Application of Complex Systems Science to the Management of Systems of Systems

Prof Vernon Ireland, University of Adelaide, and

Prof Stephen Cook, University of South Australia, Australia

IEEE SoSE 2014

Basic theme of this conjecture

Conjectures and refutations

Conjecture: I almost never see the following concepts in System of Systems

research!

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Inhabiting the complexity space between order and chaos

This space is populated by chaordic systems Chaordic systems blend order and chaos. (van Eijnatten, 2008 & Mitleton-Kelly 2003). Chaordic means:

1. Anything simultaneously orderly and chaotic; 2. Patterned in a way dominated neither by order nor chaos; and 3. Existing in the phase between order and chaos.

Holonic capacity is the holon’s ability to operate with greater mindfulness, expanded awareness, control and response-ability Control-ability is the degree to which a holon is able to influence future events, and response-ability is the ability to respond to far from novel qualities of the whole not present in the parts – because they are inherently self-organizing, self- referencing, self-iterating and self-adapting

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1. Operation of holons

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Eijnatten 2004

2. Operation of holons

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3. Operation of holons – seeking stability levels

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1. Paretian statistics and power laws

Andriani & McKelvey (2011) identify 103 power laws which include: • Size of nations by population • Hierarchy of social group size • Economic fluctuations • Growth rate of countries • Duration of recessions • Distribution of wealth • Cost of homelessness in cities • Sales of fast moving consumer goods • Movie profits • Traffic jams Not governed by Gaussian statistics but by power curves such as F ~ N-ß in which F is the frequency, N is the rank (variable) and ß is the exponent, which is constant When created on log-log scales, straight-line relationships are produced, which are recognised as Paretian statistics

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Size and rank of retail enterprises a power law

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Log of Event Size

Log of event frequency

Ma & Pa Stores (17 Million in USA)

Walmart

Power law Negative slope

2. Paretian statistics and power laws • A power-law implies that small occurrences are extremely

common, whereas large instances are extremely rare.

• This regularity or 'law' is sometimes also referred to as Zipf and sometimes Pareto.

• The laws alternately refer to ranked and unranked distributions.

• Zipf, power-law, and Pareto, can refer to the same thing

• The system shifts from exponential or log normal to a Pareto distribution because of the emergence of multiplicative outcomes.

• Caused through positive feedback loops, generated by preferential attachment, spontaneous order creation and irregularity generated gradients.

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3. Paretian statistics and power laws

• Benefits of positive feedback, also known as causative, deviation amplification

• A process becomes self-reinforcing and spirals up in an explosive way.

• An example is provided by all mobile phone manufacturers benefiting from each other’s success.

• OR advertising: ‘The burgers are better at Hungry Jacks’

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1. Scale free and fractal behaviour

• Fractal geometry was developed by Mandelbrot (1982)

• He demonstrated that irregular shapes of most natural objects, from cauliflowers to coastlines, trees and galaxies, show the same design and shape and result from the same causal dynamics.

• A fractal is a pattern or shape whose parts echo the whole. Fractals are self-similar objects.

• They demonstrate power laws from atomic nanostructures

• (10-10) to Galactic mega spaces (1022)

• Atoms and the solar system

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2. Scale free and fractal behaviour

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Coastlines

Rivers

Cauliflower

3. Scale free and fractal behaviour

• Regular patterns of behaviour and shapes (Fractals) provide positive reinforcement, if beneficial and negative reinforcement if a failure

• This can be produced by advertising or consistent enterprise processes such as ISO 9000, 6 Sigma or CMMI

• It can also occur through the resonance of pleasurable emotional experiences

• Or repeated unpleasant experience producing negative reinforcement

• Social fractals also exist: for example societies which consistently display honest, transparent and behaviour which puts others first creates a self-reinforcing force

• Failed societies, with dishonest, self-serving hidden behaviour also is self-reinforcing

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4. Scale free and fractal behaviour

• Observing fractal you get information proportional to the scale;

• The small-scale remains an equally complex microcosm of the whole.

