M
ASARYKU
NIVERSITYF
ACULTY OFI
NFORMATICSChaos Theory in Project Management
D
IPLOMAT
HESISBrno, 2014 Bc. Josef Daňa
Declaration
I hereby declare that this thesis is a result of my own work and that I worked independently. All sources and literature that I have used for preparation of this work are properly quoted with full reference to their original source and listed in bibliography.
……….
Josef Daňa, 8.1.2013
Abstract
The goal of this thesis is to present, (a) an overview of concepts originating from the Chaos theory which could be utilized as a basic theoretical framework for understanding how the Chaos theory could be applied in project management, (b) further explain how these concepts compare and contrast with traditional project management approaches, and (c) to propose a new project management approach based on the Chaos theory. Lastly, this thesis will provide specific examples of how this new approach could be applied.
Keywords:
Chaos theory, complex systems, self-organization, project management, agile methodology, T-Shaped professional
Content
1. Introduction...1
2. The Chaos theory...3
2.1. Terminology and bibliography disclaimer...4
2.2. Brief history...5
2.3. Nonlinear thinking...6
2.4. Chaos theory and Project Management...7
3. Chaos theory concepts...10
3.1. General framework – Energy flow ...10
3.1.1. Energy flow in organic matter ...11
3.1.2. Energy flow in nonorganic matter ...11
3.1.3. Preference for more efficient configurations ...12
3.1.4. Underlying principle: self-feeding cycle...13
3.1.5. Section summary...14
3.2. Self-organization...14
3.2.1. Underlying principle: Feedback loops...15
3.2.2. Feedback examples...17
3.2.3. Through self-organization to stability...18
3.2.4. Organization without external control...18
3.2.5. Emergent properties...19
3.2.6. Section summary...19
3.3. Bifurcations...19
3.3.1. Underlying principle: Limited energy flow capacity ...20
3.3.2. Bifurcation diagram...20
3.3.3. Section summary...21
3.4. Attractors ...22
3.4.1. Phase space...22
3.4.2. Attractor as distortion of a phase space ...23
3.4.3. Stability vs. instability...24
3.4.4. Repellors...25
3.4.5. Saddles...26
3.4.6. Energy landscape...27
3.4.7. Section summary...28
3.5. Fractals...29
3.5.1. Fractal as energetic optimum...29
3.5.2. Fractal dimension...30
3.5.3. Fractals and scale invariance...31
3.5.4. Fractals as real life objects...31
3.5.5. Implications of fractal structure...32
3.5.6. Section summary...32
3.6. Networks...32
3.6.1. Strong links and weak links...33
3.6.2. The strength of weak links...34
3.6.3. The network stability...35
3.6.4. Weak links as surface for stress dissipation...37
3.6.5. Optimal network structure...37
3.6.6. Network topology...40
3.6.7. Fitness model for network growth...42
3.6.8. Section summary...43
3.7. General implications and summary of the Chaos theory ...44
4. The Chaos theory in project management...46
4.1. Team self-organization...46
4.1.1. Freedom to employees...47
4.1.2. Self-organized teams effectiveness ...47
4.1.3. Teamwork feedback loops...49
4.1.4. Agile methodology...51
4.2. Group dynamics...52
4.2.1. Layers of human communication...52
4.2.2. Structural levels of communication...53
4.2.3. Behavioral profiling ...57
4.3. Emergent leadership...58
4.3.1. Assigned vs. Emergent leadership...59
4.3.2. The network perspective...59
4.3.3. Social and emotional competencies...61
4.4. T-shaped professional through the lens of the Chaos theory ...63
4.4.1. Optimal knowledge network...64
4.4.2. T-shaped educational profile stabilizing team network ...65
4.4.3. T-Shaped professional and knowledge network...68
4.5. Critical project transitions...71
4.5.1. Alternative stable states...71
4.5.2. Early warning signs of critical transitions...73
4.5.3. Early warning signs of project failure...75
4.5.4. Managing critical transitions...77
4.6. Managing projects at the edge of Chaos...79
4.6.1. Planning complex projects...79
4.6.2. Defining task complexity ...80
4.6.3. Team interaction management...81
4.6.4. Summary – Comparison of linear and nonlinear approach to project management...83
5. Conclusion...86
6. Literature...90
List of figures
Figure 1. Dictyostelium life-cycle...16
Figure 2. Bifurcation diagram...21
Figure 3. Phase space for idealized pendulum ...23
Figure 4. Basins of attraction ...25
Figure 5. Illustration of repellor shapes...26
Figure 6. Attractors, repellor and saddle ...27
Figure 7. The energetic landscape...28
Figure 8. Koch snowflake ...30
Figure 9: Topological phase transition...41
Figure 10. Reaching project objective through feedback loops ...51
Figure 11. Topological phase transition & Operating systems ...58
Figure 12. Attractor within interaction phase space ...62
Figure 13. T-Shaped knowledge network...66
Figure 14. Team – Customer network...69
Figure 15. Fractal structure of knowledge distribution ...71
Figure 16. Critical transition of productivity ...73
Figure 17. Slower recovery from perturbations ...74
List of tables
Table 1. Feedback examples...17
Table 2. Presence and absence of enough weak links in network ...39
Table 3. Difference between linear and nonlinear thinking ...44
Table 4. Teamwork feedback examples...49
Table 5. Action stances...54
Table 6. Communication domains...55
Table 7. Operating systems...55
Table 8. Example of behavioral profile ...58
Table 9. T-Shaped professional vs. project manager with insufficient soft skills...67
Table 10. Matching early warning signs to category ...76
Table 11. Linear vs. nonlinear approach to project management ...84
1. Introduction
Today’s advances in technology and organizational development allow planning and delivering Information Technology (IT) projects of increasing scope and complexity. At the same time projects often fail to be completed on time and on budget. IT project failures could cost hundreds of millions, as shows the following newspaper quotation:
“Abandoned NHS IT system has cost £10bn so far. Bill for abortive plan, described as 'the biggest IT failure ever seen', was originally estimated to be £6.4b” The Guardian, 18t h September 2013 [ CITATION Sya14 \l 1029 ].
