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Piero Mella, Chair of Business EconomicsPiero Mella, Chair of Business EconomicsFaculty of Economics, University of Pavia, ITALYFaculty of Economics, University of Pavia, ITALY
www.ea2000.it/mella - Email: www.ea2000.it/mella - Email: [email protected]
University of Pavia
The Combinatory System TheoryThe Combinatory System TheoryA New Approach for Understanding A New Approach for Understanding
and Controlling Collective Phenomenaand Controlling Collective Phenomena
1 1 - Typology of - Typology of
SystemsSystems
Piero Mella - 2005 21 – Typology of Systems
My aim is twofold:
1. to present a particular class of Complex Systems which I have defined as
Combinatory Systems.
Due to the simplicity of their structure and functioning logic, I have also provocatively proposed to name these systems as
Simplex Systems.
2. to illustrate, in particular – with the aid of simple combinatory automata – phenomena as intriguing as they are emblematic of the action of the synergetic principles in social collectivities.
This courseThis course
Piero Mella - 2005 31 – Typology of Systems
The programmeThe programme
Section 1 – Introduction: typology of systems
Section 2 – Observing collectivities through the Combinatory Systems view
Section 3 – Models and typology of Combinatory Systems
Section 4 – Examples and Business applications
Section 5 – The heuristic power of the Combinatory System Theory
Piero Mella - 2005 41 – Typology of Systems
I feel it necessary to present a general conceptual framework of the different types of systems.
I would first point out that Ludwig von Bertalanffy, the “father” of the General System Theory, defined the system as a group of interacting elements that we observe as a whole, that obeys the non-summation principle.
That is, at a macro level, the macro process and the output of the system, as a unit, are not equivalent to the sum of the micro processes and outputs of its constituent elements.
Ergo: the characteristics of the system, as a whole, are emerging and new.
Defining systemsDefining systems
von Bertalanffy, The general system theory, p.80
Piero Mella - 2005 51 – Typology of Systems
von Bertalanffy clearly stated that
… in one way or the other we are forced, in all areas of knowledge, to deal with complexity, with “wholes”, with “systems”. And this implies a basic reorientation of scientific thinking. (GST).
The message that von Bertalanffy wished to give us in his General Systems Theory is clear and powerful:
we must develop a system thinking;
our ability to observe, to understand and to explain our Universe will improve the more we are able to build models of reality in system terms.
Models based on systemsModels based on systems
Piero Mella - 2005 71 – Typology of Systems
We can build synthetical and analytical models of a system.
From an exogenous point of view, a system can be observed as a unity (macro) strongly characterized by its own states, with an autonomous significance.
The synthetical models show the macro processes of the system as a whole acting within its environment.
From an endogenous point of view, a system is conceived of as a structure of interconnected elements which develop a network of micro processes.
The analytical models show the structural map of its elements and their micro processes.
Synthetical and analytical models of Synthetical and analytical models of systemssystems
Piero Mella - 2005 81 – Typology of Systems
Structural Map Structural Map and Macro Processesand Macro Processes
Black
Box
Synthetical model
White
Box
Boundary of the system
E N V I R O N M E N T
Piero Mella - 2005 91 – Typology of Systems
The simplest way to consider dynamic (dynamical) systems is the synthetical or exogenous point of view, which leads to models which are typically mathematical.
These kind of models:
interpret these systems as black boxes,
and describe them through a system of difference or differential equations,
which express the relations among the variations of inputs and those of outputs,
considering the latter as the consequence of variations in the internal state variables.
Synthetical Models of SystemsSynthetical Models of Systems
Piero Mella - 2005 111 – Typology of Systems
processes
A more usual block model introducing the feedback loop is the following.
Systems with feedback loopSystems with feedback loop
h(I, S) g(I, S)
f(O, I)
Input
dI
State
dS
Output
dO
feedback
state transition output transition
Melay Systems.
For more general models you can see the evergreen book:
Sandquist (1985), Introduction to System science, Prentice-Hall
Piero Mella - 2005 121 – Typology of Systems
The analytical approach is typically logical.