• A boss and a subordinate, with consistent behaviour, create a self-reinforcing fractal

• Others are positively influenced by this fractal

• Fractals will occur through:

– Conversations and language emphasising innovation & creativity

– Conversations and language emphasising business success

– The organisation’s culture

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Self organised criticality

• The model is based on dropping sand grains onto a pile

• After a while an avalanche occurs (Bak, 1996)

• The model relates to choosing a space which is on the edge of chaos

• The benefit is that the edge of chaos produces the most innovative opportunities BUT can we cope

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Tiny initiating events (TIEs) • As part of operating on the edge of chaos we

need to assess the TIEs (Boisot and McKelvey (2011)

• The history of a number of disasters is that there were opportunities to react earlier and AVOID the event, if only signs had been realised and action taken

• These include: – The first and consequently the second world war –

100 million people dead – Margaret MacMillan – The two space craft disasters Challenger and

Columbia – September 11 Twin Tower disaster

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Fitness landscape

• Fitness landscape was initiated by Kauffman (1993)

• It assesses the relative fitness of alternative parameters

• This has relevance for assessment of alternative systems

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Systems in cycles of change This concept was introduced by Gunderson &

Holling (2002)

During the slow, front phase of the cycle (r to K),

connectedness and stability increase as the

system grows and expands.

It then starts to become ‘over connected’ as the

back loop begins, and at this point efforts to

continue to grow will cause collapse (K).

The back loop represents a rapid phase of

release (Ω) and reorganization (towards α),

which leads once again to a time of exploitation,

or growth (r).

The relevance of this for organisations and

leaders is the ability to intervene in appropriate

ways that take advantage of these cycles, or

even push the organisation towards a necessary

stage rather than resisting.

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Cycles of change

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Findlay & Strauss mathematically modelled long term changes (Gorod et al 2014)

Systems in cycles of change • Meadows’ (2008) concept of places to intervene is based on such

knowledge, especially concerning balancing and reinforcing feedback loops.

• Meadows recommended managers: 1. Get the beat

2. Listen to the wisdom of the system

3. Expose your mental models to the open air

4. Stay humble. Stay a learner

5. Honor and protect information

6. Locate responsibility in the system

7. Make feedback policies for feedback systems

8. Pay attention to what is important, not just what is quantifiable

9. Go for the good of the whole

10. Expand time horizons

11. Expand thought horizons

12. Expand the boundary of caring

13. Celebrate complexity

14. Hold fast to the goal of goodness

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Environment driving system structure • In general terms complex systems are more sensitive to the

context or to their environment than complicated or linear systems are

• The environment that must be responded to include:

– Cultural issues

– Political issues

– Economic issues

– Social issues

– Technological issues

– Legal issues

– Environmental issues

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Systemic and cascading risk • Helbing recognises both systemic and cascading risk

• Systemic risk is primarily whole system risk which is very different to individual risk assessed under ISO 31 000

• World Bank which concluded that approaching 1 million children had died as a result of the global financial crisis – this was caused by their parents loosing job opportunities

• Systems which can cascade into each other: – Global governance failures

– Illicit trade

– Terrorism

– Geopolitical conflict

– Food security

– Water security

– Increase of infectious diseases

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Self Organisation

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Organisations should recognise staff CAN self organise and often the results are very positive There is too much top-down leadership

Attractor cages and Path history

• Attractors act as energies that motivate.

• For most people working life is a strong attractor.

• Politics, religion and environmentalism, and other issues, may all act as attractors in someone’s dynamics.

• The cage is developed when someone sees everything through the perspective of that attractor and we all do it

• A carpenter sees problems in terms of use of a hammer and saw

• A traditional systems engineer sees problems in systems engineering terms

• George Bush saw victory in Afghanistan in terms of military victory and not in terms of winning the hearts and minds of the people

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System Dynamics

• Systems dynamics was introduced by Forester (~1960)

• Systems dynamics is a method of assessing long-term implications of a proposed course of action

• Australia’s history of governing the indigenous community is that today’s problem was yesterday’s solution

• There have been multi-cycles of this

• The negative consequences of actions associated with a policy were inadequately explored

• The core of systems dynamics is plotting and exploring positive and negative outcomes and then taking decisions which recognise these

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Sense Making and Common Meaning

• Many project teams, working on linear and traditional teams, don’t share common meaning (Cicmil)

• Often due to their coming from different backgrounds and cultures

• We interpret meaning based on our prior experiences

• How much more when a group of diverse system specialists come together

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Systems Intelligence

• Systems intelligence was introduced by Hämäläinen and Saarinen in 2004

• ‘Intelligent behaviour in the context of complex systems involving interaction and feedback’