There are also several examples of Czech government IT projects which generated much controversy and criticism for being delivered almost non- functional (crash of car registration system few hours after being launched in year 2012 [ CITATION idn13 \l 1029 ]) or for being overly expensive (electronic health card – the IZIP project [ CITATION zpr13 \l 1029 ]).
Project failures may not be connected only to government projects.
According to several research groups’ analyses and meta-studies [ CITATION Goo09 \l 1029 ], about 60-70% of all large-scale IT projects fail to achieve their goals or they are delivered late or substantially over budget. The “Standish Chaos Report” published annually by the Standish Group on success rates of IT projects comes to a similar conclusion – two thirds of all IT projects continuously fail to deliver the preplanned goals and objectives [ CITATION Cur11 \l 1029 ].
The obvious question is whether this means that more than a half of project managers are incompetent or that current project management tools are of poor practical usability.
The current literature on chaos theory as applied to project management suggests that there is a need to acknowledge the notion that IT projects are inherently less structured and linear than people would like to believe and therefore applying today’s methods on tomorrow’s projects my not bring about better outcomes [ CITATION Cur11 \l 1029 ].
Traditional project management practice almost exclusively relies on the concept of project life cycle and tools (e.g. WBS – work breakdown
structure, or CPM – critical path method) that are based on a linear style of thinking [ CITATION Cic09 \l 1029 ].
Therefore, this thesis’s goal is to present a new and nonlinear perspective on handling projects offering an alternative project planning and execution approach and possibly resulting in fewer discrepancies between project management theory and practice.
This change of perspective does not imply that current project management practice is bad or that tools used currently need to be abandoned. Instead, it may serve as an augmentation to the current theory and practice; and not as a negation or a replacement for it.
2. The Chaos theory
The chaos theory is an umbrella term for a set of concepts that offers an alternative description and explanation of the behavior of nonlinear systems (which are basically almost all naturally occurring physical, chemical, biological or social structures or systems). The name “Chaos”
comes from the fact that nonlinear systems seem to behave chaotically or randomly from a traditional (linear ) point of view.
The word random originates in medieval French idiom meaning
“movements of the horse that rider cannot predict”. The point of this metaphor is to illustrate that although the system (e.g. horse movements) possesses an unpredictable behavior, such behavior is driven by factors (e.g.
roughness of the terrain that causes horse to stumble) which cannot be understood or predicted from the horse rider’s point of view. [ CITATION Man83 \l 1029 ].
There are many natural systems whose behavior that cannot be described and explained by simply dividing the whole into its parts and study them separately from the rest of the system [ CITATION Goe94 \l 1029 ]. For example, studying the behavior of an individual ant may not provide any insight into an anthill as a system because the ant colony’s behavior is driven by the cooperation and pheromone interaction between ants [ CITATION Ren03 \l 1029 ].
In a different example, the movement of water molecules in boiling water might seem chaotic and random, however there are patterns of movements that change over time and tend to form similar structure.
Most natural systems change over time and this change does not happen in proportional and straightforward manner. A concept of proportional change is an idealization because real life phenomena change differently – sometimes smoothly, sometimes abruptly [ CITATION Gua09 \l 1029 ].
The Chaos theory provides a theoretical framework and a set of tools for conceptualizing change per se – a changing system may have appeared to be chaotic from traditional (linear ) perspective while it exhibits coherence, structure and patterns of motion from the global and nonlinear perspective. The Chaos theory also acknowledges the importance of the
interaction between the system elements (so called “interactive causality”), not the just the existence of the elements themselves [ CITATION Goe94 \l 1029 ].
A shift in perspective also requires a different type of questions being asked. The traditional way of thinking tends to frame problems in
“either/or” terms (i.e. did “this” or “that” produce the effect); it seeks singular causes that produce observed effect. In interactive causality “this or that” questions make no sense. “In fact, they put the askee in a double bind because the actual answer is “yes/yes” … or “no/no” [8, pg. 54].
A classical example of “this or that” question is the problem of Great person theory vs. Zeitgeist theory. Do advances in civilization result from the genie of an important visionary or are they feeding from the “spirit of the time”? The answer is: yes/yes. Both great personae and spirit of the time are part of the same unfolding process of society evolution [ CITATION Goe94 \l 1029 ]. This interdependence is also illustrated on the famous quote by Isaac Newton: “"If I have seen further it is by standing on the shoulders of giants" [ CITATION Wik133 \l 1029 ]. This interdependence may also explain why different teams of scientist reveal similar or same scientific advancement in more or less same time without knowing each other – the so called “Multiple discovery hypothesis”[ CITATION wik13 \l 1029 ]
2.1. Terminology and bibliography disclaimer
The Chaos theory is often interchangeably used with labels such as Complex systems theory, Complexity theory or Nonlinear/Dynamical systems theory. All these names usually refer to same set of concepts or scientific approach but in this thesis only the term “Chaos theory” is used because it is the shortest and best known by the public at large, especially because of what is called a “butterfly effect” – sensitive dependence on initial conditions.
Another reason is to avoid any potential misinterpretation or confusion with terms used to describe the observed that seems complicated or beyond our ability to fully understand as “complex”. In the context of
Chaos theory, the terms “complex” or “complexity” have a more technical meaning, and that is of “mutual interdependence.”
Some of the references used here are not exclusively connected to project management. Most of these sources are books written about Chaos theory as it applies to the domain of social sciences. First, the supporting argument for the use of “non-project management” sources is that the principles of the Chaos theory are universal, and they apply equally well to a variety of domains, e.g. physics, chemistry, economy and psychology.
Second, both teamwork and project execution are significantly influenced by the dynamics of social interaction and by psycho-social factors.
2.2. Brief history
The Chaos theory emerged during second half of the 20th century when scientist from different fields of research consistently observed similarities in the behavior of natural systems like weather, chemical reactions, movement of water molecules in container being gradually heated, etc. For example, scientists discovered that the equations invented by Edward Lorenz in 1950’s for the purpose of weather prediction could be correctly applied to other nonlinear systems. Since that time the number of such findings significantly increased and led to the development of the basics of the modern study of nonlinear systems or the Chaos theory in 1980’s [ CITATION Gle89 \l 1029 ].
