: The Emerging Science of Spontaneous Order, StevenStrogatz, Hyperion, New York, 2003, pages 189-190.

[10] Definition of chaos at Wiktionary;

[11] Hasselblatt, Boris; Anatole Katok (2003). A First Coursein Dynamics: With a Panorama of Recent Developments.Cambridge University Press. ISBN 0-521-58750-6.

[12] Elaydi, Saber N. (1999). Discrete Chaos. Chapman &Hall/CRC. p. 117. ISBN 1-58488-002-3.

[13] Basener, William F. (2006). Topology and its applica-tions. Wiley. p. 42. ISBN 0-471-68755-3.

[14] Vellekoop, Michel; Berglund, Raoul (April 1994). “OnIntervals, Transitivity = Chaos”. The American Mathe-matical Monthly 101 (4): 353–5. doi:10.2307/2975629.JSTOR 2975629.

[15] Medio, Alfredo; Lines, Marji (2001). Nonlinear Dynam-ics: A Primer. Cambridge University Press. p. 165. ISBN0-521-55874-3.

[16] Watts, Robert G. (2007). Global Warming and the Futureof the Earth. Morgan & Claypool. p. 17.

[17] Devaney 2003

[18] Alligood, Sauer & Yorke 1997

[19] Li, T.Y.; Yorke, J.A. (1975). “Period Three ImpliesChaos” (PDF). American Mathematical Monthly 82 (10):985–92. doi:10.2307/2318254.

[20] Sprott, J.C. (1997). “Simplest dissipative chaoticflow”. Physics Letters A 228 (4–5): 271.Bibcode:1997PhLA..228..271S. doi:10.1016/S0375-9601(97)00088-1.

[21] Fu, Z.; Heidel, J. (1997). “Non-chaotic behaviour inthree-dimensional quadratic systems”. Nonlinearity10 (5): 1289. Bibcode:1997Nonli..10.1289F.doi:10.1088/0951-7715/10/5/014.

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[36] Abraham & Ueda 2001, See Chapters 3 and 4

[37] Sprott 2003, p. 89

[38] Gleick, James (1987). Chaos: Making a New Science.London: Cardinal. p. 17. ISBN 0-434-29554-X.

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[45] Feigenbaum, Mitchell (July 1978). “Quantitativeuniversality for a class of nonlinear transforma-tions”. Journal of Statistical Physics 19 (1): 25–52.Bibcode:1978JSP....19...25F. doi:10.1007/BF01020332.

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[70] Peters, / Edgar E. (1996). Chaos and order in the capitalmarkets : a new view of cycles, prices, and market volatility(2nd ed.). New York: John Wiley & Sons. ISBN 978-0471139386.

[71] Dilão, R.; Domingos, T. (2001). “Periodic and Quasi-Periodic Behavior in Resource Dependent Age StructuredPopulation Models”. Bulletin of Mathematical Biology63 (2): 207–230. doi:10.1006/bulm.2000.0213. PMID11276524.

[72] Wang, Xingyuan; Zhao, Jianfeng (2012). “An im-proved key agreement protocol based on chaos”.Commun. Nonlinear Sci. Numer. Simul. 15 (12):4052–4057. Bibcode:2010CNSNS..15.4052W.doi:10.1016/j.cnsns.2010.02.014.

[73] Babaei, Majid (2013). “A novel text and image encryp-tion method based on chaos theory and DNA computing”.Natural Computing. an International Journal 12 (1): 101–107. doi:10.1007/s11047-012-9334-9.

[74] Nehmzow, Ulrich; Keith Walker (Dec 2005). “Quanti-tative description of robot–environment interaction usingchaos theory”. Robotics and Autonomous Systems 53 (3–4): 177–193. doi:10.1016/j.robot.2005.09.009.

[75] Goswami, Ambarish; Thuilot, Benoit; Espiau, Bernard(1998). “A Study of the Passive Gait of a Compass-Like Biped Robot: Symmetry and Chaos”. The Interna-tional Journal of Robotics Research 17 (12): 1282–1301.doi:10.1177/027836499801701202.

[76] Eduardo, Liz; Ruiz-Herrera, Alfonso (2012). “Chaosin discrete structured population models”. SIAM Jour-nal on Applied Dynamical Systems 11 (4): 1200–1214.doi:10.1137/120868980.

7.9. SCIENTIFIC LITERATURE 53

[77] Lai, Dejian (1996). “Comparison study of AR models onthe Canadian lynx data: a close look at BDS statistic”.Computational Statistics \& Data Analysis 22 (4): 409–423. doi:10.1016/0167-9473(95)00056-9.

[78] Sivakumar, B (31 January 2000). “Chaos the-ory in hydrology: important issues and interpre-tations”. Journal of Hydrology 227 (1–4): 1–20. Bibcode:2000JHyd..227....1S. doi:10.1016/S0022-1694(99)00186-9.

[79] Bozóki, Zsolt (February 1997). “Chaos theory and powerspectrum analysis in computerized cardiotocography”.European Journal of Obstetrics & Gynecology and Re-productive Biology 71 (2): 163–168. doi:10.1016/s0301-2115(96)02628-0.

[80] Li, Mengshan; Xingyuan Huanga; Hesheng Liua; Bingxi-ang Liub; Yan Wub; Aihua Xiongc; Tianwen Dong (25October 2013). “Prediction of gas solubility in poly-mers by back propagation artificial neural network basedon self-adaptive particle swarm optimization algorithmand chaos theory”. Fluid Phase Equilibria 356: 11–17.doi:10.1016/j.fluid.2013.07.017.

[81] Morbidelli, A. (2001). “Chaotic diffusion in celestial me-chanics”. Regular & Chaotic Dynamics. International Sci-entific Journal 6 (4): 339–353.

[82] Steven Strogatz, Sync: The Emerging Science of Sponta-neous Order, Hyperion, 2003

[83] Dingqi, Li; Yuanping Chenga; Lei Wanga; HaifengWanga; LiangWanga; Hongxing Zhou (May 2011). “Pre-diction method for risks of coal and gas outbursts basedon spatial chaos theory using gas desorption index of drillcuttings”. Mining Science and Technology 21 (3): 439–443.

[84] Pryor, Robert G. L.; Norman E. Aniundson; Jim E. H.Bright (June 2008). “Probabilities and Possibilities: TheStrategic Counseling Implications of the Chaos Theory ofCareers”. The Career Development Quarterly 56: 309–318. doi:10.1002/j.2161-0045.2008.tb00096.x.