• People with systems intelligence perceive themselves as both influencing and being influenced by the whole

• Systems thinkers ‘recognise that systems thinkers can balance the paradoxical aspects of acting intelligently without knowing the system completely, balancing control and emergence and demonstrating almost selflessness with stern resolve (Kerr (2014: 52-53) interpreting Saarinen & Hämäläinen (2007)

• a powerful aspect of SI is the acknowledgement of intelligent actions supported by personal responsibility as a backbone of those actions, thus avoiding the cognitive systems trap of believing that once we have cognitively identify the relevant systems, most of the work is done

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Systems intelligence • If organisations are accepted as being primarily chaordic

systems which combine the two states of order and chaos (change and stability) at any one time the bifocal capability of SI is well suited to the successful leadership of such an entity.

• One of the bases of systems intelligence is its realistic, hands on optimism which is key to positively reframing people’s core beliefs

• A willingness to take action without knowing how things might unfold in the future through a readiness to embrace uncertainty and surprises – what Zhu (2007) calls pragmatic sensibility

• Requires: A pragmatic sensibility, with its emphasis on the unity of idea and action, on community conversation , on grounding knowledge upon practical consequences, on openness to alternatives and differences, on engaging contrasting or conflicting perspectives

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Systems intelligence • Hämäläinen and Saarinen have a tool for measuring system

intelligence

• High system intelligence could be basis for being chosen to be in SoS teams!

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Outline of the Refutation

• Let’s be really clear about what we are talking about: what does SoSE research entail

• Much of this is fairly well known and taught in mainstream SE programs and much is axiomatic to systems thinkers, especially those active in large-scale/enterprise SoS

• Where do these ideas fit within the context of a discipline?

• SoS people are looking at better connecting the theory to practice

• Conclusion

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Positioning our Dialectic (from Johnston et al, 1999)

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Technology

Practical cultural activities:

Includes hardware, software and

their social and technical context.

Engineering

Science, art and

judgement, applied to

design construction and

use of material and

machines (includes

engineering management)

Science

Systematic study

of the physical

world and its life

forms; aimed at

knowledge and

understanding

Engineering

Science

Science adapted

for use in

engineering

practice

Focus of Electrical Engineering, SE & SoSE

Focus of Complexity Theory

Focus of SoS Research?

Another Conjecture:

Research in SoSE relates to all of

these areas including science,

technology, management,

social, organisational,

cultural, workforce development, etc.

Impact of the Research Breadth Assertion

• Complexity theory is important and relevant but is only one of many research areas of important to SoSE – see Cook & Ferris 2014

• Many of the research areas mentioned are very different to STEM research in that their theoretical base is not scientific but phenomenological – There is no theory of management (Checkland, 1981 and later)

– In many areas of engineering, theory provides only first approximations, in many other areas experiential knowledge is paramount and it is this that is ensconced in standards

– Complexity theory is represented – see next slide

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Slide

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SoSE Research Visualisation Framework Showing Coverage of SoSE 2011-13 Papers

Specialty Engineering 101

Underpinning Theoretical Frameworks of Ideas, Systems Theory, Systems Thinking 12Systems Theory for Complex Adaptive, Open, & Evolving Systems 22Codified knowledge, e.g. SEBoK, standards, guidelines, processes 12Determining (and tailoring) the SE approach for particular SOSE applications 8SOSE Research Agendas and Research Classification 7 SoSE Effectiveness 0

Strategic & Capability-based Planning 7SoSE for Network-enabled SoS 18Systems Approaches to Management 8

Model-based Systems Engineering 55Model-driven Architectures 8Expedited SoSE 2Complex Project Management 19Modelling and Simulation 10Human Systems Integration 0Enabling Information Technology-directed Approaches 27

Mission/Purpose Definition 10 Requirements Engineering 13Architectural Design 28Implementation 2Technical Analysis 85 Verification & Validation 10 Sustainment and Maintenance 2

Activity (Project) Planning 3 Activity (Project) Assessment and Control 3 Decision Management 22Risk Management 20 Configuration Management 0 Information and Knowledge Management 3 Management Metrics 0System Management, Control and Operations 15 Initiative-Enabling Processes 0Contract and Scope Management 0

