4.1.1.1. Variety of components and links

The constituents of a complex system are of varied size, heterogeneous in nature (individuals, artifacts, symbols, etc.) and indistinct (possible evolution over time) and have an internal structure. “A complex system does not behave as a simple aggregate of independent elements, it constitutes a complete coherent and indivisible structure” [TAR 86, p. 33]. This formal property brings us back to the entire concept that we discussed in section 1.2.2 in Chapter 1.

“The two notions that characterize complexity ‘are the variety of elements and interaction between these elements’. A complex system is formed by a wide variety of components organized into arborescent levels. The different levels and components are interconnected by a variety of links.” [TAR 86, p. 33]

And it is the variety of interactions between its constituents and the variety of the constituents themselves that contribute the overall evolution of complex systems.

4.1.1.2. A complex system is not a complicated system

A complex system is unpredictable. Therefore, it does not allow (by calculation), as forceful as it may be, a predicted outcome of the processes or phenomena⁴.

But complex doesn’t mean complicated.

“For example, we are able to understand and predict when and why a car engine breaks down while we are unable to understand and predict all of the factors that influence a change or a social movement (e.g. for a revolution).” [BEG 13]

When the system is complicated, we are able to find one or more solutions, because a “complicated” system consists of a set of simple things. It just takes a bit of precision, knowledge and time to understand its function. The general method is first to break down and isolate each of the elements (in simple components or in simple notions) to then be able to reassemble them. “The mechanical function of a clock or a car engine, for example, may seem complicated to us but we are able to clearly explain how it works, because we know what impact each mechanical or electronic component has on the other” [BEG 13].

To illustrate the difference between a complex system and a complicated system, Snowden [SNO 02, p. 13] pertinently noted that “when rumors of reorganization appear in an organization, the human complex system begins to mutate in unpredictable ways and forms trends in anticipation of the change. Conversely, when one approaches a plane with a toolbox in hand, nothing changes!”⁵

4.1.1.3. Open system: between complexity and chaos

A complex system is also an “open system” or in constant contact with its environment. In fact, “it undergoes external disturbances that are preconceived as unpredictable and unanalyzable. These disturbances, occurring in the environment, cause system adaptations that bring it back to a stationary state” [SNO 02, p. 32].

For those who study it, a closed system is more predictable than an open system in the sense where being totally isolated from external influences, it will be subject to internal modifications and will be found in a number of states defined by its initial conditions.

And if the latter are invariable regardless of the number of experiences, in other words, the number of times that you observe the system’s behavior, from its initial phase to its final phase (which is very difficult to attain), it will behave as an automaton that develops a known program. In this sense, it can be considered to be complex, as complicated as this program can also be! The knowledge of the various intermediate states being sufficient to define the system, its evolution and its finality become foreseeable and predictable.

But as we will see below, it is difficult to ensure the invariance of the initial conditions applied to a closed system, which makes an open system and therefore a potentially complex system (because openness is a necessary condition but not sufficient to ensure that a system is complex).

4.1.1.3.3. Algorithmic complexity and natural complexity

We can differentiate algorithmic complexity from natural complexity. The first is one that we can process with a computer, a program or an algorithm. The goal to be achieved is known, as complex as it may be. The purpose is specified, and it determines the value of the procedure. Natural complexity is inherent to “systems not totally controlled by man because they are not built by man” [ATL 79, p. 5]: biological systems such as memory and social systems. This distinction is fundamental to the extent where the theory of self-organization that we will discuss is only justified in systems of natural complexity. These are a mix of knowing and ignorance. They constitute a sort of “compromise between two extremes: a perfectly symmetrical repetitive order whose crystals are more classic physical models and an infinitely complex and unpredictable variety in details such as evanescent forms of smoke” [ATL 79, p. 5]. Simon, 1974, has already shown the difference of intelligibility between natural and artificial objects in 1969. Natural objects are analyzed with the assumption that “complexity is woven from simplicity; correctly analyzed complexity is only a mask concealing simplicity”. Therefore, it would be appropriate, according to Simon, to find the ordered shape that hides in the apparent disorder. The theory of fractals, introduced in 1975 by Benoît Mandelbrot, would be a recent illustration. “The Santa Fe Institute⁶ was created in 1984 in an attempt to study the conditions by which order occasionally emerges from chaos, which is exactly the opposite of a butterfly effect”⁷.

Let us go back and take a quick look at the foundations of information theory [SHA 48] to examine this issue in more detail.

According to this theory, all communication processes can be represented by a channel of communication between a transmitter and a receiver in which a message pass. The latter may be subject to external disturbances that generate errors, which modify the message. We call “sound” a disruption that modifies a message between its transmission and reception. For example, the letter or the symbol of an alphabet composing a loud message is received with a certain probability, but not certainty.

This sound in the channel of communication has a negative effect in the formalization of the amount of information developed by Shannon [SHA 48]. However, instead of considering the transmission of information between the sender and the receiver, Atlan [ATL 79, p. 46] invites us to observe the amount of total information in the system (S) including this transmission path. In this case, the relevant transmission path is no longer the same. It settles between the system and outside observers.

From this perspective, the ambiguity introduced by sound on a basic channel (the one seen by Shannon) can be a generator of information for the observer.

Intuitively, we perceive that the complexity notion of a system is intimately linked to the amount of information defined by Shannon.

“The more a system is composed of a large number of different items, the greater its quantity of information and the improbability of it forming ‘as it is’ by randomly assembling its constituents. That is why this quantity could be proposed as a measurement of the complexity of a system, in that it is a measurement of the degree of variety of elements that constitute it” [ATL 79, p. 45].

Complexity is often associated with newness (high amount of information), while the trivial is repeated (small amount of information).

“The quantity of information of a system, made up of parts, is then defined from the probabilities that we can assign to each kind of component on a set of supposed statistically homogeneous systems from each other; or even from all the combinations, where it is possible to achieve with its components, that form possible states of the system.” [ATL 79, p. 45].