[85] Dal Forno, Arianna; Merlone, Ugo (2013). “ChaoticDynamics in Organization Theory”. In Bischi, GianItalo; Chiarella, Carl; Shusko, Irina. Global Analysis ofDynamic Models in Economics and Finance. Springer-Verlag. pp. 185–204. ISBN 978-3-642-29503-4.

[86] Juárez, Fernando (2011). “Applying the theory of chaosand a complex model of health to establish relationsamong financial indicators”. Procedia Computer Science3: 982–986. doi:10.1016/j.procs.2010.12.161.

[87] Brooks, Chris (1998). “Chaos in foreign exchange mar-kets: a sceptical view”. Computational Economics 11:265–281. doi:10.1023/A:1008650024944. ISSN 1572-9974.

[88] Wang, Jin; Qixin Shi (February 2013). “Short-term trafficspeed forecasting hybrid model based on Chaos–WaveletAnalysis-Support Vector Machine theory”. Transporta-tion Research Part C: Emerging Technologies 27: 219–232.doi:10.1016/j.trc.2012.08.004.

[89] Dal Forno, Arianna; Merlone, Ugo (2013). “Nonlineardynamics in work groups with Bion’s basic assumptions”.Nonlinear Dynamics, Psychology, and Life Sciences 17 (2):295–315. ISSN 1090-0578.

7.9 Scientific literature

7.9.1 Articles

• Sharkovskii, A.N. (1964). “Co-existence of cyclesof a continuous mapping of the line into itself”.Ukrainian Math. J. 16: 61–71.

• Li, T.Y.; Yorke, J.A. (1975). “Period Three Im-plies Chaos”. American Mathematical Monthly 82(10): 985–92. Bibcode:1975AmMM...82..985L.doi:10.2307/2318254.

• Crutchfield; Tucker; Morrison; J.D.; Packard;N.H.; Shaw; R.S (December 1986). “Chaos”.Scientific American 255 (6): 38–49 (bibliographyp.136). Bibcode:1986SciAm.255...38T. Onlineversion (Note: the volume and page citation cited forthe online text differ from that cited here. The ci-tation here is from a photocopy, which is consistentwith other citations found online, but which don'tprovide article views. The online content is identi-cal to the hardcopy text. Citation variations will berelated to country of publication).

• Kolyada, S.F. (2004). “Li-Yorke sensitivity andother concepts of chaos”. Ukrainian Math. J. 56(8): 1242–57. doi:10.1007/s11253-005-0055-4.

• Strelioff, C.; Hübler, A. (2006). “Medium-TermPrediction of Chaos” (PDF). Phys. Rev. Lett. 96(4): 044101. Bibcode:2006PhRvL..96d4101S.doi:10.1103/PhysRevLett.96.044101. PMID16486826. 044101.

• Hübler, A.; Foster, G.; Phelps, K. (2007).“Managing Chaos: Thinking out of the Box” (PDF).Complexity 12 (3): 10–13. doi:10.1002/cplx.20159.

7.9.2 Textbooks

• Alligood, K.T.; Sauer, T.; Yorke, J.A. (1997).Chaos: an introduction to dynamical systems.Springer-Verlag. ISBN 0-387-94677-2.

• Baker, G. L. (1996). Chaos, Scattering and Statisti-cal Mechanics. Cambridge University Press. ISBN0-521-39511-9.

• Badii, R.; Politi A. (1997). Complexity: hierarchicalstructures and scaling in physics. Cambridge Univer-sity Press. ISBN 0-521-66385-7.

54 CHAPTER 7. CHAOS THEORY

• Bunde; Havlin, Shlomo, eds. (1996). Fractals andDisordered Systems. Springer. ISBN 3642848702.and Bunde; Havlin, Shlomo, eds. (1994). Fractalsin Science. Springer. ISBN 3-540-56220-6.

• Collet, Pierre, and Eckmann, Jean-Pierre (1980). It-erated Maps on the Interval as Dynamical Systems.Birkhauser. ISBN 0-8176-4926-3.

• Devaney, Robert L. (2003). An Introduction toChaotic Dynamical Systems (2nd ed.). WestviewPress. ISBN 0-8133-4085-3.

• Gollub, J. P.; Baker, G. L. (1996). Chaotic dy-namics. Cambridge University Press. ISBN 0-521-47685-2.

• Guckenheimer, John; Holmes, Philip (1983). Non-linear Oscillations, Dynamical Systems, and Bifur-cations of Vector Fields. Springer-Verlag. ISBN 0-387-90819-6.

• Gulick, Denny (1992). Encounters with Chaos.McGraw-Hill. ISBN 0-07-025203-3.

• Gutzwiller, Martin (1990). Chaos in Classical andQuantum Mechanics. Springer-Verlag. ISBN 0-387-97173-4.

• Hoover, William Graham (2001) [1999]. Time Re-versibility, Computer Simulation, and Chaos. WorldScientific. ISBN 981-02-4073-2.

• Kautz, Richard (2011). Chaos: The Science of Pre-dictable Random Motion. Oxford University Press.ISBN 978-0-19-959458-0.

• Kiel, L. Douglas; Elliott, Euel W. (1997). ChaosTheory in the Social Sciences. Perseus Publishing.ISBN 0-472-08472-0.

• Moon, Francis (1990). Chaotic and Fractal Dynam-ics. Springer-Verlag. ISBN 0-471-54571-6.

• Ott, Edward (2002). Chaos in Dynamical Systems.Cambridge University Press. ISBN 0-521-01084-5.

• Strogatz, Steven (2000). Nonlinear Dynamics andChaos. Perseus Publishing. ISBN 0-7382-0453-6.

• Sprott, Julien Clinton (2003). Chaos and Time-Series Analysis. Oxford University Press. ISBN 0-19-850840-9.

• Tél, Tamás; Gruiz, Márton (2006). Chaotic dynam-ics: An introduction based on classical mechanics.Cambridge University Press. ISBN 0-521-83912-2.

• Teschl, Gerald (2012). Ordinary DifferentialEquations and Dynamical Systems. Providence:American Mathematical Society. ISBN 978-0-8218-8328-0.

• Thompson J M T, Stewart H B (2001). NonlinearDynamics And Chaos. John Wiley and Sons Ltd.ISBN 0-471-87645-3.

• Tufillaro; Reilly (1992). An experimental approachto nonlinear dynamics and chaos. Addison-Wesley.ISBN 0-201-55441-0.

• Wiggins, Stephen (2003). Introduction to AppliedDynamical Systems and Chaos. Springer. ISBN 0-387-00177-8.