It considers systems as white boxes and tries to understand:
the nature of the internal elements constituting the structure,
the logical rules that specify how these elements interact to produce both the micro behaviours of the elements and the macro behaviour of the system as a whole.
Analytical modelsAnalytical models
Piero Mella - 2005 131 – Typology of Systems
With regard to the nature of the internal elements constituting the structure, we can distinguish between:
organized systems or structured systems: these are characterized by distinct and specialized organs connected by stable relations conceived of as the organization of the system1;
non-organized systems or social collectivities: these are composed of similar elements, or agents, without being necessarily interconnected in a stable structure (network, web or tree structure).
1 In the sense of Maturana & Varela (1980), Autopoiesis and Cognition.
Organized and Organized and non-organized systemsnon-organized systems
Piero Mella - 2005 141 – Typology of Systems
The concept of organizationThe concept of organization
“The relations that define a machine as a unit and determine the dynamics of the interactions and transformations that it can bear as a unit, represent the organization of the machine.
The effective relations that occur among the components that integrate a specific machine in a given space represent its structure.”
See: Maturana & Varela, Autopoiesis, p. 129.
Piero Mella - 2005 161 – Typology of Systems
An organ is a structural component characterized by the following four features:
a precise spatial and temporal placement (topology),
a specialized function that both specifies the admissible input and output that the component can show and delimits the interactions with the other elements,
a specific functionality, regarding the contribution to the entire structure,
a set of functioning standards that depend on the nature of the system.
OrgansOrgans
Piero Mella - 2005 171 – Typology of Systems
Organized systemOrganized systemStructure of organsStructure of organs
Structural elements or organs
The organs as differentiated elements which form a whole: the structure.
A
B
D
E
F
C
G
H
I
L
System unit
Lasting structure of organized elements that are observed as a unit that presents emerging characteristics (synthetic vision).A
B
D
E F
C L
I
Structure
Specific elements which, through the organizational relations, form a lasting structure (analytic vision).
GH
B D C
A
GE F
H
L
I
Organization
The stable relations of function, functionalityand topology that give meaning to the elementsindependently of their specificity.
Piero Mella - 2005 181 – Typology of Systems
Within organized systems, considering the nature of the organs, we can further distinguish between:
Mechanisms, if the structure is composed of physical elements and organs;
Organisms, if the structure is composed of biological elements and organs;
Organizations, if the structure is composed of individual autonomous agents forming organs.
Typology of organized systemsTypology of organized systems
Piero Mella - 2005 191 – Typology of Systems
Organizations as Organizations as multi-agent, multi-layer systemsmulti-agent, multi-layer systems
Individual element
1st-level organ
2nd-level organ
Piero Mella - 2005 231 – Typology of Systems
Organized Systems may be composed of semi-autonomous subsystems conceived of as holons.
Holons are “Janus-faced entities which display both the independent properties of wholes and the dependent properties of parts”.
Holons are subsystems that can be conceived of as:
autonomous systems, if observed in isolation,
wholes including their parts, if considered from a lower level,
parts composing a greater system, if considered from a higher level.
A Holarchy is defined as a hierarchically organized structure of holons obeying the
whole/part relationship.
Holonic SystemsHolonic Systems
Piero Mella - 2005 241 – Typology of Systems
“Parts and wholes in an absolute sense do not exist in the domain of life ... The organism is to be regarded as a multi-leveled hierarchy of semi-autonomous sub-wholes, branching into sub-wholes of a lower order, and so on. Sub-wholes on any level of the hierarchy are referred to as holons. Biological holons are self-regulating open systems which display both the autonomous properties of wholes and the dependent properties of parts. This dichotomy is present on every level of every type of hierarchic organization, and is referred to as the Janus Effect ... The concept of holon is intended to reconcile the atomistic and holistic approaches.”. (Koestler, 1967, Appendix I.1).
“The world is not composed of atoms or symbols or cells or concepts. It is composed of holons.”. (Wilber, 2001: 21).