Affordability 0Reliability, Availability and Maintainability 9 Logistics and Supportability 3 Resilience/Survivability 14 Environmental Compatibility 0Human Factors/Human System Interface 13 System Safety 14 Systems Security 26Cost Engineering 0Systems Quality Assurance 7Interoperability 14Electromagnetic Compatibility 0Qualification and Assurance 1Value Engineering 0 Tempest 0…

Modelling Tools 42

Design Tools 12Knowledge Management Tools 2Tool Integration and Interoperability 0Modelling Languages, Ontologies 11

Testbeds for Design & De-risking 17Assembly, Integration & Test Facilities 6Test and Evaluation Facilities 2Sustainment Facilities 0Modelling and Simulation Facilities 1Collaborative Learning Environments 6

Leadership 0Cultural Aspects 3Teams: Team Design, Team Building and Performance 5Incentivisation 0

Business Process Improvement 3Organisational Design, Evolution & Renewal 2Roles and Responsibilities 0

Enterprise Systems Engineering 37Ultra-Scalable Systems 0Supply-chain SOSE 0Socio-economic SOSE 3SoS Aspects of Product Design and LCM 7

Infrastructure 13Anti-Terrorism 0Health and Social Services 33Power & Energy Systems 55 Space Systems 19 Mining and Oil Exploration 0Information & Communications 22Insurance Industry 0Control systems 0Government, Defense & Security 60 Natural Environment 12Transportation 49Consumer Products and Services 6Autonomous Systems 27Service Systems Engineering 1Manufacturing and Industrial Engineering 6Cloud Computing 59

Education and Training 5

Scale-specific Domains 47

Business Aspects 3

Technical Practices 150

Enablers215

Practices317

Organizational Aspects

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Workforce Development

5

Domain-specific Aspects

409

Technical Management 66

People Aspects 8

Facilities 32

Tools 67

Whole of SOSE Approaches 154Theory and Knowledge 61

Professionalization 0

Application Domains 362

Education and Training 5Educational Infrastructure 0

Competency Frameworks 0Accreditation, Certification and Registration 0Workforce Planning and Evolution 0

Technical Enablers 39

SoSE Architecture Descriptions 22Technical Standards 0SoS Integrating Software 17

Infrastructure138

Chaos and Complexity Theory is Part of Contemporary SE Curricula

• There may not be many research papers in complexity theory in the SoS literature because it is taught in SE programs

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University of South Australia

© SEEC, University of South Australia, 2003 © SEEC, University of South Australia, 2003 4-35

Chaos and Complexity Theory

Two important discoveries established the field:

• Complex and unpredictable results could be produced in the behaviour of systems from entirely deterministic equations, eg xn+1 = arctan xn. There is no need for probabilistic elements at all!

• There is considerable order in chaos.

“Chaos” does not imply randomness or disorder rather it refers to the repeated application of non-linear mathematical equations to give rise to patterns of order.

“Complexity theory” is wider in scope: used to describe the behaviour over time of complex human and social, as well as natural systems.

University of South Australia

© SEEC, University of South Australia, 2003 © SEEC, University of South Australia, 2003 4-36

Insights from Complexity Theory (1)

Traditionally scientists had sought to to linearize non-linear systems. Capra (1996) states that this is futile as “non-linear phenomena dominate much more of the

inanimate world than we thought, and they are an essential aspect of

the network of living systems”

Chaotic systems, like weather, are critically sensitive to initial conditions and diverge rapidly making long-term forecasting impossible.

Despite that, when graphed, chaotic systems are often attracted to a particular pattern of behaviour that bounds the excursions of the system.

University of South Australia

© SEEC, University of South Australia, 2003 © SEEC, University of South Australia, 2003 4-37

The Lorenz Attractor

… you will see above an endless succession of fractal images

produced by the iterated map xnew = a + bx + cx2 + dxy + ey + fy2,

ynew = x, znew = y, with a through f chosen randomly over the

range -3 to 3. Only those cases that are bounded and exhibit

sensitive dependence on initial conditions (chaos) are exhibited.

The other 99.7% are discarded. Each iterate is plotted at (x, y) in a

hue proportional to z. Like snowflakes, these strange attractors

come in infinite variety with no two the same. Each one you see is

new and almost certainly has never been seen before.

From J.C. Sprott’s web site:

http://sprott.physics.wisc.edu/java/attract/attract.htm

DOS Version: Strange Attractors

University of South Australia

© SEEC, University of South Australia, 2003 © SEEC, University of South Australia, 2003 4-38

Insights from Complexity Theory (2)

Chaotic systems often show self-similar behaviour at different scales of observation.