The following scientists contributed to formation of the Chaos theory during 1970’s and 1980’s[ CITATION Cic09 \l 1029 ]:
Edward Lorenz – Sensitive dependence on initial condition (“Butterfly Effect”)
David Ruelle – Strange Attractors
Ilya Prigogine – Dissipative structures
Mitchell Feigenbaum – Principle of Universality (Feigenbaum’s Constant)
Benoit Mandelbrot – Fractals
Stuart Kauffman – Self-organization
The Chaos theory increasingly drew the attention of scientists around the world mainly because its principles, laws and conceptualizations are thought to be universally applicable to the behavior of almost any natural system.
Today, the Chaos theory is applied to many fields of research including
“hard sciences” like math, physics, chemistry, biology or weather forecast, as well as, in “soft sciences” like psychology, sociology, economics, political science, management, etc. More importantly, there is also existing research regarding the application of the Chaos theory to project management.
2.3. Nonlinear thinking
Since the time of Newton’s work on classical mechanics, there is a common believe that world around us works according to a simple, linear logic, e.g. Cause Effect, or A B C. This notion was further reinforced by the assumption of the French mathematician Pierre-Simon Laplace that any future event can be predicted by a set of equations describing the behavior of a system and based on a set of initial conditions (i.e. absolute determinism) [ CITATION Wik13 \l 1029 ].
Although these ideas are more than two hundred years old, even today most people, including scientists, tend to think linearly [ CITATION Pel11 \l 1029 ], e.g.:
Assume that events are usually caused by a simple (or individual) cause, e.g. “it rains because atmospheric pressure is low”
Extrapolate linear trends and follow linear dependencies between phenomena, e.g. prediction of petrol prices usually follows current trends
Conclude that small changes of the input lead only to correspondingly small changes of the output measurement or that a large effect can be achieved only the exertion of a large effort.
In nature, almost no linear systems exist, and causality is almost never simple, sequential, or independent. Real systems can rarely be broken down into independent elements of a linear causation. Furthermore, most
real life events are based on the interaction of elements and the causation is just the opposite of independent – it is interdependent. It is the combination of nonlinearity and interdependence that is crucial for understanding the “Chaotic” phenomena [ CITATION Goe94 \l 1029 ].
A system of several cuckoo clocks hanged on the wall could be used as an illustration of interdependent causality. At a glance, they might seem independent of each other; however their initially different pendulum swings would be perfectly synchronized after some time has passed, through microscopic movements transferred through the wall. The reason for the synchronization is the interdependence of pendulum swings. This phenomenon could not be explained by a traditional scientific approach seeking independent causality. By applying a different approach which is based on the Chaos theory, this could be accomplished with a higher chance of success. Therefore, the transition from independent to interdependent causality is the key change in perspective that Chaos theory offers for possible more appropriate scientific description and explanation of natural phenomena [ CITATION Goe94 \l 1029 ].
The nonlinear (or systemic) thinking can be generally described by the following attributes [ CITATION Pel11 \l 1029 ]:
A view from a broader perspective, a holistic view;
A top-down view, from the general to the specific attributes;
Focus on the processes’ dynamics (vs. a static view of the world);
Importance of the connections, the context, the interactions, and the relationships between elements;
Awareness of the role of feedback;
Long-term thinking;
Several Chaos theory concepts, introduced elsewhere in this thesis, will provide further structure and better explanation for these attributes so that they are not perceived as an “everything relates to everything” cliché.
2.4. Chaos theory and Project Management
By definition, a project is a temporary endeavor undertaken in the context of an organization to create a specific product or service [ CITATION
Ojh11 \l 1029 ]. A project is usually delivered by a team of members who possess the necessary knowledge and skills of using certain tools and techniques in order to accomplish specific project goals or tasks. However, the team members have unique personalities which could have a significant influence on the cooperation and interaction within the team [ CITATION Cur11 \l 1029 ].
The interaction between team members is in essence a dynamical system, where people mutually affect each other with ideas, moods, nonverbal communication, and emotions – whether they are aware of it or not. The thorough understanding of these dynamics is one of the critical factors of the success of a project outcome, and in my view the Chaos theory may provide a sound theoretical framework for accomplishing it.
The group dynamics of the team are not the only nonlinear aspect of a project. While the execution of any project may sometimes appear chaotic, unpredictable or disorderly (e.g. outsourced parts are delivered late, team members get sick, hardware fails, costs exceed budget). Some positive events may occur in a seemingly random manner (e.g. unusually satisfied customer, a project deliverable made an unprecedented profit, etc.) [ CITATION Sin02 \l 1029 ]. Such events may appear as unpredictable but at least some of them can be anticipated if the nonlinear perspective is applied.
According to the Chaos theory, these events are not a result of a project manager’s poor judgment, poor risk control, or lack of skills or competence. Instead, these unpredictable events are inherently bound to the process of project execution. The reality of a project execution is naturally the subject of an ongoing change and linear plans and decisions may not be able to reach far into the future. The inability to plan a project execution accurately from the beginning to the end (and face exceeding of budget and schedule as a consequence) may not be the project management’s fault. Instead, a theoretical framework which suggests that creating a plan and holding on to it for the whole time, without modifying it to reflect any dynamic changes which may have occurred, would lead to a successful outcome, may be at fault [ CITATION Cic09 \l 1029 ].
Traditional project management places a strong emphasis on explicit technical knowledge, sometimes with the disclaimer (e.g. in [ CITATION Pro04 \l 1029 ]) that these should be taken as core skills and a project manager should have the ability to judge when and how to implement them. As a result, the so called “soft skills” might be treated as competences of secondary importance or as something that does not have a significant effect on a successful project outcome. Yet, the study of dynamical systems demonstrates that these skills (e.g. communication skills, social and emotional intelligence, intuition, etc.) have greater influence on stability of project execution, than originally thought [ CITATION Cic09 \l 1029 ].