• Zaslavsky, George M. (2005). Hamiltonian Chaosand Fractional Dynamics. Oxford University Press.ISBN 0-19-852604-0.

7.9.3 Semitechnical and popular works

• Christophe Letellier, Chaos in Nature, World Sci-entific Publishing Company, 2012, ISBN 978-981-4374-42-2.

• Abraham, Ralph H.; Ueda, Yoshisuke, eds. (2000).The Chaos Avant-Garde: Memoirs of the Early Daysof Chaos Theory. World Scientific. ISBN 978-981-238-647-2.

• Barnsley, Michael F. (2000). Fractals Everywhere.Morgan Kaufmann. ISBN 978-0-12-079069-2.

• Bird, Richard J. (2003). Chaos and Life: Complexitand Order in Evolution and Thought. Columbia Uni-versity Press. ISBN 978-0-231-12662-5.

• John Briggs and David Peat, Turbulent Mirror: : AnIllustrated Guide to Chaos Theory and the Science ofWholeness, Harper Perennial 1990, 224 pp.

• John Briggs and David Peat, Seven Life Lessonsof Chaos: Spiritual Wisdom from the Science ofChange, Harper Perennial 2000, 224 pp.

• Cunningham, Lawrence A. (1994). “From RandomWalks to Chaotic Crashes: The Linear Genealogyof the Efficient Capital Market Hypothesis”. GeorgeWashington Law Review 62: 546.

• Predrag Cvitanović, Universality in Chaos, AdamHilger 1989, 648 pp.

• Leon Glass and Michael C. Mackey, From Clocks toChaos: The Rhythms of Life, Princeton UniversityPress 1988, 272 pp.

• James Gleick, Chaos: Making a New Science, NewYork: Penguin, 1988. 368 pp.

• John Gribbin. Deep Simplicity. Penguin Press Sci-ence. Penguin Books.

• L Douglas Kiel, Euel W Elliott (ed.), Chaos Theoryin the Social Sciences: Foundations and Applications,University of Michigan Press, 1997, 360 pp.

7.10. EXTERNAL LINKS 55

• Arvind Kumar, Chaos, Fractals and Self-Organisation; New Perspectives on Complexityin Nature , National Book Trust, 2003.

• Hans Lauwerier, Fractals, Princeton UniversityPress, 1991.

• Edward Lorenz, The Essence of Chaos, Universityof Washington Press, 1996.

• Alan Marshall (2002) The Unity of Nature: Whole-ness and Disintegration in Ecology and Science, Im-perial College Press: London

• Heinz-Otto Peitgen and Dietmar Saupe (Eds.), TheScience of Fractal Images, Springer 1988, 312 pp.

• Clifford A. Pickover, Computers, Pattern, Chaos,and Beauty: Graphics from an Unseen World , StMartins Pr 1991.

• Ilya Prigogine and Isabelle Stengers, Order Out ofChaos, Bantam 1984.

• Heinz-Otto Peitgen and P. H. Richter, The Beautyof Fractals : Images of Complex Dynamical Systems,Springer 1986, 211 pp.

• David Ruelle, Chance and Chaos, Princeton Univer-sity Press 1993.

• Ivars Peterson, Newton’s Clock: Chaos in the SolarSystem, Freeman, 1993.

• Ian Roulstone and John Norbury (2013). Invisiblein the Storm: the role of mathematics in understand-ing weather. Princeton University Press. ISBN0691152721.

• David Ruelle, Chaotic Evolution and Strange Attrac-tors, Cambridge University Press, 1989.

• Peter Smith, Explaining Chaos, Cambridge Univer-sity Press, 1998.

• Ian Stewart, Does God Play Dice?: The Mathematicsof Chaos , Blackwell Publishers, 1990.

• Steven Strogatz, Sync: The emerging science of spon-taneous order, Hyperion, 2003.

• Yoshisuke Ueda, The Road To Chaos, Aerial Pr,1993.

• M. Mitchell Waldrop, Complexity : The EmergingScience at the Edge of Order and Chaos, Simon &Schuster, 1992.

• Sawaya, Antonio (2010). Financial time series anal-ysis : Chaos and neurodynamics approach.

7.10 External links• Hazewinkel, Michiel, ed. (2001), “Chaos”,

Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4

• Nonlinear Dynamics Research Group with Anima-tions in Flash

• The Chaos group at the University of Maryland

• The Chaos Hypertextbook. An introductory primeron chaos and fractals

• ChaosBook.org An advanced graduate textbook onchaos (no fractals)

• Society for Chaos Theory in Psychology & Life Sci-ences

• Nonlinear Dynamics Research Group at CSDC,Florence Italy

• Interactive live chaotic pendulum experiment, al-lows users to interact and sample data from a realworking damped driven chaotic pendulum

• Nonlinear dynamics: how science comprehendschaos, talk presented by Sunny Auyang, 1998.

• Nonlinear Dynamics. Models of bifurcation andchaos by Elmer G. Wiens

• Gleick’s Chaos (excerpt)

• Systems Analysis, Modelling and Prediction Groupat the University of Oxford

• A page about the Mackey-Glass equation

• High Anxieties — The Mathematics of Chaos(2008) BBC documentary directed by David Mal-one

• The chaos theory of evolution - article published inNewscientist featuring similarities of evolution andnon-linear systems including fractal nature of lifeand chaos.

• Jos Leys, Étienne Ghys et Aurélien Alvarez, Chaos,A Mathematical Adventure. Nine films about dy-namical systems, the butterfly effect and chaos the-ory, intended for a wide audience.

Chapter 8

Emergence (disambiguation)

Emergence is the process of complex pattern formationfrom more basic constituent parts.

8.1 Literature

• Emergence (novel), a 1984 science fiction book byDavid R. Palmer

• Emergence: The Connected Lives of Ants, Brains,Cities, and Software, a 2001 book by Steven BerlinJohnson

• Emergence, a science fiction book by Ray Hammond

8.2 Music

• Emergence (Whit Dickey album), 2009

• Émergence (Natasha St-Pier album), 1996

• Emergence, a 1992 album by R. Carlos Nakai

• Emergence (Miroslav Vitous album), 1985

• Emergence (Neil Sedaka album), 1971

• Emergence: The Music of TNA Wrestling, the fifthstudio album of TNA Wrestling

8.3 Other

• Emergence, the process of return to baseline physio-logic function of all organ systems after the cessationof administration of general anesthetic agent(s)

• Emergence (Star Trek: The Next Generation), a 1994Star Trek: The Next Generation episode

• Emergence International, a worldwide communityof Christian Scientists

8.4 See also• Emergency (disambiguation)

• Emergent (disambiguation)

56

Chapter 9

Emergence: The Connected Lives of Ants,Brains, Cities, and Software

Emergence: The Connected Lives of Ants, Brains,Cities, and Software is a book written by media theoristSteven Berlin Johnson, published in 2001. Early reviewdrafts had the subtitle “What the New Science Can TeachUs About Our Minds, Our Communities, and Ourselves”instead of the “Connected life...” [1]

9.1 Report

Emergence refers to the ability of low-level componentsof a system or community to self-organize into a higher-level system of sophistication and awareness. Johnsonnotes that this self reorganizing stems from the bottom uprather than directed by an external control factor. John-son gives examples of feedback, self-organization andadaptive learning. He presents 5 fundamental principlesto support his hypothesis:

• More is different.

