"Complex Systems and Models"

Complex Systems and Models

Franck Varenne Associate Professor of Epistemology

University of Rouen & GEMASS (UMR 8598)

7th Complex Systems French Summer School

Preamble

• What do we call a SYSTEM?

• What do we call a systemic approach?

• What could be called a complex system?

Preamble: What is a SYSTEM ?

• From systèma (syn-istèma) : different entities that

– stand (istèma, from stasis : "a standing still“, a “stop”)…

– … together (syn)

• Emphasis is on: the wholeness of a set of entities

• A set of elements and relations that behave as a togetherness, as a whole, as an autonomous entity

• With its own limits or frontiers

• With its own internal rules of interaction and evolution

















General Approach of Systems (1/3)

• Focusing on the wholeness : what does it mean ?

– Bertalanffy (General System Theory, 1938, 1968, 1971, pp. v, 17) :

• Analytic paradigm : » 1- Isolating and analyzing the properties of the elements (enzymes,

cells, elementary sensations..)

» 2- Assuming that a simple reunion (addition) of these properties enable to rebuild and understand the behavior of the whole

• Systemic paradigm : » 1- Focusing on relationships and interactions between elements

» 2- Searching for isomorphisms between structures of interactions

• The focus is on the form and structure of the relationships between elements (their relational properties)


• Focusing on the wholeness : what does it mean ?

– Bertalanffy (General System Theory, 1938, 1968, 1971, pp. v, 17) :

• Analytic paradigm : » 1- Isolating and analyzing the properties of the elements (enzymes,

cells, elementary sensations..)

» 2- Assuming that a simple reunion (addition) of these properties enable to rebuild and understand the behavior of the whole

• Systemic paradigm : » 1- Focusing on relationships and interactions between elements

» 2- Searching for isomorphisms between structures of interactions

• The focus is on the form and structure of the relationships between elements (their relational properties)


• As the focus is on the form and structure of the relationships between elements (their relational properties)…

• …there is a first major consequence : on the nature of the object under study. Such a set of elements can be open and still remain a system (if relationships remain the same)

• We can draw a parallel with the classical metaphysical problem on identity of wholes having changing parts:

– The ship of Theseus according to the legend recalled by Plutarch (Parallel Lifes, 1st century) : “The ship wherein Theseus and the youth of Athens returned […] was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place...”

– Is it the same ship or a new one?

– Yes, from an Aristotelian standpoint: the “formal cause” of the ship (not its material cause) remains, the “what it is” remains the same


• As the focus is on the form and structure of the relationships between elements (their relational properties)…

• …there is a first major consequence : on the nature of the object under study. Such a set of elements can be open and still remain a system (if relationships remain the same)

• We can draw a parallel with the classical metaphysical problem on identity of wholes having changing parts:

– The ship of Theseus according to the legend recalled by Plutarch (Parallel Lifes, 1st century) : “The ship wherein Theseus and the youth of Athens returned […] was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place...”

– Is it the same ship or a new one?

– Yes, from an Aristotelian standpoint: the “formal cause” of the ship (not its material cause) remains, the “what it is” remains the same


• As the focus is on the form and structure of the relationships between elements (their relational properties)

• There is a second major consequence : on the method used to deal with the object under study (abstraction, “transdisciplinary” approach)

– A systemic view is more abstract than an analytic one: a focus on relational

properties of elements permits to neglect or even forget their intrinsic properties

– A correlative consequence is the difficulty to find any essential difference between a system and a model of a system (see later)

– A not so positive counterpart, at first glance, as we will see, but which can finally be a fertile one


• As the focus is on the form and structure of the relationships between elements (their relational properties)

• There is a second major consequence : on the method used to deal with the object under study (abstraction, “transdisciplinary” approach)

– A systemic view is more abstract than an analytic one: a focus on relational

properties of elements permits to neglect or even forget their intrinsic properties

– A correlative consequence is the difficulty to find any essential difference between a system and a model of a system (see later)

– A not so positive counterpart, at first glance, as we will see, but which can finally be a fertile one

Adjusted Approaches according to Bertalanffy (GST, Foreword, 1971, p. vi)

• Dynamical systems theory (systems with states in geometrical space that change with fixed rules) + constrained systems, bifurcation : Seifert, Ginoux

• Theory of systems with feedbacks (cybernetics), automata theory + CA, ABM, IBM & Simulations, artificial societies : Amblard, Banos, Marilleau (models, tools, methods), Monmarché (artificial ants), Sueur (coordination of animal groups)

• Theory of networks, theory of graphs + here, spatial networks approach : Barthélémy, Ducruet

What is a complex system ?

• What do we mean by the adjective “complex”? – Difficult to define

– Like all the words denoting things or properties that, by definition, are ill-defined and difficult to know: such as the noun “thing” or the adjective “vague”…

– Self-contradiction when we try to define them

• In spite of that: we can adopt an indirect approach – Not all systems are complex

– Some of them are simple : e.g. a reduction unit

– Others are complicated:

Source: Wikipedia, “Speed reduction unit”

V16 motor engine

Source: f1technical.net,

Source: Jodel.com

What is a complex system ? • We can use: showing, ostension, and listing

• Living systems : cells, organisms

• Social systems

Source: UCDavis Source: pelerin.uniterre.com

Crowds. Source: 123RF

Social network. Source: SmartInsights

Mobility. Source: Banos 2005

Network of leaders-followers association

Source: Sueur, Jacobs, Amblard, Petit &

King, 2011

What is a complex system ? • By induction from the list: our knowledge of the elements’ behavior does not

enable us to know (i.e. to describe or to anticipate) the behavior of the whole

• Can we find some specific factors to “achieve” this inability? – As inability is a privative property too, its name does not denote any particular cause or factor

(otherwise, to know some thing – what its name means – is to know it by its cause)

– Hence it is not surprising that there exist different and heterogeneous factors causing this inability • it can be due to the system itself, to the limits of our instruments, to our cognitive limits or to the limits of our

representational systems…

• Nonetheless, some factors are well-recognized in the literature : they concern the structures and the kinds of interactions operating in the system itself

• Namely, a system is often said to be complex when – It is composed of a certain amount of entities (elements or agents) interacting together

• not necessarily a great amount of elements (DAI, Swarm intelligence ≠ connexionnism in AI)

• not necessarily heterogeneous elements (CA)

– The kind of actual interactions at stake in the system or the kind of “description” or “notation” we use to describe these interactions does prevent us to sum up or describe or deduce or anticipate at all or rapidly the behavior of the whole.