Holons: the original quotesHolons: the original quotesThe term holon was coined by Arthur Koestler (1967) in his The Ghost in the Machine (Arkana, London) and has been widely analysed by Ken Wilber (1995), Sex, Ecology, Spirituality: The Spirit of Evolution, Shambhala Publications
Piero Mella - 2005 261 – Typology of Systems
Model of HolarchyModel of Holarchy
Piero Mella - 2005 291 – Typology of Systems
Non-organized systems are collectivities of individual agents forming an autonomously observable whole.
We can define a collectivity as a plurality of similar elements or agents, which are unorganized: that is, not specialized according
to function, functionality, functioning and topology, and produce an analogous micro behaviour over time, or similar micro effects, but, considered together, are capable of developing a
macro behaviour– and/or macro effects – which can be attributed to the collectivity as a whole.
For this reason these systems can be succinctly denominated Agent-Based Systems.
Collectivities as non-organized systems Collectivities as non-organized systems A definitionA definition
Piero Mella - 2005 301 – Typology of Systems
Non-Organized systems:Non-Organized systems:collectivity of analogous elementscollectivity of analogous elements
Herd of elephants Herd of elephants
Piero Mella - 2005 311 – Typology of Systems
A gaggle of greylag GeeseA gaggle of greylag Geese
Piero Mella - 2005 321 – Typology of Systems
Flock of BirdsFlock of Birds
Piero Mella - 2005 331 – Typology of Systems
School of fish School of fish
Piero Mella - 2005 341 – Typology of Systems
A cluster of bathers on a beach A cluster of bathers on a beach
Piero Mella - 2005 351 – Typology of Systems
Can can dancersCan can dancers
Piero Mella - 2005 361 – Typology of Systems
Collectivities can be
observable if the agents act simultaneously (for example, swarms, flocks, crowds, spectators at a stadium, students in a classroom, persons that are talking in a crowded room, dancers doing the Can Can),
imaginable if the agents act at different times or in different places (for example, trailer-trucks traveling a stretch of highway in a month, the noble families of Pavia who erected the 100 towers in the span of two centuries, a group of scientists who dedicate themselves to a branch of research, the consumers of a particular product during its entire life-cycle, stockbrokers working on a certain day in world or European stock markets).
Typology of collectivitiesTypology of collectivities
Piero Mella - 2005 381 – Typology of Systems
We can further divide non-organized systems into:
complex (adaptive) systems: the agents normally and prevalently interact according to local rules that establish how the micro behaviour of an agent derives from, or conditions, that of its neighbours;
combinatory systems: these represent a particular class of complex systems whose macro behaviour derives from the combination – appropriately specified – of the analogous micro behaviours (or effects) of its similar agents (hence the name Combinatory System), following macro and micro rules.
Complex and Combinatory SystemsComplex and Combinatory Systems
Piero Mella - 2005 401 – Typology of Systems
Some ReferencesSome References
For Agent Based Systems and Complex Adaptive Systems see:
Axelrod (1997), The Complexity of Cooperation, Princeton University Press
Gell-Mann (1995), Complexity, Vol. 1, no.5 ©, at:
http://www.santafe.edu/sfi/People/mgm/complexity.html
Goldspink (2000), Modelling social systems as complex: Towards a social simulation meta-model Journal of Artificial Societies and Social Simulation vol. 3, no. 2, 31, at: http://www.soc.surrey.ac.uk/JASSS/3/2/1.html
Holland (1995), Hidden Order: How Adaptation Builds Complexity, Perseus Books, Cambridge, Massachusetts
Piero Mella - 2005 411 – Typology of Systems
Some ReferencesSome References
I have conceptualized the Combinatory System Theory in:
Mella (1997), Dai sistemi al pensiero sistemico, Franco Angeli
Mella (1999), Razionalità e libertà nel comportamento collettivo, Franco Angeli
Mella (2000), Combinatory System Theory: www.ea2000.it/cst
Piero Mella - 2005 421 – Typology of Systems
Combinatory Combinatory System TheorySystem Theory
For more …
www.ea2000.it/cst[Many simulation models are shown]
Remarks, suggestions and criticisms
are welcome!
My web page and e-mail:
www.ea2000.it/mella
Piero Mella - 2005 431 – Typology of Systems