• Ignorance is useful.

• Encourage random encounters.

• Look for patterns

• Pay attention to your neighbors.

9.2 Quote

“The whole is sometimes smarter than the sum of itsparts.”

9.3 Achievements• New York Times - Notable book

• Voice Literary Supplement – Top25 books of theyear

• Esquire Magazine – Best book of the year

9.4 References[1] Johnson, Steven Berlin. (2001). Emergence: The Con-

nected Lives of Ants, Brains, Cities. Scribner. New York,NY. ISBN 0-684-86875-X 9780684868752 06848687689780684868769

57

58 CHAPTER 9. EMERGENCE: THE CONNECTED LIVES OF ANTS, BRAINS, CITIES, AND SOFTWARE

9.5 Text and image sources, contributors, and licenses

9.5.1 Text• Emergence Source: https://en.wikipedia.org/wiki/Emergence?oldid=686832053 Contributors: CYD, The Anome, WillWare,

ChangChienFu, Heron, Bdesham, Michael Hardy, Owl, Lexor, Pnm, Kku, Karada, Ronz, Angela, Andres, Palfrey, Pipis, TonyClarke,Technopilgrim, Ec5618, RodC, Charles Matthews, Nickg, Greenrd, Jeffrey Smith, Jerzy, Banno, Tlogmer, Vespristiano, Chopchopwhitey,Steeev, Rursus, Blainster, Wikibot, Aetheling, Paul Murray, Aknxy, Jleedev, Stirling Newberry, Ancheta Wis, Giftlite, Gwalla, Tomharrison, SantiagoGala~enwiki, Henry Flower, Leonard G., Finn-Zoltan, Edcolins, John Abbe, Andycjp, Loremaster, Karol Langner,BookgirlST, Histrion, Talrias, Jmeppley, IcycleMort, Robin klein, Andreas Kaufmann, Chris Howard, MiddleOfNowhere, Rich Farm-brough, Cagliost, Dbachmann, Pavel Vozenilek, Goochelaar, Bender235, ESkog, Ben Standeven, El C, Vipul, Aaronbrick, Ray Dassen,Mike Schwartz, C S, Teorth, Viriditas, Tmh, JavOs, Mdd, HasharBot~enwiki, Kitoba, Mote, Silver hr, Diego Moya, Minority Report,Hu, Radical Mallard, ClockworkSoul, Zenter~enwiki, Cburnett, Stephan Leeds, Cal 1234, Eternal March, Drat, Acadac, Kazvorpal, OlegAlexandrov, Woohookitty, PoccilScript, Kzollman, Jeff3000, Abu ari, Ludocrat, Ziji, Christianjb, DaveApter, Marudubshinki, Ashmoo,Rjwilmsi, Mayumashu, Gohn, Nightscream, Koavf, Dudegalea, Krash, JFromm, Sydbarrett74, Pe3~enwiki, Diza, Chobot, Fourdee, Bg-white, Adoniscik, YurikBot, Wavelength, Flameviper, RussBot, John2000, Rintrah, Ksyrie, Arkapravo, DarkFireTaker, BlackAndy, This-eye, Slarson, Adamrush, Rbarreira, Shadowfax0, Larry laptop, Moe Epsilon, LodeRunner, Epipelagic, MBDowd, WAS 4.250, HereTo-Help, Raveled, Curpsbot-unicodify, MagneticFlux, Bwiki, Luk, KnightRider~enwiki, SmackBot, Moxon, Saravask, ElectricRay, Tomdw,Peteresch, ZS, Cazort, Ohnoitsjamie, Betacommand, Chaojoker, Isaac Dupree, Grokmoo, Ben.c.roberts, Fuzzform, Nbarth, Hongooi,Toomuchnoise, Gbuffett, OrphanBot, Xyzzyplugh, Cybercobra, Pwjb, Richard001, NickPenguin, Jon Awbrey, A.W.Shred, Dr. GabrielGojon, Vina-iwbot~enwiki, Cast, Bcasterline, Prionesse, Harryboyles, Kreb Dragonrider, John, Rigadoun, Writtenonsand, Tktktk, Physis,Dchudz, Tasc, Wmattis, Olag, Nabeth, Tones, Papertiger, Asatruer, Joseph Solis in Australia, Antonio Prates, GDallimore, ChrisCork,Ripounet, CmdrObot, CBM, USMCM1A1, N2e, AshLin, Pfhenshaw, Emesghali, ONUnicorn, John courtneidge, Arnold.Sikkema, Logi-combat, Myasuda, Gregbard, CX, Phatom87, Fyrius, Cydebot, Clappingsimon, Steel, Peterdjones, Anthonyhcole, Mirrormundo, Studerby,Skittleys, Shirulashem, L7HOMAS, Krylonblue83, Trev M, Letranova, Thijs!bot, Wikid77, ConceptExp, D4g0thur, Headbomb, Pjvpjv,Mr pand, Dfrg.msc, Muaddeeb, Nick Number, Timf1234, Majorly, Dougher, Athkalani~enwiki, Davemarshall04, Albany NY, Andonic,Nessman, Psychohistorian, Aka042, LookingGlass, JaGa, Profitip, Logan1939, Geoinmn, CommonsDelinker, Fixaller, Erkan Yilmaz,AstroHurricane001, Rlsheehan, BillWSmithJr, Alexjryan, Soiducked, Maurice Carbonaro, Lantonov, BobEnyart, Grosscha, ChiswickChap, Aquaepulse, Tgooding, Halrhp, Jknd, Hammersoft, VolkovBot, Pleasantville, Dggreen, Toddy1, LuckyInWaco, Rollo44, VivekVish,Karmela, Rei-bot, Lordvolton, Sjeng, Littlealien182, Sintaku, Dendodge, JhsBot, Don4of4, BL2593, Myscience, Andrewaskew, LovaFalk, SieBot, Sweetp80, Djayjp, Scorpion451, Lord Phat, Sunrise, Emptymountains, Mr. Granger, Rowmn, Rojorulet, ClueBot, Kai-Hendrik, WurmWoode, Napzilla, Der Golem, Alexbot, Brews ohare, SchreiberBike, Bbbeard, Jmanigold, JKeck, XLinkBot, Saurus68,Ecolabs, Rreagan007, MystBot, Jonathanmoyer, Anticipation of a New Lover’s Arrival, The, Svea Kollavainen, Addbot, Xp54321, Clau-dio Gnoli~enwiki, MrOllie, Dyaa, SimonB1710, Mjhunton, Zorrobot, Jarble, Ben Ben, Luckas-bot, Yobot, Isotelesis, IW.HG, Exam-tester, AnomieBOT, 1exec1, Trevithj, Galoubet, 90 Auto, MorgothX, Citation bot, ArthurBot, Carbaholic, Tomwsulcer, Srich32977, Om-nipaedista, RibotBOT, Friesin76, SchnitzelMannGreek, Constructive editor, FrescoBot, LucienBOT, Dwightfowler, Machine Elf 1735,Journalmuncher, Diavel, DivineAlpha, Citation bot 1, Cbarlow, Pinethicket, Exjhawk, Aizquier, Filthylaugh, Sroel, Mjs1991, Pollinosisss,Jonkerz, LilyKitty, Inferior Olive, Reaper Eternal, Catcamus, Bento00, Djjr, EmausBot, Rusfuture, Irvbesen, GoingBatty, Tuxedo junc-tion, AlphaQuadrant, SporkBot, Libertaar, Providus, Ricardsolewiki, RockMagnetist, Just granpa, Spicemix, ClueBot NG,MohamedBishr,BarryKayton, Frietjes, SpaniardGR, Panleek, Tr00rle, Helpful Pixie Bot, Calgg, Bibcode Bot, BG19bot, Rosalegria, Dr. Whooves, Man-jusri Wickramasinghe, Michaelweinstock, Joshua Jonathan, MHeder, Warmtub, Symphonic Spenguin, Dexbot, ZutZut, Polyrahul, Limit-theorem, Danny Sprinkle, Georgeandrews, I am One of Many, Alfy32, Igjohnston, Dsomers74, Aubreybardo, Francois-Pier, SJ Defender,Deegeejay333, Peter Corning, Occurring, Chaya5260, TheEpTic, Loraof, Social Theory, You better look out below! and Anonymous: 291