• for instance: non additivity of properties, non-linearity, sensibility to initial conditions, emergence (weak, strong)





































What is a complex system ?

• Length of description: Gell-Man, 1994

– Not necessarily the number of connexions

• C > B > A

• D = C (complement)

• E = B (complement)

• F = A (complement)

What is a complex system ? • Not necessarily an absolute property: a system can only be seen as complex

• Relative to :

– our standpoint

– our goal (cognitive, operational…)

– our instrument (the current state-of-the art)

• of measure

• of analysis (models…)

• of representation (models…)

• But there exist some key features of systems or some key visions on systems that make them complex: this shared approaches legitimate the existence of a community of researchers working on complex systems

• In both cases, we use models

• But not all system that we model are complex – See counterexamples in engineering sciences using models for motors, airplanes, cars…


• Relative to :

– our standpoint



• of measure







• Relative to :

– our standpoint



• of measure







• Relative to :

– our standpoint



• of measure






End of the preamble

Complex Systems and Models: Overview

• The roles of models and simulations in the study of complex systems

– Outline on models & simulations

– A piece of history on models and complexity: laws and kinds of “simplicity”

• our diverse complexity oriented visions on systems…

• …and on models: 4 characters of complexity for a model

The roles of models in the study of complex systems

Part I. General outline on models and

simulations

Part II. A piece of history on models and complexity: laws and kinds of

“simplicity”

Part I. General outline on models and

simulations

Sources : D. Phan & F. Varenne, “Agent-Based Models and Simulations in Economics and Social Sciences: from conceptual exploration to distinct ways of experimenting", Journal of Artificial Societies and Social Simulation, 13(1), 5 , 2010 ; F. Varenne, "Framework for M&S with Agents in regard to Agent Simulations in Social Sciences: Emulation and Simulation", in Activity-Based Modeling and Simulation, A. MUZY, D. R. C. HILL & B. P. ZEIGLER (eds.), Presses Universitaires Blaise Pascal, 2010 ; Modéliser le social, Dunod, 2011 ; Modéliser & simuler – Epistemologies et pratiques, Matériologiques, 2013.

• I- “Model” : a broad characterization and 5 main functions of models

• II- 20 distinct functions of models

• III- Limitations of models : a sample

• IV- Toward the notion of “simulation”

• V- Epistemic functions of computational M&S

I-A- « Model »: a broad and pragmatic characterization

• Minsky (1965) : “To an observer B, an object A* is a model of an object A to the extent that B can use A* to answer questions that interest him about A”

• Consequences:

• Not necessarily a representation • A double relativity: 1st to the observer, 2nd to the question asked by

the observer • The model is an “object” : i.e. an entity with ontological

independence and autonomy. – It is not only a linguistic product, nor an expression nor a metaphor

• Its general function in sciences : to facilitate a mediation in the context of a cognitive questioning, a cognitive inquiry (practical cognition or theoretical cognition)

I-B- The 5 Main Functions of Models (sources : Varenne, Modéliser le social, Dunod, 2011 ; Modéliser & simuler, Matériologiques, 2013)

• I- to facilitate an observation or, more generally, an experiment (observation + controlled interaction)

• II- to facilitate the coining of an intelligible representation

• III- to facilitate theorization

• IV- to facilitate mediation between discourses and between disciplines

• V- to facilitate decision and action (mediation between our goals and our appropriate actions)

• I- To facilitate an observation or an experiment:

– 1) To make sensible (1:1 scale mockup of the human body (wax anatomical and surgical model), solar system with balls,…)

– 2) To make memorizable (simplifying pedagogical diagrams,…)

– 3) To facilitate experiments through indirect experiments on experimental models: experiment on real or imaginary (thought experiments) objects or on experimental living models (drosophila, E. coli, pigs, mice, rabbits…) that are easily accessible for

– material reasons (space, time, number, rapidity)

– financial reasons (cost)

– technical reasons (availability in a given context)

– ethical or deontological reasons

– 4) To facilitate the presentation, through its abbreviation, of the data and controlled variables of an experiment (not the representation of the experimented object): e.g. through a statistical “model of data” (statistics, data analysis, models of analysis) (in France: J.P. Benzécri: strong inductivism)

Functions of models (1/5) Source : Varenne (2011, 2013)

• II- To facilitate an intelligible presentation through a mental representation or a conceptualization:

– 5) To facilitate the compression of data to build a first kind of conceptualization through “models of data”. Question: Are the statistical moments of data conceptual constructs (HD) or real properties of data (EI)?

– 6) To facilitate the selection and classification of relevant entities and properties in a given domain: conceptual models, models of knowledge, ontologies (see the growing number of ontologies in integrative or systemic biology: not to be confused with theories!)

– 7) To facilitate the reproduction of an observable dynamic: phenomenological models, predictive models (parallel dynamics without explanative factor: no biophysical counterparts). E.g.: a fitted polynomial equation (see: “instrumentalism” on models by Friedman, 1952)

– 8) To facilitate the explanation of a phenomenon through the visualization and reproduction of mechanisms of elementary interactions : explanative models

• e.g.: mechanistic models (pump for the heart): communication of movements through contacts • electrical model for the biological neuron (Hodgkin-Huxley 1952): transmission of signals ; • energetic models for the nutrition (Biological cycles…): communication, transport and transformation of

energies • individual-based models for diffusion phenomena or phenomena arising in assemblies of cells, organs or

organisms: in ecology, epidemiology, endocrinology • network models for biological or social networks… : transportation of matters, energies or signals • computational models: distributed behaviors and interactions

– 9) To facilitate the comprehension of a phenomenon by formulating the general principles that rule a dynamic

that looks like the observed one: theoretical models. Examples: • cybernetic models • mathematical, topological models of morphogenesis (Thom, Zeeman, catastrophe theory) • thermodynamics of open systems, bifurcation theory (Prigogine) • synergetics (Haken) • fractals (Mandelbrot) • autopoiesis (Maturana, Varela)

II- Functions of models (2/5) Source : Varenne (2011, 2013)

• III- To facilitate a theorization • A theory ≠ A model

• A theory : a set of sentences (axioms and principles/rules of transformation) written in a given language - be it formalized or not – that permits the translation and the derivation of a whole set of observational sentences (among them : empirical laws) about a whole domain of entities and properties

• Subsidiary question: are there genuine theories (fundamental laws) in biology and social sciences and not only mechanisms ? See Canguilhem 1963, Demleulenaere (ed.), 2011.

