Piero Mella, Chair of Business Economics Faculty of Economics, University of Pavia, ITALY - Email: [email protected] [email protected]

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


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


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


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


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


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


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


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


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


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


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.


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


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.


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


Organizations as Organizations as multi-agent, multi-layer systemsmulti-agent, multi-layer systems

Individual element

1st-level organ

2nd-level organ


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


“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


Model of HolarchyModel of Holarchy


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


Non-Organized systems:Non-Organized systems:collectivity of analogous elementscollectivity of analogous elements

Herd of elephants Herd of elephants


A gaggle of greylag GeeseA gaggle of greylag Geese


Flock of BirdsFlock of Birds


School of fish School of fish


A cluster of bathers on a beach A cluster of bathers on a beach


Can can dancersCan can dancers


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


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


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


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


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

[email protected]


Documents

Piero Mella, Chair of Business Economics Faculty of Economics, University of Pavia, ITALY - Email: [email protected] [email protected]