• Complexity Source: https://en.wikipedia.org/wiki/Complexity?oldid=686282548 Contributors: Mav, SimonP, Rade Kutil, Ryguasu,Hirzel, Patrick, Michael Hardy, Lexor, Ahoerstemeier, Ronz, Suisui, Marco Krohn, RodC, Jstanley01, Doradus, Joy, TowerDragon, Dessi-moz, Robinh, Tobias Bergemann, Matthew Stannard, Giftlite, Tom harrison, COMPATT, Jason Quinn, Cambyses, APH, Andreas Kauf-mann, ELApro, Corti, Cacycle, Zinp, ESkog, Kiand, Liberatus, MaxHund, Flammifer, Mdd, Wricardoh~enwiki, Mrholybrain, Isaac,Bookandcoffee, Oleg Alexandrov, Ott, LOL, Digx, David Haslam, GregorB, BD2412, Imersion, Dpv, Rjwilmsi, Smithfarm, Allen Moore,FlaBot, Mathbot, Celendin, Fereidunian, Wavelength, Duracell~enwiki, Ksyrie, Trovatore, Srinivasasha, Jpbowen, Emersoni, Rwalker,Flipjargendy, Ripper234, Arthur Rubin, GraemeL, Fram, Veinor, SmackBot, [email protected], Jfurr1981, Kurykh, Pjt111,1diot, Jon Awbrey, Ninjavitus, MMX, StN, Lambiam, Nick Green, Mugsywwiii, Tasc, Levineps, Pring, Mr3641, Ioannes Pragensis, CR-Greathouse, Amalas, Innohead, John courtneidge, CX, Ggeorgie, Cydebot, Ak6128, Nicolesc, Jccarteron, Sbonin, Letranova, Thijs!bot,Nick Number, Zepard, AntiVandalBot, TimVickers, JAnDbot, Barek, MER-C, Olaf, Simguy, Douglas R. White, Ramurf, Bongwar-rior, Snowded, Rvsole, Malvaro, Nanotrix, Randomor, Hans Dunkelberg, Maurice Carbonaro, Samtheboy, Skier Dude, Monkeez, LindaVandergriff, Funandtrvl, Cerberus0, Psheld, Pleasantville, Dggreen, EBRJoseph, Philip Trueman, TXiKiBoT, Goflow6206, Sacramentis,Ninadelis, Antoni Barau, UnitedStatesian, Wingedsubmariner, Wmcg, Ordermaven, Jamelan, Kilmer-san, RaseaC, Keepssouth, SieBot,JiE, Matthew Yeager, Vanished user kijsdion3i4jf, Svick, Nikurasu, ClueBot, Binksternet, DFRussia, Jerry Wright, MLCommons, Inge-nuity Arts, Erudecorp, Alexbot, Brews ohare, Ricmagno, Bcastel3, HarrivBOT, Multipundit, Svea Kollavainen, Fluffernutter, Damiens.rf,Ashaktur, Stanbeek, שי ,דוד Elvismcgrady, Snaily, Legobot, Luckas-bot, Yobot, DrPTThomas, Examtester, AnomieBOT, Piano non troppo,Citation bot, TinucherianBot II, The Wiki ghost, FrescoBot, Sae1962, G2kdoe, OgreBot, Citation bot 1, Shaane, Rainman321, Piwinger,RobinK, Pmagrass, EmausBot, Tiptop 213, Ems2715, ClueBot NG, Jack Greenmaven, James childs, Millermk, Frietjes, Masssly, Widr,EvaJamax, Helpful Pixie Bot, Saywhat11, BG19bot, CitationCleanerBot, Anbu121, Therewillbefact, Miszatomic, ChrisGualtieri, JYBot,Krysippos, Gfvolkert, Super Nintendo Chalmers, Nigellwh, Monkbot, Vikas Katyal, 16wu16, Complexitymaster, Fellmark, SamiLayfi,KasparBot, Shupendu Chugani and Anonymous: 144