– 10) To facilitate the building of a still not mature theory: first formulation of regularities and derivations, but not founded on proper principles and axioms

– 11) To interpret a theory, to show its visualizability in terms of mental images or of thought experiments (Boltzmann)

– 12) To illustrate a given theory by another one (Maxwell): search for mathematical analogies (geometrical models) to facilitate the calculus

– 13) To test the inner coherence of a given theory (link with the mathematical theory of models in logic and mathematics

– 14) To facilitate the application of the theory, i.e. its reconnection with the data. E.g.: • An intermediate model between the theory and the model of data (rules of correspondence).

• Approximate heuristic models or asymptotical models of Navier-Stokes equations in fluid dynamics

– 15) To facilitate the hybridation and co-calculation of heterogeneous theories • e.g.: models of polyphase systems in physico-chemistry or chemistry of combustion (liquid / solid / gaseous

phase).


• IV- To facilitate the mediation between discourses about a complex - in the sense of multidimensional - phenomenon (to facilitate the formulation of the questioning - not of the formulation - of an hypothetical answer):

–16) to facilitate communication between disciplines and researchers (data-base sharing)

–17) to facilitate deliberation and dialogue.

E.g. : in environmental sciences RAINS models (Kieken, 2004) on acid rains

–18) to facilitate the co-construction of the management of mix systems, of socio-natural systems.

E.g.: companion modeling (CIRAD), participative modeling, interactive modeling of agronomic and agricultural systems


• V – To facilitate the formulation not of the questioning nor of the answer to the question but of the final decision only, i.e. to help determinate the kind of possible pre-established actions (to vaccinate or not, to buy or not…):

–19) To facilitate a rapid decision in a complex context of emergency. –E.g. model for the management of epidemics, model for the management of catastrophe

–20) To facilitate a decision in a context where models of decision finally can be counted as explanative too because, on the run, they are becoming not only descriptive but prescriptive (in that they act as self-fulfilling representations). Confusions with functions #8 or #9 are frequent.

–E.g.: models of decision in psychology, theory of decision, economics, mathematical models of derived products in finance (MacKenzie 2004)(Aglietta 2008)


III-Limitations of models : a sample

• Validation : variety of procedures due to the variety of goals • Range of their validity: a quasi-circular problem. A few remarks.

– There exist no formal nor general theory nor model of what it implies for a model to be a good one. Methodology, know-how, art (epistemology?)

– Induction must be reinforced, multiplied, multiplexed – See: multi-aspectual models, multiscale models, integrative models – See the rise of the so-called “cross-validation” techniques

• Does a model always have to be simple in all respects? – No. – For a very long time a confusion has been done between the role of

facilitation the model must have and its supposed property to be simple – In fact, it depends on its avowed function: theoretical or empirical, …? – This is the recent rise of “simulations” and “computational models” of

complex systems that has permitted to become aware of the difference and to reveal the traditional confusion (Varenne, 2007, 2008)

– Let’s have a look now on recent trends due to the spreading of simulations

IV- Toward the notion of simulation (1/4) Sources on simulations: Phan & Varenne, JASSS, 2010 ; Varenne, “Framework for M&S with Agents…”, 2010 ;

Varenne, “Chains of Reference in Computer Simulations”, to appear

• Computer simulations depend on formal models (help to test, solve, calculate, validate)

• A formal model is a formal construct (equations, system of equation, systematic descriptions of agents and methods…) possessing a kind of unity and formal homogeneity so as to satisfy a specific request : prediction, explanation, communication, decision, computability, etc.

• Concerning simulation, current definitions need to be generalized.

• It is often said that “a simulation is a model in time”, a ”process that mimics the (supposed to be the more) relevant characteristics of a target process”, Hartmann (1996). But consider:

• The variety of types of contemporary CSs.

• Today, CSs rarely are the dynamic evolution of a single formal model.

• CSs in the sciences of complex objects are most of the time CSs of complex systems of models.

• Moreover, there exist various kinds of CSs of the same model or of the same system of models.

IV- Toward the notion of simulation (2/4) • Last but not least, the criterion of the “temporal mimicry” is in crisis too: it

is not always true that the dynamic aspect of the simulation imitates the temporal aspect of the target system. Some CSs can be said to be mimetic in their results but non-mimetic in their trajectory (Varenne, 2007) (Winsberg 2008).

• For instance, it is possible to simulate the growth of a botanical plant sequentially and branch by branch (through a non-mimetic trajectory) and not through a realistic parallelism, i.e. burgeon by burgeon (through a mimetic trajectory), and to obtain the same resulting and imitating image (Varenne 2007).

Source : Simulated Poplar - Plant Architecture Modelling Laboratory (CIRAD/France) 37

• The problem: the temporal aspect is itself dependent on the persistent - but vague - notion of imitation or similitude.

• But, in fact, it is possible to give a minimal characterization of a CS without referring to an absolute similitude (formal or material) nor to a dynamical model

• Let’s say that a simulation is minimally characterized by a strategy of symbolization taking the form of at least one step by step treatment. This step by step treatment proceeds in two major phases:

– 1st phase (operational phase): a certain amount of operations running on symbolic entities (taken as such) which are supposed to denote either real or fictional entities, reified rules, etc.

– 2nd phase (observational phase): an observation or a measure or any mathematical or computational re-use of the result of this amount of operations taken as given through a visualizing display or a statistical treatment or any kind of external or internal evaluations.

– e.g., in some CSs, the simulated “data” are taken as genuine data for a model or another simulation, etc.

IV- Toward the notion of simulation (3/4)

38

IV- Toward the notion of simulation (4/4) Simulations and hierarchies of symbols

-We can draw a parallel between the hierarchy of levels of symbols in a symbols’ hierarchy and the similar hierarchies in numerical simulations and in agent-based simulations.

- The relation of subsymbolization can be interpreted in terms of an exemplification whereas the relation of denotation can be interpreted in terms of an approximate description.

39

V- Epistemic functions of M&S (1/2) Simulations of Models

• According to (Ören 2005) & (Yilmaz et al. 2006), “simulation has two different meanings: – (a) imitation of a target system and

– (b) goal-directed experimentation with dynamic models”

• The previous conceptual analyses confirm and explain further this matter of fact:

– First. We are right to say that a computer simulation is a “simulation of a model” when its specific strategy of symbolization essentially is taken as a strategy of subsymbolizing the dynamic of the model.

