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Dynamics of Complex Systems Chapter 0

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The study of complex systems in a unified framework has become recognized in recent years as a new scientific discipline, the ultimate of interdisciplinary fields. Breaking down the barriers between physics, chemistry and biology and the so-called
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  1 0 Overview: The Dynamics of Complex Systems —Examples, Questions, Methods and ConceptsThe Field of Complex Systems The study ofcomplex systems in a unified framework has become recognized in re-cent years as a new scientific discipline,the ultimate ofinterdisciplinary fields.It isstrongly rooted in the advances that have been made in diverse fields ranging fromphysics to anthropology,from which it draws inspiration and to which it is relevant.Many ofthe systems that surround us are complex.The goal ofunderstandingtheir properties motivates much ifnot all ofscientific inquiry.Despite the great com-plexity and variety ofsystems,universal laws and phenomena are essential to our in-quiry and to our understanding.The idea that all matter is formed out ofthe samebuilding blocks is one ofthe srcinal concepts ofscience.The modern manifestationofthis concept—atoms and their constituent particles—is essential to our recogni-tion ofthe commonality among systems in science.The universality ofconstituentscomplements the universality ofmechanical laws (classical or quantum) that governtheir motion.In biology,the common molecular and cellular mechanisms ofa largevariety oforganisms form the basis ofour studies.However,even more universal thanthe constituents are the dynamic processes ofvariation and selection that in somemanner cause organisms to evolve.Thus,all scientific endeavor is based,to a greateror lesser degree,on the existence ofuniversality,which manifests itselfin diverse ways.In this context,the study ofcomplex systems as a new endeavor strives to increase ourability to understand the universality that arises when systems are highly complex.A dictionary definition ofthe word“complex”is:“consisting ofinterconnectedor interwoven parts.”Why is the nature ofa complex system inherently related to itsparts? Simple systems are also formed out ofparts.To explain the difference betweensimple and complex systems,the terms “interconnected”or“interwoven”are some-how essential.Qualitatively,to understand the behavior ofa complex system we mustunderstand not only the behavior ofthe parts but how they act together to form thebehavior ofthe whole.It is because we cannot describe the whole without describingeach part,and because each part must be described in relation to other parts,thatcomplex systems are difficult to understand.This is relevant to another definition of “complex”:“not easy to understand or analyze.”These qualitative ideas about what acomplex system is can be made more quantitative.Articulating them in a clear way is 0.1  both essential and fruitful in pointing the way toward progress in understanding theuniversal properties ofthese systems.For many years,professional specialization has led science to progressive isola-tion ofindividual disciplines.How is it possible that well-separated fields such as mol-ecular biology and economics can suddenly become unified in a single discipline?How does the study ofcomplex systems in general pertain to the detailed efforts de-voted to the study ofparticular complex systems? In this regard one must be carefulto acknowledge that there is always a dichotomy between universality and specificity.A study ofuniversal principles does not replace detailed description ofparticularcomplex systems.However,universal principles and tools guide and simplify our in-quiries into the study ofspecifics.For the study ofcomplex systems,universal simpli-fications are particularly important.Sometimes universal principles are intuitivelyappreciated without being explicitly stated.However,a careful articulation ofsuchprinciples can enable us to approach particular systems with a systematic guidancethat is often absent in the study ofcomplex systems.A pictorial way ofillustrating the relationship ofthe field ofcomplex systems tothe many other fields ofscience is indicated in Fig.0.1.1.This figure shows the con-ventional view ofscience as progressively separating into disparate disciplines in or-der to gain knowledge about the ever larger complexity ofsystems.It also illustratesthe view ofthe field ofcomplex systems,which suggests that all complex systems haveuniversal properties.Because each field develops tools for addressing the complexityofthe systems in their domain,many ofthese tools can be adapted for more generaluse by recognizing their universal applicability.Hence the motivation for cross-disciplinary fertilization in the study ofcomplex systems.In Sections 0.2–0.4 we initiate our study ofcomplex systems by discussing ex-amples,questions and methods that are relevant to the study ofcomplex systems.Ourpurpose is to introduce the field without a strong bias as to conclusions,so that thestudent can develop independent perspectives that may be useful in this new field—opening the way to his or her own contributions to the study ofcomplex systems.InSection 0.5 we introduce two key concepts—emergence and complexity—that willarise through our study ofcomplex systems in this text. Examples 0.2.1  A few examples What are com p l ex sys tems and what properties ch a racteri ze them? It is hel pful to start by making a list ofs ome examples ofcom p l ex sys tem s .Ta ke a few minutes to make yo u r own list.Con s i der actual sys tems ra t h er than mathem a tical models (we wi ll con s i der m a t h em a tical models later ) .Ma ke a list ofs ome simple things to con trast them wi t h . Examples ofComplex Systems GovernmentsFamiliesThe human body—physiological perspective 0.2 2 O ve r v i ew  Simple