• Self-organization Source: https://en.wikipedia.org/wiki/Self-organization?oldid=686453628 Contributors: The Anome, Miguel~enwiki,Tedernst, Edward, Michael Hardy, Lexor, Kku, MartinHarper, EntmootsOfTrolls, Charles Matthews, Dysprosia, Nickg, Robbot, Fredrik,Rursus, Moink, Michael Snow, Mu6, Dina, Snobot, Ancheta Wis, Alensha, Pcarbonn, Margana, Karol Langner, The Land, Elektron,Pgreenfinch, Robin klein, Andreas Kaufmann, RevRagnarok, Chris Howard, Jwdietrich2, Ronaldo~enwiki, MiddleOfNowhere, RichFarmbrough, Avriette, Vsmith, Wk muriithi, Smyth, Dave souza, JimR, Dmr2, Bender235, FirstPrinciples, Shrike, Zenohockey, AlexKosorukoff, RoyBoy, Cretog8, Viriditas, .:Ajvol:., Physicistjedi, Ire and curses, Mdd, HasharBot~enwiki, Jheald, RJII, DV8 2XL, BryanKa-plan, Grammarbot, Rjwilmsi, KYPark, ElKevbo, The wub, Jeffmcneill, Mathbot, Diza, Hamidifar, YurikBot, Wavelength, Mukkakukaku,Duracell~enwiki, Pseudomonas, CLW, Curpsbot-unicodify, KnightRider~enwiki, SmackBot, Stpalli, WebDrake, Vald, Pokipsy76, M

9.5. TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES 59

stone, Skizzik, Mobius27, Thumperward, Complexica, Colonies Chris, Royboycrashfan, Fotoguzzi, Cícero, Ericbritton, Will Beback,Eliyak, Nick Green, JoseREMY, Camazine, Kerbii, Dave Runger, Mr3641, Zarex, N2e, Pfhenshaw, Cydebot, Krauss, Gmusser, Skitt-leys, Miguel de Servet, Oszillodrom, Letranova, Kilva, Noclevername, Luna Santin, Rudick.JG, Davedrh, Smartse, Phanerozoic, JAnDbot,Narssarssuaq, Athkalani~enwiki, Gerculanum, Freshacconci, GrahameKing, Vernanimalcula, Economizer, Snowded, KConWiki, Dirac66,David Eppstein, User A1, Rvsole, Masaki K, Jim.henderson, Emathematica, Pilgaard, Keesiewonder, Grosscha, Crakkpot, 1000Faces,Korotkikh, Elizabeth McMillan, Pleasantville, Dggreen, Crscrs, Rollo44, AllGloryToTheHypnotoad, Ordermaven, Northfox, Gbawden,SieBot, Thehotelambush, GeneCallahan, Adelanwar, Der Golem, Techdoer, Synergier, Gulmammad, Rhododendrites, Sun Creator, EhJJ,Bracton, SchreiberBike, Adriansrfr, Life of Riley, Koumz, Xiaoju zheng, Dthomsen8, Cyberoo, Fd42, WikHead, Thomas h ray, Addbot,USchick, Unesn6iduja, MrOllie, LarryJeff, Lightbot, Mcamus, Jarble, ,سعی Luckas-bot, Yobot, II MusLiM HyBRiD II, AnomieBOT,Jim1138, Phantom Hoover, Materialscientist, Citation bot, LilHelpa, The Banner, Omnipaedista, Chjoaygame, FrescoBot, TheSen, Ci-tation bot 1, Winterst, Gray1, Charbee, Regular Polyhedron, Jandalhandler, Ambarsande, Trappist the monk, Reflexinio, We system,Blueshifting, Noresponse, Lithistman, Hhhippo, Quickmute, JuanCano, Cymru.lass, Carl Wivagg, Allanwik, Robbiemorrison, Ems2715,NinjaQuick, TuxFighter, Jrichardliston, ClueBot NG, Fgunnars, Panleek, Joel B. Lewis, MerlIwBot, Helpful Pixie Bot, Richardjb25, Revi-sor2011, RogerBF, BG19bot, GlaedrH, DPL bot, Terrykel, Kfriston, Soler99, Zach Lipsitz, Khazar2, Nathanielfirst, IjonTichyIjonTichy,Dexbot, Makecat-bot, BurritoBazooka, Samotny Wędrowiec, Andy Quarry, Duchifat, Otherocketman, FrB.TG, Monkbot, , Mit0126,Asuscreative, Isambard Kingdom, KasparBot, Jman9058, Sangqiu5, Robcduk and Anonymous: 134

• Spontaneous order Source: https://en.wikipedia.org/wiki/Spontaneous_order?oldid=683136826 Contributors: Michael Hardy, Kku, Bigiron, Nickg, Owen, Goethean, Nagelfar, Nikodemos, Ubernetizen, Everyking, Ravn, Christofurio, Turion, Karol Langner, Rich Farm-brough, Cfailde, Bender235, Cretog8, Viriditas, Generalebriety, Mdd, Gary, Sstoneb, RJII, Siafu, NotSuper, Rjwilmsi, Phileas, Crazynas,Jrtayloriv, RussBot, PEZ, Briaboru, Pigman, Stijn Calle, RL0919, Anclation~enwiki, RG2, NetRolller 3D, SmackBot, Zazaban, Brian-ski, Bluebot, Persian Poet Gal, D-Rock, Xchbla423, NickDupree, PrometheusX303, LoveMonkey, Afaus, Byelf2007, Rigadoun, Spark-sWillFly, Vision Thing, RelicLord, N2e, Tzalumen, Cydebot, JamesAM, Thijs!bot, Biruitorul, PHaze, Carolmooredc, Athkalani~enwiki,Skomorokh, Alastair Haines, Freshacconci, Daniel Cordoba-Bahle, Tonyfaull, KConWiki, SlamDiego, Anarcho-capitalism, Teardroponthefire, Working Poor, Crakkpot, Ontarioboy, Childhoodsend, TXiKiBoT, Rollo44, Malinaccier, Esotericengineer, Jesin, Austria-cus, Macdonald-ross, Pointsmyth, Dstlascaux, Bombastus, Operation Spooner, Der Golem, Alexbot, Byates5637, 1OwenJones, Ad-dbot, Elsendero, USchick, 5 albert square, Tassedethe, Luckas-bot, Yobot, AnomieBOT, PublicSquare, Aeortiz, 90 Auto, Citation bot,Kaoruchan21, Xqbot, Srich32977, Eisfbnore, Skyerise, Dmitry St, Jonkerz, Libertatis, Thermoworld, Roastedpepper, Jbradley904, Xero-graphica, Financestudent, Helpsome, Benjamin9832, Thomask0, Rurik the Varangian, Helpful Pixie Bot, Revisor2011, BG19bot, Geistcj,PhnomPencil, Wodrow, Iansha, Platospigmonster, Fajrbot, Austrartsua, Monkbot, Loraof and Anonymous: 79