• From this viewpoint, a lapse of time taken in the dynamic of the model is iconically denoted by

a lapse of time of computation in the CS. An iconic semiotic relation takes place here because a lapse of time is denoted through another lapse of time.

• This iconic relation is not an “imitation” of a property of a target system but an imitation of an aspect of the time-consuming dynamic of the model by a time-consuming activity: a computation.

• This hidden imitation is what permits to characterize the second meaning of “simulation” - according to (Yilmaz et al. 2006) - as a kind of experimentation (on a model or system of models).

40

V- Epistemic functions of M&S (2/2) Simulations of Target Systems

Second. A CS can be called a simulation for another reason: • It can be seen as a direct simulation of an external target system and not as a

simulation of model.

• That is what (Yilmaz et al. 2006) call the first meaning of simulation: imitation.

• In this case, it is implicitly assumed that symbols at stake in the simulations are entering in some direct iconic relationships to some external properties of the external target objects.

• Contrary to what prevails in the previous case, external relations between symbols and target entities or target symbols have to be taken into account.

– Such a simulation is seen as a Virtual experiment more than as a Calculus of a model:

– It is based on Simulation Models or Computational Models (Miller &

Page 07)

– As such, it can be seen as a complex systems… and modeled

Roles of Models in Complex Systems Studies

Part II. A piece of history on models and

complexity: laws and kinds of “simplicity”

• See Varenne : « Models and simulations in the historical emergence of the sciences of complexity », in Bertelle and Aziz-Alaoui, 2009.

• Beware: a law is not a model

• A law : a constant, universal and necessary relationship between properties

• U = R.I - Ohm’s law

• P.V = n.R.T – Boyle-Mariotte’s law

• But a law can be approximated or sketched by a model (category of intelligible presentations : # 7, 8 or 9, i.e. phenomenological, explanative or comprehensive model)

Roles of Models in Complex Systems Studies

Part II. A piece of history on models and

complexity: laws and kinds of “simplicity”

• See Varenne : « Models and simulations in the historical emergence of the sciences of complexity », in Bertelle and Aziz-Alaoui, 2009.

• Beware: a law is not a model

• A law : a constant, universal and necessary relationship between properties

• U = R.I - Ohm’s law

• P.V = n.R.T – Boyle-Mariotte’s law

• But a law can be approximated or sketched by a model (category of intelligible presentations : # 7, 8 or 9, i.e. phenomenological, explanative or comprehensive model)

Current situation in the empirical sciences

• From mathematical modeling to computational modeling (since WW 2) – The increase of computer simulation practices

– Convergence between the modeling of natural systems and the modeling of artificial systems

• Computational models are becoming “complex”

• But models are said to be simple…

→ contradiction ?!

• Idea: complex models remain selective as they capture only some characters of complexity at the same time

Outline

• A short story of formal modeling practices

– “Complexity”: an evolving (dynamic) concept

– The “complexity vector”

Main source: “Models and Simulations in the Historical Emergence of the Science of

complexity”, Varenne, Springer, 2009 (accessible on HAL website).

Model, Simplicity and Formal Model

• Short REMINDER :

• Minsky (1965) : “To an observer B, an object A* is a model of an object A to the extent that B can use A* to answer questions that interest him about A”

• “Simple”: “something you can deal with”, that is: – you can contemplate it in a comprehending (synoptic) view – or you can efficiently manipulate it (with no mistake or with controls on mistakes) – or you can design it all by yourself, without “external” aid (but what is external?)

• Most of the time: a “model” = a simple or a simplified representation

• “Formal model”: a formal construct possessing a kind of unity, homogeneity and

simplicity

46

Simple Models of Simple Systems (1/4) The role of perfection

• Relativity of the “simple” and of the “complex” • According to P. Duhem To save the phenomena (1908)

– E.g.: in Ancient Greece (Aristotle) • sublunar world (subject to generation and corruption) opposed to supralunar

world • due to their achievement and perfection, celestial (supralunar) movements

were believed to follow simple geometric laws : i.e. geometric figures built with compass and ruler (“simple”: relative to a human instrument)

• In this context : simple = true laws of perfect entities

– On the contrary, in the late Antiquity, (Posidonius, Simplicius or Proclus),

• the physicist is concerned with the very essence of the celestial entities • whereas the astronomer has only to ”save the phenomena”, i.e. to speak

about the apparent figures, sizes and distances of celestial entities (Duhem, 1906).

Simple Models of Simple Systems (1/4) The role of perfection

• Relativity of the “simple” and of the “complex” • According to P. Duhem To save the phenomena (1908)

– E.g.: in Ancient Greece (Aristotle) • sublunar world (subject to generation and corruption) opposed to supralunar

world • due to their achievement and perfection, celestial (supralunar) movements

were believed to follow simple geometric laws : i.e. geometric figures built with compass and ruler (“simple”: relative to a human instrument)

• In this context : simple = true laws of perfect entities

– On the contrary, in the late Antiquity, (Posidonius, Simplicius or Proclus),

• the physicist is concerned with the very essence of the celestial entities • whereas the astronomer has only to ”save the phenomena”, i.e. to speak

about the apparent figures, sizes and distances of celestial entities (Duhem, 1908).

Simple Models of Simple Systems (2/4) The role of infinite

• Another change in the western thought: – Nicholas of Cusa (1404-1464) : the sublunar world was no

more seen as “unachieved” (i.e. “imperfect” for the ancient Greeks) but, more positively, as infinite because it was seen to inherit a kind of infinity and complexity from its divine creator.

• So physicists, as astronomers, newly had to renounce to

seek something more than a salvation of phenomena.

• They were told to limit themselves to fictitious essences and hypothetical causes: – Kind of iconoclasm: relationship with nominalism – Roots of modern positivisms

Simple Models of Simple Systems (2/4) The role of infinite

• Another change in the western thought: – Nicholas of Cusa (1404-1464) : the sublunar world was no

more seen as “unachieved” (i.e. “imperfect” for the ancient Greeks) but, more positively, as infinite because it was seen to inherit a kind of infinity and complexity from its divine creator.

• So physicists, as astronomers, newly had to renounce to

seek something more than a salvation of phenomena.