3. Chaos theory concepts
In this section, some essential concepts of the Chaos theory are introduced. These concepts are important for understanding the project execution and the team cooperation dynamics. Some of these concepts, like the butterfly effect (sensitive dependence on initial conditions) or fractals (self-similar objects), may be familiar to the general public, while some, like self-organization, attractors, study of networks, emergent properties or bifurcations, may be less known.
3.1. General framework – Energy flow
The concept of energy flow is important for understanding the underlying motives for organization and evolution of living systems. The theory of energy flow in the context of this thesis may provide answer to questions such as “Why there is self-organization?” or “Why the dynamics of systems works the way they do?”
Theory of energy flow explains why systems are not static but dynamic.
The energy is quantitatively stable – it is not possible to destruct or create energy, it is only possible to change it from one form to another. As a consequence, no system or machine can “consume” energy in order to do work. What really creates work is the flow of energy; and the flow of energy is caused by fields of energy with different concentrations (or simply by “disequilibrium”). Different concentrations create power that presses energy to flow towards equilibrium. It is not the amount of energy what determines the ability of a system to do work, but its distribution [ CITATION Goe94 \l 1029 ].
“The very crux of what drivers change has to do with distributions, or in other words, with the relationships between different concentrations in the field. Energy flow by its nature is a product of relationships between things” [8, pg. 60].
3.1.1. Energy flow in organic matter
In a simple organism like a plant cell, some of the energy intake is used for the benefits of creating an internal structure (a metabolism) that would allow processing of even more energy. This cycle is an example of simple thermodynamic system that possesses evolutional behavior [ CITATION Byr98 \l 1029 ]. From the energy flow theory point of view, the history of evolution is the history of increasing energy flow as organisms attained more complex metabolism that allowed them to process more energy, increase metabolism rate, and so forth [ CITATION Goe94 \l 1029 ].
In the nature there is always a need for increasing the energy flow (i.e. for growth and evolution) – so eventually the one growing cell splits into two new cells and so forth. At some point of their evolution, cells start to cooperate, differentiate their functions and form a multi-cellular organism. This allows such organism to have specialized cells which perform specific function and affords that organism (or colony of originally single cells) the ability to process energy in a more efficient way [ CITATION Wik131 \l 1029 ].This is only one example that illustrates the notion that in nature, there is always a preference for increasing the energy flow.
3.1.2. Energy flow in nonorganic matter
An example of preference for increasing energy flow in non-living systems is a room located in the middle of a house with a temperature higher than the temperature of all other surrounding rooms (let’s say 25°C vs. 20°C).
The second law of thermodynamics states that systems spontaneously progress toward thermodynamic equilibrium i.e., a state of balance.
Therefore, the temperature of the warmer room (25°C) will get lower and temperature of all other rooms (20°C) will rise so the temperatures will be somewhere in the middle (in ideal conditions, neglecting the heat loses etc.)[ CITATION Goe94 \l 1029 ].
The energy in a form of heat will dissipate through the walls, doors and, for example, through the gap under the door. It is well known from everyday life that heat leaks more easily through holes and crannies than through walls. What is less known is that once a hole gets bigger (e.g.
somebody opens the door ) the rate of heat dissipated through walls gets
significantly lower and most of the heat will transfer through the open door.
Metaphorically speaking – the room “prefers” to transfer the heat in the most efficient way, “closing” the less efficient channels (dissipation through walls), and “gives a higher priority” the more efficient channels (open door ) for transferring energy (heat). This preference is explained in the following subsection.
3.1.3. Preference for more efficient configurations
The examples above, i.e. simple plant cells gradually evolving into multi- cellular organism and thermodynamic system that utilize more efficient ways of energy transfer ) are presented in order to illustrate the same principle:
In nature, preference is given for system configurations (living or not) which allow for a better transfer of energy. This is a consequence of the second law of thermodynamics – the better the energy transfer is, the faster the systems get into a state of entropy (in case of nonliving systems – the room) or the larger amount of entropy is produced (in case of living system – the multi-cellular organism) [ CITATION Goe94 \l 1029 ].
Energy transfer within nonliving system exists only for a limited amount of time – up to the moment when system reaches equilibrium. Its
“lifespan” is dependent on local energetic gradients. On the other hand, living organisms are never in state of equilibrium for which they are referred as “far from equilibrium systems.” The far from equilibrium state is being kept up by a metabolism that allows them to live autonomously, regardless of the local energetic gradients [ CITATION Goe94 \l 1029 ].
As already mentioned in 3.1.1, the evolution of life is about evolution of entropy production, that is, the more evolved the living creature the more energy is consumed for maintaining its metabolism, the more entropy is produced. The human brain is the most complex and evolved organ known, and it is capable of processing immensurable amount of information (calculation capability of human brain is estimated as approx.
37 petaflops [ CITATION Web12 \l 1029 ]). It consumes up to 20% energy
of the human body in terms of oxygen and glucose demand [ CITATION Lin01 \l 1029 ]. From the energy flow stand point, the brain is by far the most evolved “machine” for entropy production.
3.1.4. Underlying principle: self-feeding cycle
Preference for configurations with higher rate of energy transfer described in the previous subsection is based on the so called “self-feeding cycle”
principle. This principle is illustrated with a very well known aphorism saying that “the rich get richer” and it represents the quintessence of nonlinear dynamics [ CITATION Sch10 \l 1029 ].
In the room temperature example, when a door is opened, the warm air near the door would quickly move towards the cooler room. This movement pulls air molecules near the main “stream” of air heading towards the cooler room. The more warm air molecules are pulled by the stream, the bigger and stronger the stream gets. As a consequence, much larger amount of the heat energy is transferred through the open door (the energy channel with best energy transfer potential) than dissipated through the walls [ CITATION Goe94 \l 1029 ].
This self-feeding cycle lies at the heart of many everyday life phenomena, such as fashion trends or computer operation system platform preferences.