• Complex system Source: https://en.wikipedia.org/wiki/Complex_system?oldid=683223752 Contributors: Bryan Derksen, AdamRetch-less, Lexor, Karada, Ronz, Mkoval, Kimiko, RodC, Tpbradbury, Tschild, Noeckel, Robbot, RedWolf, Chopchopwhitey, Centrx, KarolLangner, Jmeppley, ELApro, Guppyfinsoup, Chris Howard, Jwdietrich2, &Delta, FT2, Pjacobi, CanisRufus, Truthflux, La goutte depluie, Mdd, Passw0rd, Hu, Danthemankhan, Acadac, Versageek, Ott, Sengkang, Jshadias, Rjwilmsi, KYPark, Salix alba, The wub,FlaBot, JFromm,Miketam, Diza, Vonkje,Wavelength, RussBot, Fmrafka~enwiki, Duracell~enwiki, Thsgrn, Jpbowen, Yonidebest, Zzuuzz,Msuzen, Arthur Rubin, Adastra~enwiki, Luk, Palapa, SmackBot, Supermanchander, [email protected], Took, Cazort, Sectryan,Commander Keane bot, Portillo, Betacommand, Adam M. Gadomski, Frap, Xyzzyplugh, Kevinbrowning, Choesarian, MisterCharlie, JonAwbrey, Betamod, Dankonikolic, Christopher Agnew, Sina2, MagnaMopus, Sir Nicholas de Mimsy-Porpington, Filippowiki, Jrouquie,Megane~enwiki, Spook`, Ace Frahm, Magntuve, Papertiger, Rhetth, Tawkerbot2, Mr3641, CmdrObot, Amalas, N2e, Pfhenshaw, McVi-ties, Ballista, Cydebot, Peterdjones, Skittleys, Jrgetsin, Letranova, WinBot, Oatmealcookiemon, JAnDbot, Cic, Snowded, Paresnah, Xtifr,Calltech, Malvaro, G.A.S, Ifaomo, Yobol, Nono64, Erkan Yilmaz, Overix, Nigholith, J.A.McCoy, DeKXer, Grosscha, DarwinPeacock,Thecinimod, Dggreen, Childhoodsend, Antoni Barau, JayC, IPSOS, Mfmoore, Don4of4, Steve Masterson, Northfox, GarOgar, James-sungjin.kim, Iamthedeus, Emmazunz84, Vanished user kijsdion3i4jf, MathShaman, Yhkhoo, Edugalt, Razimantv, Niceguyedc, Schreiber-Bike, DumZiBoT, Jytdog, SilvonenBot, Addbot, DOI bot, RicardoSanz, Tide rolls, Yobot, Cmbarton54, Examtester, AnomieBOT, Steam-turn, ArthurBot, Apothecia, The Wiki ghost, FrescoBot, Citation bot 1, Geropod, Slatteryz, TobeBot, E.V.Krishnamurthy, RjwilmsiBot,Skamecrazy123, EmausBot, WikitanvirBot, Skater00, Tommy2010, ZéroBot, Traxs7, ElationAviation, Simondc, Greg Royston Molineux,Cmanske, Ego White Tray, , ChuispastonBot, Rezabot, Panleek, Helpful Pixie Bot, Richardjb25, Bibcode Bot, BG19bot, Bereziny,,زكريا Brad7777, Dtotoo, Chris troutman, Nigellwh, Paul2520, Ea2206, Lev Kalmykov, Monkbot, Phoenix 123 abc, Loraof, PennyDarling,Rionbr, KasparBot and Anonymous: 142

• Integrative level Source: https://en.wikipedia.org/wiki/Integrative_level?oldid=676493930 Contributors: RodC, Tzeh, Cobaltbluetony,Mdd, Malcolma, SmackBot, VoABot II, ForestAngel, Chiswick Chap, Sustainablefutures2015, Excirial, Claudio Gnoli~enwiki, Om-nipaedista, Erik9bot, Sonicyouth86, BG19bot, Usaff911, Tonmoy sarwar, Shaners26, Hi5dudes, VanishedUser sdu9aya9fs654654 andAnonymous: 2

• Chaos theory Source: https://en.wikipedia.org/wiki/Chaos_theory?oldid=686428704 Contributors: AxelBoldt, Tobias Hoevekamp,Sodium, Mav, Zundark, Gareth Owen, Arvindn, Roadrunner, SimonP, David spector, Heron, Gumpu, Edward, Michael Hardy, Tez, Lexor,Isomorphic, Chinju, Karada, Iluvcapra, Ahoerstemeier, William M. Connolley, Snoyes, Darkwind, Kevin Baas, Evercat, Smack, Schnee-locke, Charles Matthews, Adam Bishop, Dino, Dysprosia, Jitse Niesen, Doradus, Munford, K1Bond007, Jose Ramos, Fairandbalanced,Bevo, Traroth, Banno, JorgeGG, Phil Boswell, Robbot, Bernhard Bauer, Goethean, Gandalf61, Chopchopwhitey, MathMartin, Sverdrup,Academic Challenger, Ojigiri~enwiki, Zubras, Paul Murray, Dave Bass, Dbroadwell, Wile E. Heresiarch, Tobias Bergemann, Enochlau,Decumanus, Giftlite, Smjg, Fennec, Gene Ward Smith, Vir4030, Kim Bruning, Everyking, Curps, Sunny256, Pucicu, Chowbok, Utcursch,LucasVB, Antandrus, Mako098765, Quarl, Vanished user 1234567890, Karol Langner, Rdsmith4, Oneiros, Pmanderson, Zfr, Sam Hoce-var, Lumidek, Jmeppley, Joyous!, Barnaby dawson, TheObtuseAngleOfDoom, Shiftchange, Discospinster, Rich Farmbrough, TedPavlic,Avriette, Guanabot, Vsmith, Dave souza, Lulu of the Lotus-Eaters, Fluzwup, Paul August, Bender235, Neurophyre, Loren36, Fenice,Brian0918, El C, Pjrich, Alereon, AJP, Rwh, Semper discens, Billymac00, John Vandenberg, Thomas G Graf, Flammifer, ObradovicGoran, Mdd, Cyrloc, Msh210, Defunkt, Prashmail, Alansohn, Arthena, Keenan Pepper, CommodoreMan, Lectonar, WhiteC, BryanD,Sligocki, Hu, Bart133, PaePae, Helixblue, HenkvD, Evil Monkey, Cal 1234, RainbowOfLight, DV8 2XL, Embryomystic, Kazvorpal,Dan100, OleMaster, Simetrical, Linas, Ramsremedies, Scriberius, Igny, VanFullOfMidgets, LOL, Scid, Guardian of Light, KickAir8P~,Ruud Koot, MONGO, Kelisi, GregorB, XaosBits, Graham87, Magister Mathematicae, Anarchivist, Jorunn, Rjwilmsi, Joakim Munkham-mar, KYPark, XP1, TheRingess, Brighterorange, Scartol, The wub, Bhadani, Yamamoto Ichiro, Mathbot, Greg321, Sunayana, Nivix,RexNL, Nabarry, Incompetnce, Smithbrenon, Nicholasink, Chobot, Evilphoenix, Bgwhite, Cactus.man, Gwernol, YurikBot, Wavelength,Deeptrivia, Pmg, Hillman, Nmondal, Splash, JabberWok, Prokaryote1234, Stephenb, Jugander, Chaos, Alex Bakharev, Rsrikanth05, DavidR. Ingham, Dtrebbien, Grafen, Winonanick, JocK, Dhollm, Raven4x4x, Moe Epsilon, Zwobot, Epipelagic, Romarin, Dlyons493, Suso,Bota47, Dan131m, Cat2020, Zunaid, WAS 4.250, Phgao, Ninly, Imaninjapirate, Arthur Rubin, GraemeL, DGaw, Madrazz, Vicarious, Re-