• They were told to limit themselves to fictitious essences and hypothetical causes: – Kind of iconoclasm: relationship with nominalism – Roots of modern positivisms

Simple Models of Simple Systems (3/4) Modern physics and new essentialism

• Galileo – The Assayer, 1623 : “Philosophy [i.e. physics] is written in this grand book — I mean the universe — which

stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth”

– Discourse on two new sciences, 1638: “The law of falling bodies”, x = K . t² (experiment: rolling balls on a ramp)

• Newton (1687) : – Fundamental relation of dynamics (2nd law) : F = m . a

– Law of universal gravitation : F = G.M1.M2 / d² (d = distance between the two mass points of M1 and M2)

• After Crombie (1969) : from 1687 to the end of 19th century, most physicists thought that this laws captured in a simple way the simple essence of the mechanical phenomena. They explain AND predict (save the phenomena) at the same time.

→ A kind of essentialism (opposed to the nominalism of the late Middle-Age)

















• Instruments: – Beware ! A new tool is hidden behind this (new) “simplicity” = the integro-differential

calculus, with the operative notions of derivatives and integrals

– Newton and Leibniz had designed well-fitted mathematical techniques of notation and of derivation from this notation, i.e. techniques of computation

• Specific domain of application (“simplicity” of the target system). Strong hypotheses on the nature of things under study were verified:

– There is only one frame of reference for space and time in nature (sensorium Dei): consequently, absolute space and time positions can be shared by the different entities coexisting in this frame.

– All phenomena are of mechanical nature or can be reduced to mechanical laws. Seen this other way around: we study only the phenomena that obey the prescribed laws…

– Dynamical systems can be isolated from each other. They can be decomposed and recomposed by simple (vectorial) addition. Their contribution to forces too.

– Interactions between wholes can be exhaustively described as summations of interactions between parts of these wholes.

Simple Models of Simple Systems (4/4) The roles of the instruments and of the specific domain

• Instruments: – Beware ! A new tool is hidden behind this (new) “simplicity” = the integro-differential

calculus, with the operative notions of derivatives and integrals

– Newton and Leibniz had designed well-fitted mathematical techniques of notation and of derivation from this notation, i.e. techniques of computation

• Specific domain of application (“simplicity” of the target system). Strong hypotheses on the nature of things under study were verified:

– There is only one frame of reference for space and time in nature (sensorium Dei): consequently, absolute space and time positions can be shared by the different entities coexisting in this frame.

– All phenomena are of mechanical nature or can be reduced to mechanical laws. Seen the other way around: we study only the phenomena that obey the prescribed laws…

– Dynamical systems can be isolated from each other. They can be decomposed and recomposed by simple (vectorial) addition. Their contribution to forces too.

– Interactions between wholes can be exhaustively described as summations of interactions between parts of these wholes.

Simple Models of Simple Systems (4/4) The roles of the instruments and of the specific domain

Simple Models of Complex Systems (1/4) Poincaré and chaos

• History again • In 1892, Poincaré showed that easily writable non-linear

Hamiltonian equations could lead to chaotic behavior = high sensibility to small differences in initial conditions

» Doing this, he did not show that the world is complex neither that the solar system really is chaotic (≠ Laskar 1989)

• But this result shows a split between the attributes of the different properties of the Hamiltonian formalism. Such a formalism possesses at least three distinct properties:

– (1) it is a notation;

– (2) it enables symbolic manipulation and combination

– (3) it leads to formalized solutions.

Simple Models of Complex Systems (2/4) The “complexity vector” F

• Three distinct properties for a formalism: – (1) it is a notation (N) – (2) it enables symbolic combination and manipulation (C) – (3) it leads to formalized solutions (S)

• For each, let’s introduce a distinctive attribute: “Simple”/”Complex”

• Vector F (for Formalism):

F(attribute of Notation, attribute of Combination, attribute of Solution)

• For instance, the claim about the formalism used by Poincaré can be represented by the complexity vector:

F (S, S, C)

Which means : the possibility of the Hamiltonian to always lead to a simple solution is denied

• Two key questions can now be addressed: – 1- what are the relationships between such a complexity of the

formalisms and the complexity that can be detected or measured in experimental works in physics or chemistry?

– 2- to what extent are those complexities of properties of different entities (a formalism and a real system) of the “same” nature?

• These questions are not only on complexity but on the validity of

the model of complexity for real systems (e.g.: chaotic models of turbulent fluids). – If the model is complex, how can I prove that its complexity is of the

same nature as the one at stake in the portion of the world it models?

Simple Models of Complex Systems (3/4) Complexity of the world / Complexity of the formalism

• The shift to chaos models in many disciplines remains in fact in the continuity of the traditional hope to capture and reproduce in a simple way (at least at the level of the notation: non-linear integro-differential equations) what seems complex in reality.

• So, these approaches mostly consist of confronting “simple” models (at least at the level of notation) to complex “reality”. E.g.: in theoretical ecology.

• Indeed, current physicists and theoretical biologists (Prigogine, Jensen, Kauffman) consider that most of the systems are open, not closed nor separable, contrary to what was assumed in the newtonian approach.

• Nevertheless, they still are in search of the simplest and most generic mathematical notation for a wide range of complex systems.

They want to make a F2(S,S,S) from a F1(S,S,C).

• It has the philosophical advantage and argumentative power to apparently

reconcile nominalism and essentialism: both can be adopted

Simple Models of Complex Systems (4/4) Mathematical models of complex systems





















They want to make a F2(S,S,S) from a F1(S,S,C)








They want to make a F2(S,S,S) from a F1(S,S,C)

E.g. : the SOC of sandpiles (Bak, Tang, Wiesenfeld 87) has been simulated with CAs before being modeled


• Complexification can go further thanks to computers : F(S,S,C) (simple CA) or F(S,C,C) (complex CA)

• “A cellular automaton is a collection of ‘colored’ cells on a grid of specified shape that evolves

through a number of discrete time steps according to a set of rules based on the states of neighboring cells. The rules are then applied iteratively for as many time steps as desired” Source: Wolfram MathWorld. (Ulam, Metropolis and von Neumann)

Complex Models of Complex Systems (1/3) Cellular Automata

• Complexification again: MAS after CA

• MAS according to Gilbert (2008):

– Autonomy (like CAs: no general controller)

– Social capacity (communication) – Reactivity (adapted to the environment) – Proactivity (purposeful: goal, values…)

F(C,C,C) • Notation is being complexified: through software-based models of

simulation • Hence the necessity to standardize the notation process : e.g. the ODD

protocol (Overview, Design concepts, Details) of the Volker Grimm’s team

Complex Models of Complex Systems (2/3) Multi-Agents Systems (MAS) of Complex Adaptive Systems (CAS)

“A multi-agent based model of the housing development that incorporates all of

the resource models and the behavioural typology and interactions of the occupant

agents”. Source : ”Complex Science for a Complex World”, http://epress.anu.edu.au/cs/mobile_devices/index.html

Complex Models of Complex Systems (3/3) Multi-Agents Systems (MAS) - Example #1

http://epress.anu.edu.au/cs/mobile_devices/index.html

Simulating Ancient Societies – MAS - Example #2 Virtual experimental archeology - Tim Kohler (Washington State University) & George Gumerman (School of American Research - Santa Fe)

The « Pueblo » people or Anasazi have lived during centuries in a south-west region of the USA They suddenly abandoned the region in the 14th century (AD).