For example, 90% of computer users use Microsoft Windows platform [ CITATION net13 \l 1029 ]. The dynamics driving such trends are similar or the same. For some reason (e.g. better problem solution, usability, design) a certain group of users, sometimes called “early adopters1”, starts using a product. They recommend the product to other potential users and this leads to more people buy it, and so forth. Some customers might even select to buy the same product only because of its growing popularity, disregarding the “rational” or “objective” reasons for buying it, or because they want to have a product that is compatible with products most of their friends and relatives own, as well.
1 An early customer of some product who provides reference to other customers; also
As a result, the number of customers grows exponentially, according to the law of nonlinear dynamics, the self-feeding cycle, or the so called “rich get richer” principle[ CITATION Goe94 \l 1029 ].
3.1.5. Section summary
The theory of energy flow provides a plausible explanation of why a natural preference seems to exist for energy channels and system configurations that allow higher rates of energy transfer. This preference is based on the nonlinear dynamics principle that is inherently bound to the essence of our physical reality, the second law of thermodynamics, and represented by the self-feeding cycle.
The preference for configuration that allows higher energy transfer is universal and applies to all systems (physical, chemical, biological, etc.). It also explains the tendency for growth, evolution and self-organization of matter.
3.2. Self-organization
Flocks of birds, schools of fish, ant colonies – these are all examples of self-organized group behavior that might look complex but in fact they exist as a result from simple rules of interaction. Self-organization is a phenomenon that occurs in many natural systems. It is a process of development of global order and form in systems and is based on the interaction between individual system entities with no central control or orchestration [ CITATION Cam01 \l 1029 ].
Man-made objects and products possess shapes and functions that were designed and calibrated with a conscious intent from the very beginning.
In nature, there are no designers or engineers; systems grow, evolve into new forms, and gain new functions as a result of interaction within the system itself, and, at the same time, between the system and its environment. All this happens on the basis of a process called self- organization [ CITATION Hak08 \l 1029 ].
3.2.1. Underlying principle: Feedback loops
The global order and form of a system, originating in the self-organization process, at any given moment, is a result of a balance between energetic potential of the system and resource possibilities of the environment. As mentioned earlier, natural systems tend to prefer energetic channels that allow energy to flow faster, i.e. they prefer to grow and evolve. This tendency represents a positive feedback. However, the resources in the environment of the system required for growth are usually limited. These limitations represent a negative feedback. Therefore, the process of self- organization is the process of interplay between positive and negative feedback [ CITATION Cam01 \l 1029 ].
A description of positive and negative feedback is provided by[ CITATION Pel11 \l 1029 ]:
A positive feedback is any process or a type of behavior that leads to progress, growth, a novel solution of a problem or expansion of an entity into the environment; is what drives system out of equilibrium (a push forward).
A negative feedback is any process or a type of behavior that causes regulation, slows down growth, initiates stabilization; represents
“resistance” of the environment; is what drives system towards equilibrium (a pull back).
In general, feedback loops represent two motives; one is for growth and expansion, and the other for regulation which comes from the environment’s resistance due to limited resources. The motive for growth even in environments with limited resources is based on the principle of cooperation which drives originally self-contained entities towards self- organization. When large numbers of entities cooperate, the average resource income for individual entity is higher than if the cooperation does not exist [ CITATION Cam01 \l 1029 ].
For example, a dictyostelium is a slime mold living as individual amoeboid cell in conditions of sufficient food resources. Under food starvation however, individual cells start to produce chemical substance that causes them to aggregate with one another. A colony of approximately 100,000 of these cells forms a shape of what resembles of a slug which is capable of movement as individual entity. This way the colony moves to a region with potentially new food resources. If the food resource is not sufficient and starvation continues, the process of self- organization of the colony leads into formation of even more elaborate structure that reminds of a single mushroom. As the mechanical tension in the structure caused by the aggregation of cells rises, it reaches certain threshold, the head of the mushroom is “shot away” and it settles in a new region while rest of the colony stays in the original position. The colony is split into two parts and covers a larger area than originally which provides for a better average food supply for the individual cells [ CITATION Smi10 \l 1029 ]. The evolution of a colony formation is illustrated
on below:
Figure 1. Dictyostelium life-cycle2 2 Source: [ CITATION Smi10 \l 1029 ].
3.2.2. Feedback examples
Feedback cycles (positive and negative) may be either internal or external.
A prey seeking wolf illustrates both. Hunger is the internal positive feedback, i.e. the need for food, which motivates the wolf to hunt. The internal negative feedback may be coming from inadequate hunting skills, while the external negative feedback may be coming from the lack of any prey or the prey efficient escape.
The interplay of feedback loops may be also illustrated in human communication as well. Examples of feedbacks are provided by Table 1.
Table 1. Feedback examples
Positive feedback Negative feedback External
(interpersonal)
Approval Appreciation Acceptance
Open mindedness
Disapproval Criticism Rejection
Conservativeness Internal
(intrapersonal)
Self-confidence Assertiveness Compassion
Lack of self-confidence Fear
Disinterest
Self-organization can also be observed in physics or in chemical reactions.
A snowflake, for example, is resulting from the interplay of a positive and negative feedback represented by the water attribute of expansion upon freezing, and the crystallization blocking the expansion (the environment resistance, i.e. the low temperature), respectively. The resulting shape and structure represents a stable energy state, a global order rising out as a consequence of the mutual effects of two antagonistic powers [ CITATION Gle89 \l 1029 ].
The process of self-organization can be observed in practically every scientific domain, e.g. in physics, mathematics, chemistry, biology, cybernetics, etc. [ CITATION Hak08 \l 1029 ].
3.2.3. Through self-organization to stability
Dynamic systems evolve over time and reach stable states through the interplay of feedback. These feedback cycles allow system to reach stable energy states. If there is abundance of resources systems grow and evolve and if there is shortage of resources, systems’ growth slows down or stops. Continuous lack of resources could result in system devolution.
However, the devolution of systems could result in increase of resources as the consumption decreases. Ultimately, the balance between systems and environment’s resources oscillates over time, always seeking stable energetic states through the process of feedback loops interplay. At every given moment a system is in dynamic equilibrium and the self- organization allows that system function in more energy-efficient manner, maximizing the energy flow, and entropy production [ CITATION Goe94 \l 1029 ][ CITATION Gua09 \l 1029 ].