Chaotic systems, eg biological populations, often show bifurcations in the results because more than one “strange attractor” is acting on the system.

Systems at the “edge of chaos” are extremely reactive and are capable of extraordinary performance.

University of South Australia

© SEEC, University of South Australia, 2003 © SEEC, University of South Australia, 2003 4-39

Fractals Display Self Similar Features

University of South Australia

© SEEC, University of South Australia, 2003 © SEEC, University of South Australia, 2003 4-40

Bifurcations

Roughly speaking, a bifurcation is a

qualitative change in an attractor's

structure as a control parameter is

smoothly varied. For example, a

simple equilibrium, or fixed point

attractor, might give way to a periodic

oscillation as the stress on a system

increases. Similarly, a periodic

attractor might become unstable and

be replaced by a choatic attractor.

In Benard convection, to take a real world

example, heat from the surface of the earth

simply conducts its way to the top of the

atmosphere until the rate of heat generation

at the surface of the earth gets too high. At

this point heat conduction breaks down and

bodily motion of the air (wind!) sets in. The

atmosphere develops pairs of convection

cells, one rotating left and the other rotating

right.

In a dripping tap at low pressure, drops come off the tap

with equal timing between them. As the pressure is

increased the drops begin to fall with two drops falling

close together, then a longer wait, then two drops falling

close together again. In this case, a simple periodic

process has given way to a periodic process with twice

the period. If the flow rate of water through the tap is

increased further the behaviour becomes chaotic.

http://www.exploratorium.edu/complexity/CompLexicon/bifurcation.html

University of South Australia

© SEEC, University of South Australia, 2003 © SEEC, University of South Australia, 2003 4-41

The Importance of Complexity Theory

Most physical systems exhibit chaotic behaviour at some level of resolution.

Complexity theory does not deal with repetitive and predictable behaviour but embraces change and evolution in dynamic systems. (It moves beyond the stable equilibrium paradigm.)

Quoted from Begun (1994) in Jackson (2000): “Events are connected to

other events – they occur in systems. Systems are subsystems of larger systems. Relationships among variables rather than single variables, become the primary object of study. Efforts to isolate single variables and their effects become feeble or even ludicrous”.

It suggests that there may be some long-term patterns that underlie complex systems.

It may be possible to determine simple rules that govern complex systems behaviour at some level of resolution.

A Review of Systems Theory for SoSE (Adams, 2011)

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• Emergence

• Hierarchy

• Communications

• Control

The Elements of a Discipline

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Methodology

M1

Framework

of Ideas F

Methodology M2

Area of

Concern

A

embodied

in …

applied

to …

Enabling

Applied

• FMA framework from Cook and Ferris 2007 (after Cropley et al 2005 and Checkland and Howell 1997)

The FMA Conception Helps Provide Clarity

• F – The Framework of ideas embraces complexity theory • M1 – The Methodologies applied to performing SoSE that draw on Fs

to inform practice • A – the Areas of concern – ie the engineering of SoS and related

enabling activities

• What is a good Framework of ideas? (Anderson, 2014) – Theories work by making connections – They work by providing explanatory links on how, when and where A is related

to B – Theories link concepts into an explanatory Framework – Frameworks should be internally consistent – Frameworks should be have predictive power – Frameworks should inform praxis

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Let’s Examine the Matters Raised

• Which of these are Fs; which Ms? • Are they operationalisable concepts? • The list:

– Inhabit the space between order and chaos – Holonic subsystems – Paretian statistics and power laws – Scale free and fractal behaviour – Self organised criticality – Tiny initiating events (TIEs) – Fitness landscape – Systems in cycles of change – Environment driving system structure – Systemic and cascading risk – Self organisation – Attractor cages and path history – System dynamics – Sense making and common meaning – Systems intelligence

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INCOSE Recognises the Need for a Theoretical Framework of Ideas

• INCOSE – Systems Science Working Group

• INCOSE – System of Systems Working Group

• INCOSE – Complex Systems Working Group

• INCOSE/ISSS Collaboration

• Many valuable products have been produced but there is much to do!