How to explain this? Source : NSF - http://www.nsf.gov/news/news_summ.jsp?cntn_id=104261

http://www.nsf.gov/news/news_summ.jsp?cntn_id=104261

Fundamental ideas of Kohler’s simulations

• Agents are interacting and evolving

• They are evolving

• 1) according to incorporated rules of behavior and • 2) according to their evolving environment (hence : MAS).

• We have diverse and dynamic environmental data

• Initial conditions: random distribution of the households

• The aim: observe on the simulation if it can predict (represent) the

ulterior effective evolution (which has been recorded by the archeological data)

Source : « Simulating Ancient Societies », Scientific American, 2005, Timothy A. Kohler, George J. Gumerman and Robert G. Reynolds

Results

• “Complexity”/”Simplicity” depend on material and symbolic instruments available for solving the problems of notation, combination, resolution.

• Different instruments are available at different periods of history

• An interpretation of the evolution thanks to the “Complexity Vector”:

– Newton laws for 2 bodies : F(S,S,S) – Newton laws for 3 bodies : F(S,S,C) – CA : F(S,C,C) – MAS : F(C,C,C)

• Remaining questions: – What precisely do simulations add to models? – Emergence in MAS // Emergence in real systems ?l open questions: – What precisely do simulations add to models? – Emergence in MAS // Emergence in real systems ?

Lessons from this piece of history




– Newton laws for 2 bodies : F(S,S,S) – Newton laws for 3 bodies : F(S,S,C) – CA : F(S,C,C) – MAS : F(C,C,C)






– Newton laws for 2 bodies : F(S,S,S) – Newton laws for 3 bodies : F(S,S,C) – CA : F(S, S, C) or F(S,C,C) – MAS : F(C,C,C)






– Newton laws for 2 bodies : F(S,S,S) – Newton laws for 3 bodies : F(S,S,C) – CA : F(S, S, C) or F(S,C,C) – MAS : F(C,C,C)

• Remaining questions: – What precisely do simulations add to models? – What are the relationships between models of simulations and mathematical models? – The dynamics of models in the study of complex systems – What precisely do simulations add to models? – Emergence in MAS // Emergence in real systems ?


• From the Complexity vector to the Three visions on complexity

• From the Three visions on complexity to the characters of complexity for a model

Complex systems and models

From the complexity vector to the Three visions on complexity

• Source: “Visions de la complexité: le démon de Laplace dans tous ses états”, authors : Deffuant, Banos, Chavalarias, Bertelle, Brodu, Jensen, Lesne, Müller, Perrier, Varenne, to

appear in Natures Sciences Sociétés.

• The key idea of this text is that visions on complexity are depending on the context but that they nevertheless can be reconciled by seeing them all as three different challenges to the Laplace’s demon

• According to Laplace, the determinism at stake in the universe can be explained in terms of a total predictability of every events of the universe by a “sufficiently vast intelligence”, Philosophical Essay on Probabilities – 1814, New York, Wiley, 1902, p. 4 :

First vision (1/4) • Mathematical complexity: the sensibility to initial

conditions • Some non-linear deterministic systems lead to chaotic behaviors: cf.

Poincaré, Edward Lorenz (1963), The “Butterfly” effect

• “Even if the program of the Demon is simple [Notation and Combination both get the attribute “simple” in the vector F (S, S,…)] the precision of our knowledge of IC cannot be infinite [hence sufficiently vast]”

• As a consequence, we cannot escape facing chaotic behaviors of those deterministic systems. Another example: fractals

• F(S,S,C): • Low Kolmogorov complexity [Combination: amount of combination types in the program]

– The K. complexity of a binary string is the size of the shortest program that can generate the string

• High Bennett complexity [or logical depth or content in computation : number of computation steps for the resolution or number of combination token in the execution of the program]

– The B. complexity of a binary string is the number of steps - or the time of computation – of the minimal program that generates it

First vision (2/4)

• Computational complexity: – There exist non-terminating algorithms (they belong to undecidable problems): Turing

showed there can be no general algorithm to determine whether algorithms halt (halting-problem)

– Algorithms have different time- or Bennett complexity

– Moreover, due to the halting problem (or to other problems related to Gödel limitation theorems), these complexities are hard or impossible to know a priori

– This is the reason why it is easier to use practically the Kolmogorov measure of complexity (which can be seen only as a measure of the randomness)

– Although the best way to discern “organized complexity” in real systems such as the one present in cells, towns or other social organizations is to rely on Bennett Complexity (Bennett, 1988 ; Delahaye, 2009)

– But Bennett complexity is related to the theoretical or practical (most of the time we can’t decide!) necessity to simulate, that is to “weak emergence” in the sense of Bedau 96.

First vision (3/4)

• Physical complexity: interaction and emergence

– P.W. Anderson : “More is Different” 1972: when the collective behavior of the elements of a physical system is difficult or impossible to deduce from the individual behaviors of these elements

– In this case, the program which could achieve this prediction is both very long and very time-consuming: it is Kolmogorov-Complex and Bennett-Complex

– F (S, C, C)

The common approach in this first vision • A vision of complex systems through systems of formalization: models are

systems

• Models inherit some selective characters of the complexity of the systems they models

• But not all : in this sense, they remain simplifying mediators

• They ease our ability to note, to denote (to refer to) systems, to refer to data and to models of data : but, their counterpart is their difficulties in Resolution and/or Combination

• If this formal counterpart finally can be bypassed by decomposition, analytic modeling and additive recomposition, then, at the end of the day, the system reveals that is complicated, not complex in itself

• Dynamics of models according to this vision: from F(S,S,C) or F(S,C,C) to F(S,S,S)

Second vision (1/3) • Integration of heterogeneous aspects of the system

in a model of simulation: F (C, C, C)

– Use the power of expression of computer languages to integrate different aspects, parts or scales of the system

– Pluriformalization (Varenne, 2003, 2007) leads to the integration of multiple knowledge (real or epistemic limitations ?)