3.2.4. Organization without external control
The process of self-organization is essentially a natural process of interaction between numerous entities without any central controlling unit orchestrating this global order. For example, termite colonies are capable of building surprisingly elaborate mounds with ventilation shafts, dormitories, arched domes, gardens for fungal cultivation, etc.
[ CITATION Wil07 \l 1029 ], however, there is no “architect” or “site manager” who “coordinates” the work. Such complex behavior resulting in construction of elaborated mound is a consequence of multiplicity of pheromone interactions between individual termites. These termites follow simple rules like “if you sense a pheromone trail, follow it”, “if you find a food supply, pick it up and return it to the mound while leaving a pheromone trail”, etc. Following these rules and the multiplication of this behavior leads to global order through the feedback cycles [ CITATION Ren03 \l 1029 ].
Transportation systems may provide another example of the emergence of global order with no external control. There are set rules that which each driver has to follow, e.g. “stop on red”, “slow down when you are getting near the car in front of you” or “do not enter crossroads if you cannot leave it immediately”, etc. When drivers respect these rules there is no
need for external control in order to achieve fluent traffic in normal circumstances.
3.2.5. Emergent properties
Global order arising from mutual interaction of entities cannot be predicted or inferred based on the behavior of an individual entity. The existence of a termite mound cannot be explained by the behavior of an individual termite. A fluent traffic flow cannot be explained from the perspective of a single car driver. The human consciousness cannot be derived based on the activity of an individual neuron cell. “The whole is greater than the sum of its parts”, says famous quote from Aristotle. A new quality emerging from the collective activity of many entities or agents is called the “emergent property” or “emergent phenomenon”
[ CITATION Gua09 \l 1029 ].
3.2.6. Section summary
Self-organization is defined as the process of mutual interaction between numerous entities, operating in energy efficient states while maximizing the energy flow, reaching dynamical stability, and global order based on seemingly chaotic local behavior. Global order is a new quality of a system and it is called “emerging property”.
3.3. Bifurcations
Self-organization is a process depicting how systems evolve and change their structure. Such changes of structure or reconfigurations are called bifurcations. “Bifurcation is a transformation from one type of behavior to a qualitatively different type of behavior” [8, pg. 40]. What is more important however is the fact that these qualitatively different states of a system result from the same function (or one mathematic equation) of system behavior [ CITATION Goe94 \l 1029 ].
3.3.1. Underlying principle: Limited energy flow capacity
Certain system configurations allow only limited energy transfer therefore; these systems transform in order to increase the possible energy flow [ CITATION Goe94 \l 1029 ] . For example, while a horse continuously increases its speed, its movements change from walk into trot, canter and gallop. Each of these gaits has a specific pattern of joint and muscle movement, allowing the horse to reach certain speed threshold. After reaching a threshold, the horse must reconfigure the way it uses its legs in order to further increase its speed. The transition between walk, trot, canter and gallop is an illustration of what is called “bifurcation” in the context of the Chaos theory [ CITATION Gua09 \l 1029 ].
In above example, the riding horse speed is the control parameter. As this parameter changes, the system (horse leg movements) goes through periods of stable configuration, punctuated by abrupt transition to a qualitatively different configuration, allowing the further control parameter increase [ CITATION Goe94 \l 1029 ].
3.3.2. Bifurcation diagram
The qualitative change of a system behavior may be presented in a bifurcation diagram. A bifurcation diagram is a graph that provides an overview of how the behavior of a system changes with the change of a controlling parameter. The bifurcation diagram also presents a different view of how change takes place. Traditional (linear ) science views change as a smooth, continuous, and traceable. Bifurcation diagram presents change can sometimes be smooth and sometimes a very abrupt process.
Moreover, it is not possible to assign certain individual input as the cause for a qualitative change – bifurcation happens as a result of a global state of the system [ CITATION Goe94 \l 1029 ].
A simple bifurcation diagram is shown on Figure 2. Bifurcation diagram.
The single curve at the beginning of the graph represents the system in one stable state. As the system evolves, the ability of the old configuration to process energy flow diminishes and the tension grows. After reaching a certain threshold (the bifurcation point), the old configuration becomes unstable and the system may split into two new configurations, which represents two stable solutions to the “crisis.” The new configuration
dissolves the tension and restores the system’s ability to process energy effectively, until the next “crisis”.
Figure 2. Bifurcation diagram
3.3.3. Section summary
Both emergence and bifurcation result from an energy crisis in a system.
Bifurcation is the transformation from one type of behavior to a qualitatively different type of behavior. Such transformation can be presented on a bifurcation diagram which provides an illustration of how system’s behavior varies over time and that a change can be both smooth and abrupt.
3.4. Attractors
The concept of bifurcation demonstrates that a particular system may possess many types of behavior while only a single parameter is followed.
In other words, one mathematical equation may have multiple qualitatively different solutions. Furthermore, a system may be in a stable or unstable at different times.
Stability is an optimal energy state; therefore seeking such state is a dominant attribute of any dynamical system, and this significantly affects its behavior. Systems may even exhibit similar patterns of behavior based on a very diverse input parameters. In other words, whatever the initial conditions are, the resulting state of system behavior will be the same or very similar. Generally speaking, system parameters are dominant over input values. This attribute of dynamical systems is also referred as
“equifinality” [ CITATION Wat99 \l 1029 ]. The Chaos theory further describes structure of this phenomenon by the concept of an “attractor.”
3.4.1. Phase space
In order to understand how attractors influence behavior of a system, it is important to explain the concept of phase space. Phase space is a representation of all possible states of an observed system; therefore it can be interchangeably referred to as a state space. Each axis of the phase space represents one variable [ CITATION Ter08 \l 1029 ]. One of the most used examples for demonstration of a simple phase space is the idealized (frictionless) pendulum, which has two variables: velocity and position (Figure 3).
Figure 3. Phase space for idealized pendulum
Every point on the circle phase space of the pendulum represents one moment of the pendulum swing. Phase space is providing a global overview of every possible state of the pendulum in space and time.