60 CHAPTER 9. EMERGENCE: THE CONNECTED LIVES OF ANTS, BRAINS, CITIES, AND SOFTWARE

ject, Kungfuadam, DVD R W, Soir, Benjamindees, Marquez~enwiki, SmackBot, 4dhayman, ManaUser, Maksim-e~enwiki, Sethmasters,Stellea, The hoodie, InverseHypercube, KnowledgeOfSelf, Unyoyega, C.Fred, Rosaak, Thunderboltz, Flux.books, PeterSymonds, Gilliam,Sbonsib, Skizzik, GwydionM, Izehar, Bluebot, Persian Poet Gal, RDBrown, Telempe, Alex brollo, SchfiftyThree, GabrielPere, Complex-ica, Bazonka, Sudharsansn, CSWarren, DHN-bot~enwiki, Jdthood, Yanksox, Hellfire81, QuimGil, Gorgeorgeus, Can't sleep, clown willeat me, MyNameIsVlad, Jahiegel, Rrburke, Spectrogram, Nakon, Anmnd, Mini-Geek, Thismarty, Profyorke, Wybot, DMacks, Sashato-Bot, Lambiam, Mukadderat, Luigi-ish, Kuru, Lakinekaki, Lapaz, Buchanan-Hermit, Joshua Andersen, Chodorkovskiy, JorisvS, Dumelow,Jim.belk, IronGargoyle, Mosgiel, Atomic Duck!, Brazucs, Dicklyon, Xiaphias, Invisifan, Candybars, Dr.K., Dfred, Inquisitus, Rlinfinity,Xionbox, Asyndeton, Mdanziger, PSOfan2000, Iridescent, Shoeofdeath, Cumi~enwiki, Rhetth, Daveyork, Experiment123, Tawkerbot2,Chetvorno, Timrem, PurpleRain, CRGreathouse, Crownjewel82, Aherunar, Avanu, TheTito, Neelix, Grein, Mct mht, CX, Yaris678, GogoDodo, Lugnuts, Pascal.Tesson, Alpharius~enwiki, Tawkerbot4, DumbBOT, Chrislk02, Romon, Letranova, Thijs!bot, Epbr123, Hervegirod,UXs, Sagaciousuk, Scientio, Oliver202, Headbomb, Zardoze, Perrygogas, West Brom 4ever, James086, Nezzadar, Charukesi, UniversalHero, Widenet, Gfalco, Northumbrian, AntiVandalBot, Devanshi.shah, Ben pcc, Doc Tropics, Jcsellak, Jj137, JAnDbot, Ashishval44, Hu-sond, Gandhi gaurav, MER-C, Sophie means wisdom, Igodard, Hut 8.5, MSBOT, Kirrages, Captain head, Peteymills, Coffee2theorems,Jill.marleigh, Magioladitis, Diderot7, VoABot II, Catslash, JamesBWatson, Mbc362, Carlylecastle, [email protected], Brother Francis,Catgut, Ensign beedrill, Mjkelley79, David Eppstein, Kotinopoulos, Vssun, JoergenB, DerHexer, JaGa, Bryt, Falcor84, Waitati, Cocytus,Stephenchou0722, DancingPenguin, MartinBot, Arjun01, Poeloq, InnocuousPseudonym, Tomasao, Ayonbd2000, Erkan Yilmaz, J.delanoy,Oshron, Trusilver, AstroHurricane001, MikeBaharmast, Maurice Carbonaro, Zakholdsworth, Thegreenj, Ian.thomson, JAK2112, Salih,Katalaveno, Enuja, QuasiAbstract, V.V zzzzz, Coppertwig, Chiswick Chap, NewEnglandYankee, Policron, MKoltnow, Zojj, MetsFan76,TottyBot, Ahshabazz, Lamp90, Prot D, Yodler, JavierMC, Nnnagig, Cmarnold, Idioma-bot, JLBernstein, Funandtrvl, Phlounder, Yoeb137,Torcini, Mimigary, Pleasantville, DSRH, Tunnels of Set, Jeff G., JohnBlackburne, AlnoktaBOT, HeckXX, Richardseel, DancingMan,Philip Trueman, TXiKiBoT, Oshwah, Gggggdxn, Red Act, A4bot, Tagalong99, IPSOS, Voorlandt, Magmi, Corvus cornix, Garravogue,Rubseb, PDFbot, Katimawan2005, 3p1416, Kızılsungur, Inductiveload, Kaiketsu, Kilmer-san, Wolfrock, Jacob501, Sheildofthunder, TheThe Fool on the Hill, Blazen nite, HiDrNick, Symane, SamuraiGabe, Radagast3, Maxlittle2007, SieBot, Tosun, Cwkmail, This, thatand the other, Zsniew, Revent, Vanished User 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9.5. TEXT AND IMAGE SOURCES, CONTRIBUTORS, AND LICENSES 61

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62 CHAPTER 9. EMERGENCE: THE CONNECTED LIVES OF ANTS, BRAINS, CITIES, AND SOFTWARE

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