systemsPhysicsChemistryBiologyMathematicsComputer ScienceSociologyPsychologyEconomicsAnthropologyPhilosophySimple systemsComplex systems (a)(b)      C     h   e   m     i   s    t   r   y     B     i   o     l   o   g   y     P   s   y   c     h   o     l   o   g   y        P       h     y     s       i     c     s     M  a   t   h  e  m  a   t   i  c  s       C    o     m     p       u      t    e     r        S    c       i    e     n    c    e      S   o   c     i   o     l   o   g      y       E   c   o   n   o    m     i   c   s      A    n    t    h    r   o    p   o     l   o    g    y       P      h      i      l     o     s     o     p      h     y Figure 0.1.1 Conceptual illustration of the space of scientific inquiry. (a) is the conventionalview where disciplines diverge as knowledge increases because of the increasing complexityof the various systems being studied. In this view all knowledge is specific and knowledge isgained by providing more and more details. (b) illustrates the view of the field of complexsystems where complex systems have universal properties. By considering the common prop-erties of complex systems, one can approach the specifics of particular complex systems fromthe top of the sphere as well as from the bottom.  A person—psychosocial perspectiveThe brainThe ecosystem ofthe worldSubworld ecosystems:desert,rain forest,oceanWeatherA corporationA computer Examples ofSimple Systems An oscillatorA pendulumA spinning wheelAn orbiting planetThe purpose ofthinking about examples is to develop a first understanding ofthequestion,What makes systems complex? To begin to address this question we can startdescribing systems we know intuitively as complex and see what properties they share.We try this with the first two examples listed above as complex systems. Government •It has many different functions:military,immigration,taxation,income distrib-ution,transportation,regulation.Each function is itselfcomplex.•There are different levels and types ofgovernment:local,state and federal;townmeeting,council,mayoral.There are also various governmental forms in differ-ent countries. Family •It is a set ofindividuals.•Each individual has a relationship with the other individuals.•Th ere is an interp l ay bet ween the rel a ti onship and the qu a l i ties ofthe indivi du a l . •The family has to interact with the outside world.•There are different kinds offamilies:nuclear family,extended family,etc.These descriptions focus on function and structure and diverse manifestation.We can also consider the role that time plays in complex systems.Among the proper-ties ofcomplex systems are change,growth and death,possibly some form oflife cy-cle.Combining time and the environment,we would point to the ability ofcomplexsystems to adapt.One ofthe issues that we will need to address is whether there are different cate-gories ofcomplex systems.For example,we might contrast the systems we just de-scribed with complex physical systems:hydrodynamics (fluid flow,weather),glasses,composite materials,earthquakes.In what way are these systems similar to or differ-ent from the biological or social complex systems? Can we assign function and discussstructure in the same way? 4 O ve r v i ew  0.2.2 Central properties of complex systems After beginning to describe complex systems,a second step is to identify commonal-ities.We might make a list ofsome ofthe characteristics ofcomplex systems and as-sign each ofthem some measure or attribute that can provide a first method ofclas-sification or description.•Elements (and their number)•Interactions (and their strength)•Formation/Operation (and their time scales)•Diversity/Variability•Environment (and its demands)•Activity(ies) (and its[their] objective[s])This is a first step toward quantifying the properties ofcomplex systems.Quantifyingthe last three in the list requires some method ofcounting possibilities.The problemofcounting possibilities is central to the discussion ofquantitative complexity. 0.2.3  Emergence: From elements and parts to complex systems There are two approaches to organizing the properties ofcomplex systems that willserve as the foundation ofour discussions.The first ofthese is the relationship be-tween elements,parts and the whole.Since there is only one property ofthe complexsystem that we know for sure — that it is complex—the primary question we can ask about this relationship is how the complexity ofthe whole is related to the complex-ity ofthe parts.As we will see,this question is a compelling question for our under-standing ofcomplex systems.From the examples we have indicated above,it is apparent that parts ofa com-plex system are often complex systems themselves.This is reasonable,because whenthe parts ofa system are complex,it seems intuitive that a collection ofthem wouldalso be complex.However,this is not the only possibility.Can we describe a system composed ofsimple parts where the collective behav-ior is complex? This is an important possibility,called emergent complexity.Any com-plex system formed out ofatoms is an example.The idea ofemergent complexity isthat the behaviors ofmany simple parts interact in such a way that the behavior ofthewhole is complex.Elements are those parts ofa complex system that may be consid-ered simple when describing the behavior ofthe whole.Can we describe a system composed ofcomplex parts where the collective be-havior is simple? This is also possible,and it is called emergent simplicity.A usefulexample is a planet orbiting around a star.The behavior ofthe planet is quite simple,even ifthe planet is the Earth,with many complex systems upon it.This example il-lustrates the possibility that the collective system has a behavior at a different scalethan its parts.On the smaller scale the system may behave in a complex way,but onthe larger scale all the complex details may not be relevant. E xa m p l e s 5
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