Errors caused by sound introduce a new variability within the system. Thus, the increase in the degree of variety (or degree of differentiation or complexity) of a system, based on a random disturbance from its environment, is measured by the increase in the amount of Shannonian information that it contains.

Henri Atlan transposes this increase in the amount of Shannonian information in a loud system as far as the complexity of an organized system, such as biological organisms or a social organization. This conversion leads the author to design “the evolution of organized systems or the phenomenon of self-organization as a process of increasing both structural and functional complexity resulting from a succession of disruptions caught, each time followed by a recovery to a level of greater variety and lower redundancy” [ATL 79, p. 49].

The increase in complexity “can be used to achieve greater performances, most notably with regard to the possibilities of adaptation to new situations, thanks to a variety of responses to diverse stimuli and randomness in the environment” [ATL 79, p. 45].

In fact, a very organized system, such as an algorithmic complexity system, for example, will be totally predictable and, consequently, poor as to its content information in a Shannonian sense. Otherwise, if it is completely erratic and random, its predictability will be void. It is therefore not complex, but chaotic.

“It is when the content information is intermediate in terms of predictability and average probability, that complex systems can be found.” [WAL 12, p. 1023]

It is in this limited space that it is possible to predict potential emerging phenomena with, undoubtedly, a certain degree of uncertainty. Other definitions of complex systems or associated concepts, mainly from thermodynamics, also exist and can be used depending on the circumstances, as we will see below.

4.1.1.4. Feedback, self-organization and homeostasis

4.1.1.4.1. Feedback

A fundamental feature of a complex system (already studied above) is its circular causation. In more explicit terms, individual or collective constituents of the system behavior provide feedback on their own behavior. These elements will individually or collectively change their environment, which in turn will constrain them and change their states or possible behaviors.

This circular process applied to systems, as opposed to the linear and unidirectional Shannon model, is in the foundations of social theory of communication. Expanding cybernetic thinking to all living systems, which our learners are a part of, Bateson [BAT 77] uses this concept of feedback to explain a very broad set of phenomena, such as language, biological evolution and schizophrenia... but also learning. Thus, it deals with learning as a feedback phenomenon: “change can define learning”, he says. For him, “the word ‘learning’ undoubtedly indicates a change of one kind or another” [BAT 77, p. 133].

What is essential in a complex system is therefore not so much the number of factors or dimensions (factors, variables) related to the system constituents, but the fact that “each of them indirectly influence others, who themselves influence it in return, making the system’s behavior an irreducible whole”⁸. In other words, in a complex system, knowing the properties and behavior of isolated elements is useful but not sufficient in order to predict the overall behavior of the system. To predict this behavior, it is necessary to take them all into account, which usually involves making a simulation of the studied system, a simulation we will look at in detail in section 6.2 in Chapter 6.

4.1.1.5. Existence of emerging properties

Perpetual reorganizations of systems can sometimes produce unexpected and unpredictable behaviors. We say that such behavior is “‘counter intuitive’ in the words of Jay Forrester or counter-variant: when following a specific action, we expect a given reaction, although a completely unexpected and often an opposite outcome is often obtained. These are the games of interdependence and homeostasis. Politicians, businessmen or sociologists don’t know much about the effects” [DER 75, p. 129].

If there is one thing that characterizes many complex systems, it is certainly the existence of emerging properties, either in the living or inert world. These phenomena, which are also emerging, are well known in the world of matter. Atoms, for example, bind to produce a new entity with new properties: the molecule. For example, who could have predicted that from gas molecules, such as dihydrogen (H₂) and oxygen (O₂), we could produce a liquid substance with completely new characteristics, water (H₂O)? In addition, these water molecules crystallize in the cold to produce an unpredictable new compound, ice crystals...

The first conclusion that can be drawn from these phenomena is that it is difficult to predict the overall behavior of the system from the mere knowledge of the properties and behavior of isolated elements.

A complex system has, in fact, new and higher properties than those that we would have obtained as the sum of the properties of its constituents.

Let us also keep in mind from these examples that complex systems are not linear “since the new function or the new state does not appear gradually, but suddenly: water freezes, life appears” [WAL 12, p. 1022]. Many other emerging phenomena can be cited beyond the phenomena derived from the world of matter. For example, when we think about the human mind or conscience... Do they not emerge from a “simple” organic aggregate?

“The obvious emerging phenomena that have been shown during the evolution of the physical and social universe are undeniably the appearance of life, the emergence of thought and the genesis of institutions (language, currency). However, we can observe a variety of emerging phenomena at a more modest pace such as turbulence in fluids, cell clusters, colonies of insects or the prices of goods. [...] These emerging phenomena can take various forms, ranging from simple combinations of properties of microscopic entities or relations between these entities concerning the appearance of characteristics or original macroscopic entities.” [WAL 09, p. 2].

Thus, emerging phenomena can occur “through all natural sciences, such as physics, chemistry, biology, but also at the level of those dealing with the environment, climate, society, energy distribution systems and the internet” [WAL 12, p. 1022].

It then becomes possible to imagine that social interactions within digital learning environments from the last generation could also be the cause of emerging phenomena... Could we not imagine, for example, MOOCs quickly becoming real parallel universities that compete with conventional universities, calling into question the methods and teachings of the latter, even while MOOCs were designed to be at the service of universities? Alternatively, could we not conceive of the opposite assumption, whereby MOOCs would finally be abandoned by users, like a fashion phenomenon, even though they currently seem fated to success?