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INCOSE/ISSS View of Linking Systems Science to Practice through Systems Thinking

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Mapping T-AREA-SoS Themes to

INCOSE SoS WG Pain Points (Henshaw, 2013)

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T-Area-SoS Research Themes

Authorities LeadershipConstiuent

Systems

Testing,

Validation &

Learning

Autonomy,

Interdependencies

& Emergence

SoS

Principles

Capabilities &

Requirements

Human and Organisation Aspects

Technical Management of SoS

Measurement and Metrics

Evaluation of SoS

Predicting, Management of Emergence

Definition and Evolution of SoS Architecture

Theoretical Foundations for SoS

Trade-Off

Characterisation and Description of SoS

Multi-Level Modelling

Energy Efficient SoS

INCOSE SoS Pain Points

Mapping by J. Dahmann Note: security added later

A Personal View

• We have moved on somewhat from:

“Complexity theory’s biggest contribution to SE is letting us know what we can’t know or predict” (Cook 1996)

• How far have we come ?

• What SoSE practitioners need is a theoretical framework of ideas that directly informs practice.

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Summary of the Refutation

• SoSE research covers a broad range of topics

– A theoretical background stemming from complexity theory is but one of many important areas

• Complexity theory is not foreign to many SoSEs, after all an INCOSE stalwart runs a series of complexity conferences …

• Much needs to be done to be able to develop complexity theory to the maturity needed to become a dominant influence in the Framework of ideas for SE, SoSE. It needs to be operationalised

• It is well understood that there is a need for research into building the theoretical basis of SoSE and SE

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A Response to the Refutation

Questions?

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References • Andriani, P. & Mckelvey, B., (2011), Using scale free processes to explain punctuated change in management-relevant

phenomena, International Journal of Complexity in Leadership and Management, Vol 1, No 3, 211-249; • Bak, P., (1996), How Nature Works, New York, Copernicus; • Boisot, M., & McKelvey, (2011), Complexity and Organisation-Environment Relations: Revisiting Ashby’s law of Requisite Variety;

in Allen, P, Maguire, S. & McKelvey, B., (2011), 280-298; • Cicmil, S. & Hodgson, D. (2006a), new possibilities for project management theory: a critical engagement, project management

Journal, August, 111-122; • Cicmil, S. Williams, T., Thomas, J., & Hodgson, D. (2006b), Rethinking Project Management: Researching the actuality of projects,

International Journal of Project Management, 24, 675-686; • Findlay, J. and Strauss, A., (2014) in Gorod, A., White, B., Ireland, V., Ghandi, S.J. & Sauser, Taylor and Francis, New York; • Gunderson, L.H. & Holling, C.S.,(2002), Panarchy - Understanding Transformations in Human and Natural Systems, Washinton,

Island Press; • Hämäläinen, R. P., & Saarinen, E. (2004). Systems Intelligence: Discovering a Hidden Competence in Human Action and

Organizational Life (1st Edition ed.). Helsinki: Systems Analysis Laboratory, Helskinki University of Technology. • Kauffman, S.A., (1993), The Origins of Order, New York, Oxford University Press; • Hämäläinen, R. P., & Saarinen, E. (2006). Systems Intelligence: A Key Competence for Organizational Life. Reflections: The SoL

Journal, 7(4), 17-28. • Hämäläinen, R. P., & Saarinen, E. (2007). Systems Intelligence in Leadership and Everyday Life. (R. P. Hämäläinen, & E. Saarinen,

Eds.) Helsinki: Helsinki University of Technology. • Hämäläinen, R. P., & Saarinen, E. (2008). Systems Intelligence - A New Lens on Human Engagement and Action. (R. P.

Hämäläinen, & S. Esa, Eds.) Helsinki: Systems Analysis Laboratory, Helsinki University. • Mandebrot, B.B, (1982), The Fractal Geometry of Nature, New York, Freeman; • Nafday, A.M Strategies for Managing the Consequences of Black Swan Events, Leadership and Management in Engineering, Vol.

9, No. 4, October, pp. 191-197; • Senge, P. (1990), The Fifth Discipline – the Art and Practice of the Learning Organisation, Sydney, Random House; • Taleb, N. (2007), The Black Swan, London, Penguin; • Zhu, Z. (2007). Complexity Science, Systems Thinking and Pragmatic Sensibility. Systems Research and Behavioral Science, 24(4),

445-464. • Zipf, G.K., (1949), Human Behaviour and the Principle of Least Effort, New York Haffner;

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