3.4.2. Attractor as distortion of a phase space
An attractor draws a system to a certain state representing a local energetic optimum. An attractor distorts phase space in a similar way as gravity distorts space-time. An attractor has an effective range in which it can attract “objects” (states of the system), which is called a basin. The stronger the attractor is the wider has the basin [ CITATION Gua09 \l 1029 ].
A real life pendulum would not swing ad infinitum; it would lose its energy and eventually stop its movement. Consequently, its phase space would not be a circle, but a spiral, ending at the origin of the graph, at coordinates [0, 0]. In this case, the origin of the graph is a single point attractor.
The concept of attractor adds two important elements to the science’s conceptual scheme – the idea of attraction itself and the idea of a form.
The ancient philosophical idea of a pull toward an ideal form originates in the natural tendency of systems to seek energy optima [ CITATION Goe94 \l 1029 ].
3.4.3. Stability vs. instability
There are many types of attractors, from single point attractors to strange attractors with complex and esthetic form. From general perspective, there are two types of attractors – stable and unstable. Most of the attractors are regarded as a stable structure. When system enters its basin in a phase space, it will follow the same rules of motion [ CITATION Gua09 \l 1029 ].
The behavior of a system entering basin of the attractor is illustrated on Figure 4. The upper part of the picture presents the distortion of a phase space caused by two attractors (most dynamical systems have more than one attractor ), each with energetic optimum marked as –x0 and x0. The crosshatched and blank parts of the lower part of the picture represent basins of attraction of those attractors. Whenever system enters the basin of one attractor, it will be “pulled” to the energetic optimum of the particular attractor. Once the system settles in the centre of attractor, it will remain there forever [ CITATION Ott06 \l 1029 ] .
Figure 4. Basins of attraction
3.4.4. Repellors
Attractors are distortions of a phase space that draws objects into its basin. Repellors have opposite effects – they drive system state away from its basin. Repellors represent system states of high energy that, in the current state, cannot be effectively transferred. This discrepancy drives system to leave the basin of a repellor, seeking states that would allow the energy to flow [ CITATION Ott06 \l 1029 ] .
Repellors are unstable structures for what it is hard to predict where the system will move within the phase space. Trajectories of movement within domain of repellor in a phase space depend on repellor structure and shape (Figure 5. Illustration of repellor shapes , edited according to [ CITATION pro08 \l 1029 ]) – hard lines denote shape of a repellor, arrows demonstrate motion of system within phase space. The closer the lines are to each other (e.g. the centre of the spiral repellor on the right hand side of Figure 5), the less predictable is the system’s behavior, as only micro-scale inputs (that are usually treated as negligible) are sufficient for changing the “lane” of the repellor shape. As a result, two
objects put in the centre of a repellor might end in very different regions of a phase space [ CITATION Gua09 \l 1029 ].
Figure 5. Illustration of repellor shapes
3.4.5. Saddles
A system also demonstrates unstable behavior when at borderline area of adjacent basins of attraction. These repelling lines are called saddles. The border itself is infinitesimally small – in fact, the borderline is not a line but it has a fractal structure (which will be introduced in next section). As a result, it is virtually impossible to predict which way the system will move away within a phase space if put at the saddle [ CITATION Gua09 \l 1029 ].
Two attractors (A), a repellor (R) and a section of a saddle (S) are marked on Figure 6.
Figure 6. Attractors, repellor and saddle
The concept of attractors explains why a system posses traits of stable and unstable behavior under various circumstances. Within the domain of an attractor, the system is stable, robust, and resistant to change. In fact, the behavior of dynamical systems within the domain of attractor is also self- stabilizing, maintaining its current patterns of motion even if disturbed by random perturbations. The behavior of a system is unstable, hard to predict, and context dependent when it is in the domain of repellor at a saddle. Furthermore, in unstable areas of phase space, even small inputs may lead to large effects [ CITATION Goe94 \l 1029 ].
3.4.6. Energy landscape
In dynamical systems, there is usually more than one attractor in a phase space. Moreover, the shape of the attractor may be further structured, e.g.
there may be even minor attractors within the basin of mayor attractor.
The global structure of the phase space may be portrayed by the concept of energy landscape (or energetic landscape).
The energetic landscape is a concept illustrating different energy levels throughout the phase space. The lower the energy level, the deeper or stronger is the attractor, therefore the more influence it has one the behavior of the system [ CITATION Wal04 \l 1029 ].
The energetic landscape also shows the relations and borderlines between attractors, saddles, repellors, etc. An example of an energetic landscape is presented by the Figure 7, where depressions with red dots represent attractors (dotted circle is the basin of attraction), elevations represent repellors and border between two attractors is created by a saddle [ CITATION Eli07 \l 1029 ]:
Figure 7. The energetic landscape
Metaphorically speaking, attractors, repellors and saddles create
“depressions”, “hills”, “valleys”, etc., on the landscape of phase space, with similar implications – when hiker is in the valley surrounded by mountain on each side, any trip would be uphill which would require energy investment. This means that when system is about to cross the saddle, it has to accumulate enough energy – the so called “activation energy” [ CITATION Cse06 \l 1029 ].
Passive systems (those with no income of energy) cannot cross the saddle – once fallen into the domain of any attractor, they will inevitably end in its center, marked by the red dot on Figure 7 [ CITATION Eli07 \l 1029 ].
3.4.7. Section summary
Phase space is an abstract map of every possible state of an observed system. Attractors are distortions of a phase space, a local energetic optima to which all trajectories of system behavior will converge over time. They represent stable structure as system entering its basin will follow similar patterns of motion. Behavior within the domain of attractor is stable, predictable, robust to change, and self-stabilizing.
Repellors and saddles represent unstable structures. Trajectories of behavior within the domain of repellor diverge away from its center.
Behavior of system in the domain of repellor is unstable, hard to predict, and susceptible for change through immeasurable inputs.
Energy landscapes provide an overview over energy levels and energy optima within phase space with multiple attractors, repellors and saddles.