• Phenomenological reconstruction: multi-scale, multi-aspectual, multi-physical (plants, hearts,

embryos…)

Second vision (2/3) More precisely : the case of Systems of models or

Integrative models of simulation (Varenne, 2009, p. 16)

• A system of models can be presented as a vector of formalisms or a matrix of properties having different attributes of simplicity for each of their properties.

• For instance, a multilevel computer simulation in population ecology can intricate – (1) some solvable differential equations working at each step at the level of the population F1 (S, S, S)

– (2) some models of real space or social space in a graph or network formalism F2(S, S, C)

– (3) some models of agents possessing a complexity of combination (in terms of diversity and variability) because they are cognitive agents or relatively

complex reactive ones F3 (S, C, C). It can be represented as follows:

[F1 (S, S, S), F2 (S, S, C), F3 (S, C, C),…]

This vector of formalism (or matrix of properties) cannot be easily reduced to a huge formalism having its own homogeneity, simplicity or complexity properties. So, most of times, such CSs have first to be experimented: through analyses of sensibility, of robustness, etc.

Hence, beside more traditional and direct mathematical researches on complex formalism, more and more modelers (working often in applied sciences) are seeking models of such complex software-based simulations ([Duboz 2004], [Edwards 2004], [Huet et al. 2007], [Huet et al. 2008]).

Significantly, the effort to standardize and re-homogenize (to remathematize) multimodels in industry had stemmed from the same previous and necessary movement of complexification, i.e. of integration and co-calculation of heterogeneous models [Zeigler et al. 2000].

Second vision (2/3) More precisely : the case of Systems of models or

Integrative models of simulation (Varenne, 2009, p. 16)

• A system of models can be presented as a vector of formalisms or a matrix of properties having different attributes of simplicity for each of their properties.

• For instance, a multilevel computer simulation in population ecology can intricate – (1) some solvable differential equations working at each step at the level of the population F1 (S, S, S)

– (2) some models of real space or social space in a graph or network formalism F2(S, S, C)

– (3) some models of agents possessing a complexity of combination (in terms of diversity and variability) because they are cognitive agents or relatively

complex reactive ones F3 (S, C, C). It can be represented as follows:

[F1 (S, S, S), F2 (S, S, C), F3 (S, C, C),…]

This vector of formalism (or matrix of properties) cannot be easily reduced to a huge formalism having its own homogeneity, simplicity or complexity properties. So, most of times, such CSs have first to be experimented: through analyses of sensibility, of robustness, etc.

Hence, beside more traditional and direct mathematical researches on complex formalism, more and more modelers (working often in applied sciences) are seeking models of such complex software-based simulations ([Duboz 2004], [Edwards 2004], [Huet et al. 2007], [Huet et al. 2008]).

Significantly, the effort to standardize and re-homogenize (to remathematize) multimodels in industry had stemmed from the same previous and necessary movement of complexification, i.e. of integration and co-calculation of heterogeneous models [Zeigler et al. 2000].

Second vision (3/3)

• Big-Data problems ? : new techniques of data-mining, new development of automated heuristics

– But let me raise a question: is automated induction (massive statistical, multivariate, bayesian approaches) a complexity aware and complexity-oriented study of complex systems?

– It is a use of mathematical models as instruments of analysis and not as instruments of synthesis and representation

– Hence, it reveals an experimental use of models (Category #1 of the functions of models)

– As such, they are not explicitly sensible to feedback nor to downward causation (interlevel interactions)

Examples of integrative models of simulations

(in biology)

And some remarks on their methodological and epistemological consequences

Aulne - Source : Bionatics ( http://www.bionatics.com ) Rapidly growing tree mature at about 60 years with long trunk and narrow crown. Distinctive outline in winter. Height 20m or more.

85

http://www.bionatics.com/







Accacia Lahia - Source : Bionatics ( http://www.bionatics.com ) A perennial flat-topped species of tree found in Africa. 86








Abricotier japonais - Source : Bionatics ( http://www.bionatics.com ) Low spreading tree with pink flowers in spring. 87








Application in architecture - Bionatics : http://www.bionatics.com

What for ?

88








Internal and External Interactions

Source: AMAP (CIRAD, INRIA, INRA, IRD, CNRS, Montpellier) 89

Interactions, flexions, mechanical constraints → prediction of wood quality


http://umramap.cirad.fr/amap1/phototheque/detail.php?num=13917&recherche=synthèse&num_page=344&type_affichage=1&tri=0&collection=&mots_cles_recherche=&mots_cles_annee=&mots_cles_lieu_collecte=&mots_cles_type=

Source : Philippe de Reffye (Digiplante-Inria-ECP-INRA, Amap Cirad)

Applications in predictive agronomy : coffee, corn, …

91

Applications in predictive agronomy


Applications in urbanism…

Source: AMAP (CIRAD, INRIA, INRA, IRD, CNRS, Montpellier)

93

Application in paysagism Source: AMAP (CIRAD, INRIA, INRA, IRD, CNRS, Montpellier) : réhabilitation d’une carrière 94

Virtual heart - Denis Noble et al. (Oxford – Physiome Project)

“The ‘Oxford Cardiac Electrophysiology Group’ led by Professor Denis Noble is an example for having developed a virtual model of the human heart, which integrates the kinetic characteristics of the molecular and cellular mechanisms of heart activity into detailed anatomical heart models and allows forecasts to be made on the physiology and pathophysiology of the heart”, Dr. Roland Eils (German Cancer Research). Source : http://bio-pro.de/magazin/thema/00173/index.html?lang=en&artikelid=/artikel/03079/index.html

95

Physiome Project : Auckland, Oxford, San Diego

Source : http://www.nature.com/nrm/journal/v4/n3/box/nrm1054_BX2.html

96

-1- Multi-aspectual

-2- Multiscale

- 3- Multi-physical : electrical, mechanical, chemical phenomena

- 4- Multidisciplinary: chemistry, mechanics, electricity, biology…

- 5- Multifield : physical sciences, biological sciences, behavorial sciences, social sciences, …

-6- Multi-epistemic : multiplicity of epistemic status of the submodels of each scale or each aspect: (Varenne, 2007, 2008)

- explanative submodels with verified or hypothesized mechanisms - phenomenological submodels (stochastic processes, Monte Carlo…) - digitalization of captured scenes - IRM scannings -…

97

The era of the « Multis »

Third vision (1/2)

• The irreducibility of the consciousness, of the knowing subject : opacity of the subjectivity, complex dynamics (diffusion, reaction, imitation, bifurcation…) of collective feelings and opinions

• High sensibility to context: cognitive (interpretative) more than only reactive agents (more feedbacks)

• Social agents are all the more altering their context

• Hence, in particular in this domain of the study of complex systems (social sciences), the importance of (sometimes) explicitly representing the intra- and inter-level feedbacks

Third vision (2/2)

• Models of simulation enable to simulate explicitly some of the (describable) rules of subjective interactions of social agents

• It can lead to the simulation of a new kind of emergence : the so-called “Strong emergence” (Müller 2003) or “Relative strong emergence” (Phan et al. 2013)

Refinement of the complexity vector : Characters of complexity for a model

F(Notation, Combination, Resolution)

2nd vision 3rd vision 1st vision

ChaCo (Notation, Integration, Condensation, Execution)

Ease and length of description Heterogeneity K.Complexity B.Complexity

Are these characters irreducibly heterogeneous?

• Who knows?

• But, practically, we see that we often can “make a deal”:

E.g., we can get a ChaCo (S,S,S,C) from a ChaCo(S,C,C,C) (through algorithm analysis, simplification of simulations ex post, remathematization, …)

Hence: We often can exchange a character of complexity for another one that is more tractable with the tools at our disposal


• Who knows?


E.g., we can get a ChaCo (S,S,S,C) from a ChaCo(S,C,C,C) (through algorithm analysis, simplification of simulations ex post, remathematization, …)



• Who knows?


E.g., we can get a ChaCo (S,S,S,C) from a ChaCo(S,C,C,C) (through sensibility analysis, algorithm analysis, simplification of simulations ex post, remathematization, …)



• Who knows?


E.g., we can get a ChaCo (S,S,S,C) from a ChaCo(S,C,C,C) (through sensibility analysis, algorithm analysis, simplification of simulations ex post, remathematization, …)


Conclusion The dynamics of models

• No unique order relationship in complexity for models as characters of complexity are numerous and different

• It is understandable than the vision 1 tends to claim its hegemony

• But it must be understood in terms of a dynamics of models compared to other visions

• To work with such a vision is to work on complex models in order to find simpler ones : i.e. either with an easier notation or a higher homogeneity or a shorter algorithm or a quicker execution time

See Varenne, 2009, p. 10: “physicists or theoretical biologists most of the time want to build a formalism F2(S, S, S) from a formalism F1 (S, S, C) or F1 (S, C, C).”













Thank you!

• Some references:

– Aziz-Alaoui M.A. & Bertelle C. (eds), From System Complexity to Emergent Properties, Springer, 2009.

– Bennett, C., “Logical Depth and Physical Complexity”, in Rolf Herken (ed.), The Universal Turing Machine – a Half-Century Survey, Oxford University Press 1988, pp. 227-257.

– Deffuant, Banos, Chavalarias, Bertelle, Brodu, Jensen, Lesne, Müller, Perrier, Varenne, “Visions de la complexité: le démon de Laplace dans tous ses états”, to appear in Natures Sciences Sociétés.

– Delahaye, J.P., Complexité aléatoire et complexité organisée, Paris, Quae éditions, 2009.

– Gell-Mann, M., The Quark and the Jaguar: Adventures in the Simple and the Complex, NY, Henry Holt, 1994.

– Holland, J., Hidden Order, Addison-Wesley, 1995.

– Mainzer, K., Thinking in complexity, Springer, 1997.

– Miller, J.H. & Page, S.E., Complex Adaptive Systems, Princeton University Press, 2007.

– Mitchell, M., Complexity: A guided Tour, Oxford University Press, 2011.

– Müller, J.P., “Emergence of Collective Behaviour and Problem Solving”, Emergent Societies in the Agents Word IV, Lecture Notes in Computer Science, Volume 3071, Springer, 2004, pp. 1-20.

– Newman, M., “Complex systems: A survey”, Am. J. Phys. 79, 800-810 (2011). Preprint: http://arxiv.org/abs/1112.1440

– Phan, D. & Amblard, F., Agent-based Modelling and Simulation in the Social and Human Sciences, Oxford, The Bardwell Press, 2007.

– Phan, D. & Varenne, F., “Agent-Based Models and Simulations in Economics and Social Sciences: from conceptual exploration to distinct ways of experimenting", Journal of Artificial Societies and Social Simulation, 13(1), 5, 2010. Free access: http://jasss.soc.surrey.ac.uk/13/1/5.html

– Varenne, F., "Models and Simulations in the Historical Emergence of the Science of Complexity", in M.A. Aziz-Alaoui & C. Bertelle (eds), From System Complexity to Emergent Properties, Springer, 2009, pp. 3-21. Preprint : http://hal.inria.fr/docs/00/71/16/24/PDF/Varenne_Models_Simulations_Complexity_Emergence_Springer_2009.pdf

– Varenne, F., "Framework for M&S with Agents in regard to Agent Simulations in Social Sciences: Emulation and Simulation", in Activity-Based Modeling and Simulation, A. MUZY, D. R. C. HILL & B. P. ZEIGLER (eds.), Clermont-Ferrand, Presses Universitaires Blaise Pascal, 2010, pp. 53-84. Free access: http://www.msh-clermont.fr/IMG/pdf/04-Varenne_53-84_.pdf

– Varenne, F., “Modèles et simulations dans l’enquête scientifique : variétés traditionnelles et mutations contemporaines” in F. Varenne & M. Silberstein, Modéliser & Simuler – Epistémologies et pratiques de la modélisation et de la simulation, Paris, Editions Matériologiques, 2013, pp. 11-49.

– Varenne, F., “Chains of Reference in Computer Simulations”, to appear in S. Vaienti, P. Livet (eds.), Simulations and Networks, Aix-Marseille, Presses de l’Université d’Aix-Marseille, coll. IMéRA, 2013. Preprint : http://philpapers.org/rec/VARCOR

http://arxiv.org/abs/1112.1440

http://jasss.soc.surrey.ac.uk/13/1/5.html

http://jasss.soc.surrey.ac.uk/13/1/5.html

http://hal.inria.fr/docs/00/71/16/24/PDF/Varenne_Models_Simulations_Complexity_Emergence_Springer_2009.pdf

http://www.msh-clermont.fr/IMG/pdf/04-Varenne_53-84_.pdf







http://philpapers.org/rec/VARCOR

http://philpapers.org/rec/VARCOR

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