4.1.2.1. Conjunctive versus disjunctive logic

“The analytical method needs disjunctive logic since the results of the breakdown must be definitively distinguished and separated” [LEM 99, p. 32]. However, according to the author and all the thinkers he cites, this logic does not, “account for phenomena that we perceive in and by their complex conjunctions...” [LEM 99, p. 33]. He blames in addition the analytical school supporters “seeking to adapt the problem available to models rather than seeking models of substitution that best meet the problem” [NON 00, paragraph 2]. The use of analytical models requires a simplification of the studied phenomenon, so when a breakdown or division sets off from the hypothesis, in order to address a complex situation, the register must be changed. It is required to go from the registry of disciplined knowledge review to that of active enlightening knowledge methods.

To guide and argue his reasoning, Le Moigne refers to some stable benchmarks which he called axioms. He thus said gather “the contemporary state of maturation of axiomatics based on the texts of Heraclitus, Archimedes, Leonardo da Vinci, GB. Vico or Hegel” [LEM 99, p. 35], in the form of three axioms that fit well within a constructivist epistemology (the paradigm of the constructed universe). In this argument, this radically comes in opposition with positivist epistemology (the wired universe paradigm) that always relies, according to the author, on Aristotelian axioms of analytical modeling and disjunctive logic.

Let us quote the three axioms of systemic modeling referred to by the author [LEM 99, p. 36]:

• – the axiom of teleological operationality or synchronicity: a modelable phenomenon is perceived as an intelligible action and therefore teleological (not erratic, showing some forms of regularity);
• – the axiom of teleological irreversibility (or diachrony): a modelable phenomenon is perceived, transforming and project forming over time;
• – the axiom of inseparability or recursion (or excluded outsiders, or conjunction, or autonomy): a modelable phenomenon is perceived inseparably joining the operation and its product, which can be a producer for itself.

Referring to these three axioms, it appears that we can actually ensure the precision and cognitive consistency of modeling reasonings [LEM 99, p. 35].

Each new theoretical contribution is then associated with “a canonical model that represents the new system” [NON 00, paragraph 2]. The first is the canonical form of the general system that leads the author to define four founding concepts, grouped in pairs in procedures: the cybernetic procedure includes active environment and project concepts, while the structuralist procedure includes synchronic operation and diachronic transformation. The inseparability of these concepts leads to the conceptualization of the general system, understood as “the representation of an active phenomenon perceived identifiable ‘by’ its projects in ‘an’ active environment in which it functions ‘and’ transforms teleologically” [LEM 99, p. 40].

At the beginning of Chapter 5, we will revisit the concepts underlying cybernetic and structuralist procedures. In a more mnemonic way, “the general system is described by an action (a tangle of actions) in an environment (‘carpeted with process’) for some projects (purposes) functioning (doing) and transforming (becoming)” [LEM 99, p. 40]: therefore, for the author, the basic concept of systemic modeling is not its structure, but the action it represents by a black box or a symbolic processor that takes account of the action.

“Modeling a complex system first involves modeling a system of actions.” [LEM 99, p. 45].

4.1.2.2. A complex system and canonical model process

The modeling of a complex action is characterized by a general process notion, which is defined by its exercise and result. The author represents the process using three functions: the temporal transfer function, the function of morphological transformation and spatial transfer (see Figure 5.21).

“We define a process by its exercise and result (an ‘implex’ therefore): there is a process when there is, over time (T), modification of the position in a ‘Space-Form’ reference, and a collection of ‘products’ identifiable by their morphology, and thus by their form (F). The preconceived conjunction of a temporal S transfer (moving in space: transport, for example) and a temporal F transformation (morphology modification: an industrial treatment transforming flour and water into bread, for example) is by definition a process. Its outcome can be recognized: a movement in a ‘Time-Space-Form’ reference, identified by its exercise.” [LEM 99, p. 47]

In this regard, Martin et al. noted:

“In this theory, the observed system is apprehended in the form of a collection of tangled actions, the process notion being conceptualized by that of action. If the process is a formal construction expressed in the language of mathematics (differential equation) in ‘Time–Space–Form’ references, the description of the action expresses itself in natural language in response to the question, ‘What does that do?’ Although this theory is based on the action concept, no formal description framework of an action is proposed (Larsen-Freeman and Cameron, 2008).” [MAR 12]

We will see later that these authors propose a formalism for the action concept we want to deepen and that will be very useful for modeling DLEs considered as complex systems.

4.1.2.3. Complex system and action interrelation

Returning to feedback concepts, Le Moigne characterizes each processor by its “inputs” and “outputs”, at every “ti” moment, before establishing three archetype processors that he adapts specifically into three transfer functions: temporal, spatial and morphological. He also distinguishes processors mainly processing symbols (or information) from others (mainly processing tangible goods) [LEM 99].

He then takes an interest in cases where the number of considered processors becomes high (frequent cases in complex systems) and then proposes differentiating the system into “many subsystems or ‘levels’, each level with the capability to be modeled by its network and relatively interpreted independently as soon as the inter-level coupling interrelationships have been carefully identified” [LEM 99, p. 53].

“We’ll have the opportunity to show [he says] that this deliberate a priori articulation of a complex system ‘in multiple functional levels’ (by intermediary projects) will lead to a very general canonical model which will often lead in turn to an intelligible modeling of its organization.” [LEM 99, p. 57]

4.1.2.4. An archetype model of the articulation of a nine-level complex system

K.E. Boulding [BOU 04a] and subsequently J.-L. Le Moigne [LEM 99, p. 58] offered a definition of an organization based on the definition of increasing levels of complexity of a system, each level also containing all the characteristics of lower levels. The article ‘General System Theory, the Skeleton of Science’ (the “framework of science”, [BOU 04a]) presents Boulding’s famous nine levels [BOU 04a] analysis, and we will quickly present it here. Keep in mind the significance of each of these levels when applying the approach to DLE modeling that we saw in Chapter 5. We will avoid redundancy by this time citing the way Le Moigne has interpreted them. What makes this nine levels analysis important is not so much the manner in which it is formulated, but the way it has contributed to “clarifying the terms of use of the systemic approach or methodology”¹².

We will only cite briefly the first six levels, referring the interested reader to the description of other levels, either by the original document (op. cit.), the work of Tardieu, Nanci and Pascot [TAR 79], or the reinterpretations made by Le Moigne [LEM 99] in Chapter 5.

• – Level 1: “The first level is that of static structure”¹³ [BOU 04a, p. 202]. The phenomenon to model is identifiable but passive and without need.
• – Level 2: The phenomenon is active. It does, meaning it “‘transforms’ one or more ‘inflows’ into one or several ‘outflows’” [TAR 86, p. 60].
• – Level 3: It is active and regulated. “It presents ‘patterns of behavior’”.
• – Level 4: It inquires. “The information allows a processor to know something about the activity of another processor in the system or its environment. The regulation of a system, thanks to a flow of information, is the basic concept of cybernetics” [TAR 86, p. 60]. The system transmits regulation instructions, reflecting changes in the system’s state.
• – Level 5: It determines its activity. This level of complexity suggests links that will be established between a “control system” and an “operating system” that we will later define. Here, the system is seen capable of making decisions concerning its own activity.

We will come back fairly quickly to this fifth level of organization and cover level 6 in the section relative to the concept of organization as well (section 4.1.2.5). Note that at this time the definition of tree diagram concepts (seen in section 4.1.2.3) and the concepts of organization levels proposed by Boulding (seen in section 4.1.2.4) is a critical first step in modeling complex systems.

“From the first level corresponding to static and simple objects of physics and chemistry up to the last level of socio-culture, the movement is that of increasing complexification. The understanding of the system represented by the ninth level involves all the previous levels.” [CAM 07, p. 16].

“This presentation of complexity, in addition to its educational interest, offers a methodological interest. It illustrates the specific approach of a speaker (or curious person) when becoming acquainted with the object information system [...]. Social organizations, the goal of our modeling, are at the highest level; the ninth.” [TAR 86, p. 59]

4.1.2.5. Active organization: operating system and control system

If there is a central concept that allows us to carefully describe a complex system, it is that of active organization.

“Say that a business, a municipality, a family, a government, an industry, an ecosystem, a university, a hospital, a club, etc., are complex systems. This is already the application of some strong assumptions that we’ve recognized. It relates to a complexity of irreversible, recursive and teleological actions that we propose designating (or modeling). The organization of this modeling exercise is through a pivot concept (today very well clarified) known as active organization (that E. Morin proposes calling Organis-action and F. Perroux the Active Unit).” [LEM 99, p. 73]

The organization is here considered as “active” because it is the one who determines its own activity. If the behavior of the system was solely dependent on external interventions, it would not be complex but simply predictable. The complexity appears with the emergence of autonomic capabilities within the system. The behavior of a complex system regulates endogenously; therefore, it is the one ensuring that its behavior is consistent with what was expected and eventually determines to act for modification. The organization is therefore made up of, “on the one hand, an ‘operating system’ (OS), the place of activity allowing transformation of incoming and outgoing flows and, on the other hand, a ‘control system’ (CS) capable of, in view of the information representing the activity of the operating system, reacting according to a certain project (certain objectives) to make decisions [...]. The dynamics of the organization [active organization] concern, on one hand, ‘the functioning of the operating system’ and on the other hand, ‘the functioning of the management system’” [TAR 86, p. 61], as suggested in Figure 4.4.

4.1.2.6. Information system

“Information allows the organization to adapt its behavior at every moment by regulating, transforming and rebalancing in order to be in harmony with the environment. Therefore, information leads to a process of permanent adjustment of the organization by channels (the system adapts by accommodation) and codes (the system adapts by assimilation) of communication with respect to a project.” [NON 00, paragraph 2]

At the sixth level of organization, modeling the information system (IS) is introduced. It ensures a coupling between the information considered during its storage and information considered at the time of its use. In fact, “in developing its decisions, the system does not consider instant information, such as, for example, a conventional thermostat, or a reflex arc; it also considers the information it has stored” [LEM 99, p. 61].

At this level, the control system cannot only have representation information on the current state of the operating system (for example, who is exchanging information on a discussion thread, looking back at our activity example on MOOCs), but also on the past states of the operating system (number of registered users having been active on the discussion thread during the last training session, for example).

The questions that will now arise to complete level 6 concern, on the one hand, the dynamics in the organization’s information system (where system information/operating system interactivity exists) and, on the other hand, the dynamics of the operating and control system within the information system. We refer the interested reader to the details of these three representations in “the Merise method” [TAR 86, p. 65] seen in section 3.5 in Chapter 3.

Nevertheless, and essentially:

“The organization’s information system (IS):

• – records (in symbolic form) representations of the functions of the operating system (behavior of the complex system);
• – stores them;
• – makes them available, generally by means of an interactive form, to the decision-making system. Which, after having developed its action decisions (orders), also records and stores them through the IS, transmitting them ‘for action’ to the operating system.” [LEM 99, p. 87]

4.1.2.7. The canonical model of a three-level organization system: OS, IS and DS

It is possible to represent the organization with an established model:

• – decision-making system;
• – information system;
• – operating system.

Figure 4.6 shows a possible diagram of this organization.

Le Moigne adds that “the canonical model of system organization, connecting the three levels: operation, information, decision-making, is universal. You can always start an organization’s modeling of a complex system using this genotype model” [LEM 99, p. 87].

4.2.2.1. A world of knowledge: a complex system

To have the project of modeling a world of knowledge, such as latest-generation DLEs, referring to the constructivist paradigm of systemic complexity modeling, may seem like an audacious exercise. But moreover, assuming that all acquisition of knowledge can adapt to a world not necessarily built for the sole purpose of learning may prove to be the challenge. However, we wanted to address this challenge by perceiving cognitive organization and the human cognitive system as self-organizing complex systems capable of learning in a world organized for this purpose (rather than built in the formal sense of the term), by combining two shifts of thought of which the union seemed, only a few years ago, utopian. Let us argue the choice here, when the main development is (at the personal request of Jean-Louis Le Moigne) in the “Cahier des Lectures MCX (Modélisation de la Complexité)” of the “Réseau Intelligence de la Complexité” [TRE 09b].

The first of these shifts is based on the complex systems theory, which assumes that any learning opportunity results from the disruption of a system subject to external disturbances. Whether this system be social or cognitive, it then reorganizes by increasing its degree of variety or complexity.

“[As a system, it is enriched by this disruption by the means of] a non-directed learning process, in the sense where this learning is by no means a program established in human memory, or in the natural or social environment of this memory. [...] The efficient cause of this learning is the random encounter of system memory and noise factors from its environment. [...] This learning product is a succession of psychological categories always finer or differentiated, whose list and construction methods are likely to be involved at any stage of the process.” [ANC 92]

We can intuitively understand this phenomenon when thinking of the classical theory of evolution: “Mutations, which are precisely DNA replication errors, are considered to be the source of the progressive increase of the diversity and complexity of living human beings” [ATL 98]. The increase in complexity in a system can produce a positive effect on them; it becomes a learning source. However, this theory is also taken for granted in the sense that this self-organizing process can only operate in systems with natural complexity, or inherent complexity, to “systems not totally controlled by man because they are not made by man” [ATL 79, p. 5], such as biological systems like memory, social systems, etc.

The second shift takes an interest in an opposing way to the “building” of these worlds, hence the apparent paradox. By their prescriptive nature, teaching design (or Instructional Design) models are in fact essentially based on behaviorist-type epistemological approaches in order to “teach” the subject. Conversely, constructivist learning environments emphasize interactive environments that seek the personal experience of the subject, initially through collective activities, supported by the instructor and social group, and then through individual activities. The connectivist approach goes even further referring mainly to metacognitive, or even meta-metacognitive processes to which learners must access in order to learn through the network [SIE 05, BAT 77, p. 323]. In the latter cases, learning is no longer dependent on stricto sensu “teaching”. Formally, in constructivist, or even connectivist models, the learning process operates independently of cognitive situations constructed by the teacher or by the designer. At most, these environments require, on the part of the latter, “creation” of “real” environments using the context in which the study is appropriate [JON 09]. Since this is a matter of “artificially” designing “real” learning situations or simulating situations connected to a natural context, the teaching model design patterns gradually accommodated the constructivist beliefs and practices. The constructivist paradigm is now added to the founding paradigms of instructional design models after, first, behaviorist, then cognitivist [TRE 08].

From our point of view, one of the keys to the success of “the application of the complex systems theory to the modeling of new generation DLEs” lies in the connection between these two shifts. For Lemire [LEM 08, p. 38], building a world of knowledge first involves “weaving links between approaches to the modeling of reality and a general system”. This a way of explaining the changing world perceived as a system; to better understand and change with it, without wanting to force it. It is also pretending to take advantage of its evolution. It is learning more about the system in which we are making progress through the use of illuminating modeling or learning to better recognize ourselves as a cognitive system integrated into this encompassing system. By modeling such systems that surround us or live in us, our actions become metacognitive acts. It is by “applying a methodology to the systemic approach that models constructed from perceived realities become the representation of what is received as and by a general system” [LEM 08, p. 37]. From these considerations, the objective is clearly formulated as an invitation to model what characterizes a real world, conducive to the self-construction of knowledge.

4.2.2.2. Latest-generation DLEs: an “open” system

Remember that what characterizes latest-generation DLEs, whose MOOCs are currently the best representatives, is primarily their openness to the world, as well as the consequences of this openness. The first ‘O’ (for Open) of the acronym MOOC ostensibly shows: online courses become open to all. As we recall from our book l’Appropriation sociale des MOOC en France [The social appropriation of MOOCs in France] [TRE 16a, p. 15], registration restrictions (place, time, age, degree) such as registration fees are dropped. Open means that everyone has access unlike traditional online teaching (distance learning), which requires registration with access conditions difficult to negotiate (degree, availability, staff, language proficiency, registration fees, etc.). This is one of the major features of MOOCs, which confirms and undoubtedly strengthens its originality. We can also immediately judge the consequences of this availability caused by the presence of the letter “M” for Massive in the acronym. The massive aspect of an MOOC is certainly what makes the biggest impression when you discover one. Most people questioned on this matter also begin by quoting some impressive numbers (hundreds of thousands of people) corresponding to the number of registered users. When you ask a teacher to describe his teaching methods, he immediately mentions about 30 students in front of him, and even more in the case of a university course. In an MOOC, there is not 30 or 50 registered, but 150,000 or even more. To our knowledge, the most registered for a single MOOC course has been 230,000 users to date. Imagine yourself in front of 230,000 students! This is substantially the size of the American population who came to listen to Martin Luther King Jr. (MLK) in his famous “I have a dream” speech in Washington in front of the Lincoln Memorial on 28 August 1963. Therefore, there exists an endless variety in the learner profiles, in their geographical and socio-cultural origins, in their prerequisites, but also in their ways of learning, in teaching methods, in assistive devices and assistance offered, etc. And since the complexity of a system is measured (even quantitatively) by its variety, there is no compunction in considering a latest-generation DLE as a complex system. As Tardieu et al. wrote [TAR 86] “The two notions that characterize complexity are the variety of elements and interactions between these elements”. Concerning interactions, we have seen that, within MOOCs, participants self-teach and motivate in an interactive and animated space [CRI 12], which, in view of the variety of systems constituents, increase the variety of interactions between these participants. Remember also that George Siemens²⁰ is convinced that “formal education no longer represents the majority of our learning in that there are a large variety of ways to learn today, through communities of practice, personal networks and through work-related tasks”.

4.2.2.3. Unpredictable nature of DLEs

It is also necessary to acknowledge the chaotic evolution of these environments that characterize complex systems. Their effects are unpredictable by nature. Going back to the exemplary case of MOOCs, nobody could in fact predict, in 2013, what they would become and least of all what they were supposed to bring to French society. Some of the most serious newspapers and media outlets also did not hesitate in predicting the end of traditional university education: “a model that could revolutionize the education system; with no need to follow prestigious educational courses”.²¹ And these may not just be the “visionary” qualities of Geneviève Fioraso²², then Secretary of Higher Education, who led the French government into the MOOC adventure in January 2014. This was rather the fear of missing out on any future profits, without being certain of receiving them at the end. The approach was, therefore, to not risk missing “a moving train”, while we knew very well its destination. Even today, nothing allows us to say with certainty to what extent this major innovation will change or not change the landscape of the French academic world and beyond. This unpredictability allows us to say that a latest-generation DLE can be studied as a complex system and not as an ordinary or “merely” complicated system (see section 4.1.1.2). Furthermore, complex (or chaotic) does not mean hazardous. In addition, there lies the interest in studying complex systems with systemic complexity modeling tools. As we have seen in section 4.1.1.3, between a completely predictable and a chaotic system (completely unpredictable) are complex systems (systems with average predictability).

The whole point of systemic complexity modeling is unveiled: the emergence of certain phenomena can be anticipated by modeling with a certain probability of accuracy.

Therefore, we can consider not only all sorts of predictions that will be useful to developers and users of DLE, but also policies that do not cease to request enlightening reports on these social issues. This is why we devote a whole section to this topic (section 4.2.5).

4.2.2.4. Consequence of the limits of analytical modeling and disjunctive logic

Disjunctive logic specific to analytical modeling (AM), as opposed to individual conjunctive modeling specific to systemic modeling (SM), aims to independently study the constituents of a system: “the breakdown results must be definitively distinguished AND separated” [LEM 99, p. 32]. In fact, it does not allow for “the realization of phenomena that we perceive in and by their complex conjunctions” [LEM 99, p. 33].

For example, let us take the example of the energy and work concepts in physical sciences. Applied to a body under gravity in space (for example, a rock resting on our hand a meter from the ground), we define the potential energy of this body by the amount of the work (in the physical sense of the term, that is, force times displacement) it is “potentially” capable of producing during its fall (if we drop the rock, of course). Therefore, it is easy to find the value of its potential energy: m.g.z (m.g being the weight of mass (m) in a gravitational field (g) and z the distance from the rock to the ground). We see through this example that it is impossible to define the concept of energy without talking about work and vice versa. These concepts cannot understand each other and can only observe each other in their conjunction.

Many other examples can be cited to illustrate this need to conjoin rather than separate. In the case that concerns us, we ask the question to know what is the point of separating the “subject” and the “tool” or the “subject” and its “community”, just as Engestrom did in his model. Can these system constituents not also be seen in their conjunction? Bogdanov²³ [BOG 81, p. 63] cited by Le Moigne [LEM 99, p. 33] considers the act of joining as fundamental, and separation as derivative; “the first is direct, the second is the result: all begins with the act of joining”.

Let us look back for a moment at the anthropocentric approach of the Rabardel techniques [RAB 95] seen in section 1.2.4 in Chapter 1. Is it not also intended to transcend this mind/matter dualism to approach the cognitive development of the subject by placing it in its social and material environment? Piaget and Vygotsky also worked together to overcome a Cartesian dualistic vision (mind/matter) by locating the thought mechanism and its development at the crossroads of an outside/inside, middle/subject loop.

According to Bogdanov:

“The two conceivable actions of man in nature, whether practical or cognitive actions, are to join and to separate. [...] Join his body or attention to the system to be considered; apply a conscious effort, which is still a conjunction. It is a similar situation for cognition: no distinction is possible without a preliminary comparison, which is still an act of conjunction. In this case, disjunction is also secondary.” [BOG 81, p. 63]

Bateson [BAT 77, p. 275] reinforces the idea of inseparability of the “subject” and the “tool”. To do this, he takes the example of a blind man and his cane (tool) used to help guide him. “The cane is simply a way [he says] in which transformed differences are transmitted, in a way that the cutting of this channel removes a part of the systemic circuit that determines the possibility of locomotion for the blind man”. Michel Serres [SER 15] also shares that view in a French metaphor: “la tête de Saint Denis” (English translation: the head of Saint Denis). He made an analogy between “our head” and “our computer”. We have, he says, “our head in our hands” since we are more than ever in an externalization logic of our cognitive functions in the direction of tools capable of memorizing and processing information instead of us. These tools become part of ourselves (our head is in our hands) and therefore inseparable: the subject and the tool are one.

But what should we then think of all these models that assert systemic nature and that, as we ourselves have done, represent only the components of a system, connected through relationships? Le Moigne provides an explanation:

“Between 1960 and 1980, many treaties outlined, under the name Systems Analysis (plural matter), a methodology of analytical modeling hidden under a systemic jargon that was able to, at the time, allude to the fact that before we agreed that this systems analysis only attributed to closed and complicated but not complex systems analysis modeling. But since 1975, we can consider that the systemic and fundamental engineering sciences have begun to emerge from their initial conceptualization and epistemological maturation phase, to enter into a strictly instrumental and methodological phase: it will then be possible to present systems modeling in its originality, without coating it in the finery of analytical modeling in order to improve its respectability.” [LEM 99, p. 7]

It is therefore, unbeknownst to users, very often “through scientific willingness” as the author emphasized [LEM 94, p. 8], “that the use of ‘analysis system’, ‘system approach’, and ‘application of systems theory’” concepts has almost always led them to practice analytical modeling that only had systemic in its name. This is the lack of adaption to these internal epistemic critical exercises that should be familiar to any scientific and technical activity. However, it is not difficult to first ask oneself “what does that do, in what sense, for what, becoming what?” rather than wondering firstly “what is it made from?”.

4.2.2.5. For a functional and non-organic approach

To model a DLE, we have taken the position of only supporting a secondary attention to its structure to focus on rather “what it does”. We will represent each of its actions or complexes of actions by “a black box or the symbolic processor that takes action into account” [LEM 99, p. 46]. We will see in Chapters 5 and 6 that this decision occurs in practice when entering modeling: not with objects but with functions (“functional diagrams” in OMT and “use cases” in UML). It is also possible to verify that this choice is confirmed at the level of the necessary simplifications that we will have to make regarding the data to be processed. The use of multivariate descriptive statistical techniques aiming to intelligently conjoin our factorial axis data and producing representative classes (clusters) of specific populations (which facilitate dendrograms) once again demonstrates the adoption of this conjunctive logic.

4.2.5.1. A common interpretation of the concept of “processes”

In sections 2.4.1 and 2.4.2 in Chapter 2, we mentioned the evolution of successive instructional design and training models (EML) aimed to respectively create scenarios for learning situations and training mechanisms.

“With the evolution of learning theories and the rise of ICT in education, the scenario has become an indispensable tool to guide the work of the teacher and the learner. This tool has a central place in computerized environments.” [HEN 07, p. 16]

Whether they are “educational” or “training” engineering, these models have the common character that they are both “exploratory tools that help developers to define the outlines of an ITS; these languages also allow the various actors to exchange view points within a development team to achieve a viable solution” [NOD 07a, p. 85].

We recognize in Oubahssi and Grandbastien’s canonical model [OUB 07], explained in section 2.4.2 in Chapter 2 (which refers to the ISO 9000 standard), a striking conceptual analogy with the systemic complexity model, based on the concepts of “processes” and “processors”. At the ISO 9000 level, a process is represented by a processor and defined “as a set of correlated or interactive activities that transforms entry elements into output elements” [OUB 07], while in systems complexity modeling, a process can be represented by a system of multiple actions or by a process that can be a tangle of processes that will systematically be represented by the black box. It is also defined “by its exercise and result (an ‘implex’ therefore)” [LEM 99, p. 46].

For Oubahssi and Grandbastien:

“The input elements of a process usually form output elements of one or several other processes. Each process is described, at a first level, by its input and output data (process result). Several processes can occur in the lifecycle of a product. The processes involved in the lifecycle of a product describe the set of related means and activities that transform incoming elements into outgoing elements. These means may include personnel, finance, facilities, equipment, techniques and methods. Figure 4.7 represents a process in a simple way.” [OUB 07]

For Le Moigne:

“It was agreed to designate a processor by Pr, the symbol of the black box by which ‘a process’ is represented (Figure 4.8). Each processor (Pr) can be characterized in each period (t_i) by the values assigned to its ‘inputs’ and ‘outputs’ (inputs and outputs are outlined by vectors, whose components are designated by the modeler referring to his modeling project modeling).” [LEM 99, p. 48]

“The preconceived identification of N processors and input and output couples by which one characterizes them is not given by the problem that the modeler considers” [LEM 99, p. 54]. This will therefore be a part of the projects that we will address in the modeling design process. The latter will be built by successive iterations “between projects and symbolic representations that the modeler has made” [LEM 99, p. 54].

To conclude on this point, we acknowledge that the central process concept, which lies at the heart of systemic complexity modeling, does not come into conflict with that of traditional instructional design (or training); no antinomic character is initially detected.

4.2.5.2. Modeling complexity by object-oriented modeling

Beyond the developed theoretical aspects aimed at showing the interest in applying the complexity theory to the modeling of latest-generation DLEs, we wanted to offer a concrete continuation to this project. We intended to implement the recommended approach by developing models for research. We had to adopt a modeling language, but obviously not just any language: a language in line with the epistemological conceptions of SM, but that was also capable of meeting the challenges that we set.

After some reflection, we turned first to a “technical” modeling and then secondly to a modeling language specific to this technique. It related to “object-oriented” modeling, and especially Rumbaugh²⁶ et al’s OMT (Object Modeling Technique) [RUM 95]. We have chosen this because it follows the main “principles” of the complex systems theory by offering both a functional representation of the system (the system “created”) and a dynamic representation (the system “becomes”), synchronously, without established order (the system “is created and becomes so by doing”).

We will justify this important choice (that of the OMT modeling “technique”) point by point before clarifying the object-oriented modeling language that we have retained. With the choice of modeling language being a direct consequence of the “technique”²⁷ used, it will be easy to justify, as this language was in part developed by the same author as the OMT “technique”, James Rumbaugh.

The first advantage of object-oriented modeling is that it is visual and allows for modeling a DLE not only to analyze it but also to design it. Therefore, it is a sort of an “all-in-one” product. Moreover, object-oriented modeling is also based on an exploratory and participatory approach (that we were absolutely looking for), allowing the modeler to recognize user needs very early by continuously exchanging viewpoints with them (iterative process) using an understandable medium for all (intelligibility character specific to SM).

One of the features of object-oriented modeling, which could be initially seen as a barrier, is that it is often presented as an approach that opposes “functional decomposition modeling”, which can be annoying concerning the basic concept of system modeling which is the action. “SM leaves behind the question, ‘What does that do?’: what are ‘the functions’ and transformations, or ensured operations or operations to be ensured?” [LEM 99, p. 46]. However, looking more closely, it is not the functional aspect that is questioned in the object-oriented approach, but rather artificial decomposition of the overall function of the system in more simple functions to understand or program. In other words, object-oriented modeling does not enter into the project in terms of its functions, but it opposes any hierarchical and artificial segmentation, as indeed does SM with concerning AM. By contrast, object-oriented modeling recommends an entrance into the modeling project, precisely asking, “what is its purpose?” or “what will be its purpose?” (what needs it answers or will have to answer). This is why this approach advocates modeling the needs before anything else, making an inventory of the functions, organizing the needs between functions so as to show their interrelationships.

We also needed to clarify the “object” concept that could be perceived by SM supporters as unsuited to a systemic view of modeling. To illustrate this reluctance, let us cite a passage from Le Moigne [LEM 99, p. 46], who willingly claims to be a provocateur with regards to our argument: “The basic concept of SM is not the object, [...] but the action [..]”. So why choose an object-oriented modeling technique?

On the SM side, Simon, 1969, quoted by Lecas [LEC 06, paragraph 52], insists on the tangible reality of “objects” produced by the engineering sciences: the computer, operating accounts, and forecast budget are objects like others and therefore objects of scientific studies. However, he indicates immediately afterwards that it will benefit from the fact that “these objects are defined as the result of an identifiable project” to reverse the knowledge method: instead of dissecting the computer, the budget to discover the natural laws that govern their behavior, he proposes modeling the cognitive process; the process developed by the project that defines and explains possible and intentional (and no longer necessary and determined) behaviors. This is precisely the sense that Le Moigne gives to the basic concept of SM when he leaves the SM “object” to favor the “action”.

In object-oriented modeling, the “purpose” is anything but a component of the system such as the one representing analytical modeling (AM). It is a concept that assembles (conjunctive approach) actions and information in the same entity (which may be artifactual, natural or man-made) rather than separate them. This approach is very different to a conventional analytical approach in which data structures and behavior are often only weakly related.

Before closing this argument concerning the adaptability terms of object-oriented modeling to SM, notice that the OMT approach follows remarkably well the fundamental principles of the iterative and incremental approach advocated by SM, characterized in particular by Boulding’s seven levels of complexification [BOU 04a]. For example, in OMT modeling, as soon as actions that require “decisions” appear, their treatments are never immediately represented in the model. They will be in the later stages as soon as the decision-making system has been constructed. And to remember these actions (awaiting decisions), they are represented, as suggested by the authors [RUM 95, p. 181], by sporadic traits (see Figure 5.20).

4.2.5.3. Using UML as a modeling language

Heavily based on the paradigm of “object-oriented” modeling, to us, UML (Unified Modeling Language) seemed to perfectly suit the needs expressed so far. Therefore, we quickly adopted it, especially as James Rumbaugh, OMT founder, is also “one of the founding fathers of UML (along with Grady Booch, founder of the Booch language and Ivar Jacobson, founder of the OOSE language)”²⁸. Unified means that UML results in the merging of these previous languages, all “object-oriented”. UML is now a standard adopted by the Object Management Group (OMG).

In detail, it is a graphical modeling language which, from pictograms, allows you to view a functioning system. It is not a method, since each is free to use the diagrams deemed to be good. No other approach is therefore advocated. Each uses the diagram types it desires, in the order it desires; it is sufficient that the diagrams implemented are consistent with each other before eventually moving to a development (to design or simulate). It is indeed possible, in a second instance, to move from the system “representation” (the model) to “executable”. Used just as much by humans as by machines, the graphical representations have sufficient formal qualities to be automatically translated into a skeleton source code (development in Java, Python, C++, etc.). UML officially came about in 1994, while UML version 2.0 dates back to 2005. This was a major release bringing radical innovations and widely extending the UML scope. The last official version according to the OMG (Object Management Group)²⁹ is UML 2.5 (March 2015).

Here is a list of some UML modeling software available on the market³⁰: StarUml, ArgoUml, BoUml, PowerDesigner, etc. On our side, we have used ArgoUml 0.34 for a few brief illustrations in Chapter 5 and StarUml 2.7.0 for a more “formal” representation, especially from the perspective of a simulation of the system described in Chapter 6 (practical component).

UML offers a couple of diagrams (varying in number depending on the versions) grouped into diagram families: “static”, “behavior”, “interaction or dynamic”. We will obviously not review all of these diagrams. It should be noted that entry into modeling is usually done by “use case” diagrams (representing the performing system) rather than static diagrams (representing the existing system), which is once again in full compliance with the recommendations of SM. Concerning complex systems theory, it begins with the identification of the projects or intentions of the modeling system that constitute the model. It is from these projects that SM will propose to initiate the model design process. UML follows this logic; it is only after the “use cases” diagrams, obtained and constructed using data from interviews with users, tracking tools, dashboards and simulations (see section 6.2 in Chapter 6), that other charts will be deployed.

Moreover, UML is a semi-formal description language that has a dual advantage: it can be presented in the form of a set of quickly comprehensible diagrams and has the ability to be transformed (using software) into programming languages (C++, Java, Python, XML, etc.)³¹: we therefore felt that it was well suited to the formalization of our problem. In fact, different domains have created transformation software tools going from UML schematic models to formal applications (most often a computer application) through successive refinements. Therefore, to us it seems that such tools could be used to serve a team of teachers wishing to focus on a set of UML diagrams to formalize learning situations in a DLE, the tool to transform these visual diagrams via an XML formalization in a compliable structure (for example, a simulation or an implementation on a platform). This means of course that the education team has a sufficient command of the UML language, which is not the most difficult to master.

Nodenot, Laforcade and Le Pallec re-establish, for example, mechanisms offered by UML to provide a visual language (CPM³²), useful in distance education:

“To describe the sequencing of activities, detail the resources exchanged between actors during these activities, identify their performance condition based on the values taken by resources or results of previous activities, etc. ‘UML diagrams’ are also used by these languages to express most notably the lifecycle of resources and activities as well as the significant events of the concepts described. [...] The design process begins with use cases diagram production. Each diagram is then refined by other diagrams to use boxes and then by one or more ‘activity charts’ to describe what is happening within an activity defined at the top level. In the case of ‘collaborative activities’, each corridor ‘of the activity diagram’ allows for the determination of specific tasks conducted by an actor as well as the sequencing of these tasks. At each of the abstraction levels, ‘class diagrams’ and ‘state-transitions diagrams’ allow for the characterization/specification of modeling elements highlighted in other diagrams.” [NOD 07b, p. 92].