3.5. Fractals
Fractals are self-similar objects created by the process of self-organization of matter via the interplay of feedback loops. Self-similarity means that object has similar shape when observed from different scales, e.g. a branch of a tree looks like a small tree, or a large cloud far away looks like a similar to a small cloud in proximate distance. Concept of fractal was proposed by French mathematician Benoit Mandelbrot who proposed that fractal geometry is innate structure of nature, from shape of flame, thunder or river, up to the density of galaxies in universe or structure of internet network [ CITATION Man83 \l 1029 ].
3.5.1. Fractal as energetic optimum
In section 3.2.2, there was an example of a snowflake whose structure was resulting from the self-organized process of interplay of two factors – water expansion and crystallization. The resulting shape represents a final energetic equilibrium between these two forces. In fact, structure of the snowflake is a fractal, i.e. self-similar. When zooming in on a snowflake, the zoomed region looks like a little snowflake. Idealized snowflake structure is illustrated by the Koch snowflake ( Figure 8).
Figure 8. Koch snowflake
Reason for self-similarity is that the antagonistic forces (expansion vs.
crystallization) have same effect on all scales of zoom. For understanding of this phenomenon it is important to understand the difference between classical and fractal dimension.
3.5.2. Fractal dimension
In classical Euclidean geometry there are only 3 dimensions that describe space – width, height and depth. In order to describe objects in this geometry, arbitrary units of measure are used, e.g. inches or centimeters.
According to Mandelbrot, 3D objects are idealized version of real life objects whose dimensions are not whole numbers, as they are not ideally smooth, straight, or round. As a consequence, measures taken within idealized geometry using arbitrary scales are also idealized. Moreover, taking measures using only one scale is an artificial habit that does not follow the nature of real objects [ CITATION Man83 \l 1029 ].
This can be illustrated by the “Coastline paradox” which portrays the difficulty with determining the length of a coastline of an island. The length will be influenced by the measuring scale (or ruler ) – the smaller the ruler, the more details are taken into the measurement [ CITATION Wei13 \l 1029 ].
Mandelbrot’s implication is that the length of the coastline is virtually infinite when zooming into the structure of coastline and using more and more detailed ruler. In other words, the length of a coastline is counted as finite only because an arbitrary scale is used and further granularity of the coast is neglected. Furthermore, the shape of the coastline is a fractal because it has a similar structure when observed from distance as it does when zoomed in by various multipliers [ CITATION Man83 \l 1029 ].
3.5.3. Fractals and scale invariance
Fractal structure of objects (e.g. the snowflake or coastline) is created because self-organization of antagonistic forces (i.e. positive and negative feedback) operates in the same manner on all possible scales. Those self- organized forces which create the main structure of the snowflake are the same as those creating any randomly zoomed region of it. Both the global shape and the shape of details are resulting from the interplay of equally affecting forces. This phenomenon is called “scale invariance” [ CITATION Bar03 \l 1029 ].
3.5.4. Fractals as real life objects
The structure of a fractal is virtually infinite as a spontaneous consequence of self-organization, scale invariance, and energy flow.
Metaphorically speaking, a fractal “aims for” filling out the limited volume with the largest possible surface. The larger the surface is, the better is the energy flow that allows most efficient transfer of energy, and maximal entropy production, according to the second law of thermodynamics[ CITATION Man83 \l 1029 ][ CITATION Goe94 \l 1029 ] [ CITATION Gle89 \l 1029 ].
Virtually infinite surface of fractals allows best contact of the system with its environment, e.g. branching of lungs have fractal structure that allows highest possible transfer of gases between air and blood in an organism [ CITATION Abd01 \l 1029 ].
Fractals are also physical expressions of nonlinear processes of self- organization through which many natural objects are created. This means that fractal is not only a scientific concept but also a real life object. There are numerous natural shapes that possess fractal structure, e.g. Romanesco broccolis, canyons, sea shells, leaves, trees, waterfalls, river deltas, etc.
[ CITATION McN10 \l 1029 ].
3.5.5. Implications of fractal structure
In the context of this work, fractals have the following important implications, a) they provide an additional way of describing dynamical systems’ processes and behavior; b) self-similarity throughout various scales implies that reducing the whole into its parts does not simplify the observed phenomenon, c) sensitive observation of micro-scale processes may provide essential information about macro-scale processes [ CITATION Gle89 \l 1029 ].
3.5.6. Section summary
Fractals are self-similar objects created through the process of self- organization, i.e. through interplay of two antagonistic forces (positive and negative feedback). These forces are effective on every possible scale of observation as a result of scale invariance. Fractal surface is virtually infinite what allows maximal possible transfer of energy and entropy production. Fractals are both abstract concept and real life objects.
3.6. Networks
A study of networks, the so called “Network Science” is a new interdisciplinary academic domain originating in the Chaos theory and studying complex systems. The first issue of Network Science Journal was
published in the spring of 2013 [ CITATION Net13 \l 1029 ] and illustrates that the “zenith” of network science which is yet to come.
The Chaos theory studies systems with numerous mutually interdependent entities. There is a transfer of energy or information between these entities or, generally speaking, there are connections and relationships between these elements. These elements (called “nods”) and connections (called “links”) altogether create a network. The “Network”
perspective allows the behavior and attributes of a system to be described and predicted in terms of its stability, evolvability3, ability to dissipate stress, ability to transfer information, etc. [ CITATION Cse06 \l 1029 ].
The network science can be applied to various subjects of study, e.g.
[ CITATION Bar12 \l 1029 ]:
The interaction between proteins, genes, or metabolites that allows integration of processes within living cells
The wiring of neural cells for better understanding of brain functions
Relationships between family, friends, or co-workers, and how they influence the quality of interaction
The interconnectedness and attributes of internet websites, transmission lines, or power grids
Trade networks transferring goods and services
Financial and economic patterns
Most of these network examples result from self-organization and they share lots of common features, from their topology to their dynamism [ CITATION Cse06 \l 1029 ].
3.6.1. Strong links and weak links
In order to understand structural stability and other properties of networks, it is important to present the concept of strong and weak links because their ratio in a network has a significant influence on its structural attributes. The following definitions of strong and weak links definition are according to Csermely [ CITATION Cse06 \l 1029 ]:
