2.1.1. Relationship between organization and product: basic principles

In the previous chapter, we saw that nonlinear dynamical systems (NLDS) are subject to complex behaviors. They are “programmable networks” whose functions and interactions are not necessarily linear. We encounter them in all fields: industrial, financial, economic, social, political, etc.

When we have qualitative systems, it is relatively easy to build a mathematical model of the phenomenon or system evolution, to evaluate it and study its behavior. When we have quantitative information, the development of the model is much more difficult; so is the study of the model.

In a manufacturing system dedicated to the assembly and testing of complex technological sets, the problem is what will determine the quality of the product and the performance of the manufacturing process: “will it remain stable? Will productivity be optimal? Does the production system remain under control?” So many questions that a production manager asks himself or herself.

First, it should be noted that in a conventional system, most tasks are often performed directly. These same tasks to be performed are under the control of a human being and several elements must be taken into account to characterize the level and nature of an organization in which human resources are involved, namely:

• – Competences: these are linked to a constituent entity of a system and correspond to a task, function or mission entrusted to it. Competences refer to concepts such as aptitude, talents, skill, knowledge and experience or know-how necessary to ensure the successful completion of this task. These are the competences, available at the level of an entity, that will bring added value to the product or service being transformed. In the context of this study, competency is strongly correlated with the autonomy of this entity.
• – Culture: this refers to all the uses, traditions and customs, shared beliefs and convictions, ways of seeing, doing and knowing how to that ensure an implicit code of behavior and cohesion within a system or organization. As we can see, the cohesion of a system implies that a certain number of entities are linked together in order to form a network. The cohesion of the network is then ensured by links and interactions.
• – Emulation and motivation: the first term refers to a state of mind or willingness to equal or surpass someone or something. Similarly, motivation is a process that triggers, continues or stops a behavior. These two concepts are used to express the activation or inhibition of a link, the reinforcement or not of an action or interaction.

The functioning and behavior of such an organization depends of course on these three elements and their combination. The French mathematician René Thom examined this problem through his theory of “catastrophes”, which allowed him to highlight transition phenomena and discontinuities, of which we will mention only two examples:

• – the distribution of competences and the communication system between groups of operators are fundamental. Some imbalances always end up resulting in an explosion or implosion of behavior, which inevitably has an impact on the result;
• – the interactions that condition the feedback effects are essential. Similarly, the interaction force will be the result of learning sessions, progressive and iterative reinforcement or inhibition of links between entities.

2.1.2. Reminder of the operating rules of an organization

As we have just seen, the effectiveness and efficiency of an organization carries with it the skills, culture and motivation of the system. A good distribution between these skills and good coordination between the different entities is based on a system of links with the four main characteristics.

2.1.3. The challenges of such organizations

In self-organized systems, adaptability and the emergence of new orders are the strong points that allow them to react dynamically to changing demand conditions and needs.

With the advent of the Internet, this reactivity is permanent and responds to a constraint that is becoming more pressing every day and that we have great difficulty integrating into our processes: “faster, faster, etc.”. In this case, how can we find the right balance between the “credibility” of systems (the reliability and quality of systems are always built according to learning curves, well determined and which require time!) and the change in “disaster” mode (in the mathematical sense of the term which implies the notion of discontinuity and revolution by going through successive cycles or phases: disorder-reconfiguration-order)?

One approach is therefore to use the “dynamic stability” model, which is very well known in large companies. We will limit ourselves here to describing some aspects related to our new economic, social and cultural paradigm.

2.1.4. Concepts of sociability and emergence of order

In a didactic context, sociability (this word dates from the 17th Century) refers to the ability of a system to associate and bring together a number of similar entities and make them live agreeably and harmoniously at all times. By extension, sociability expresses the character of a group of living beings that promotes human relationships, particularly intellectual or social relationships [WIL 00]. This founding father of sociobiology explains in his book that most of the behavioral components of living organisms, and of course the conduct of human or social groups such as ants, have a genetic predestination. Thus, the sociability of groups of living beings is statically embedded in genes and becomes an integral part of their nature.

However, sociability can be seen as the manifestation of a dynamic process and the belonging of an entity to a larger group, and therefore to a social body, because there are mutual influences. These profoundly transform their own functioning and behavior. The emerging properties of this living group are of considerable power. Indeed:

• – each entity involved in the life of a group processes a variable amount of information and the amount of information processed in parallel by the whole group is considerable;
• – a living being (or agent) belonging to a social system processes less information by itself than a solitary being or agent. They operate in a limited “neighborhood” and are subject to local constraints and objectives. They work very astutely in their local environment;
• – as part of a whole, a living agent contributes to more complex information processing and works, without wishing to do so a priori, towards the emergence of global behavior. The system then acts as a single organization;
• – in a group of individuals, the communication therefore modifies the activity of each entity in any form whatsoever. It allows the exchange of statuses, needs and orders of actions. This ensures that the needs of the entire system are met more accurately and consistently than if each entity were to attempt to assess the overall demand on its own. However, can aggregate demand be measured at its fair value and assimilated by all agents in the system?
• – in a social body, constituting a single and coherent system, the roles of each individual will become more precise over time and become very specialized but very closely dependent on the whole, which is itself the consequence of collective action;
• – knowledge of the finest operating details and actions at the level of an individual does not allow us to understand and predict the evolution of the system as a whole.

The evolution of a complex system obeys a global objective, and it will therefore be organized to best meet its objectives in a given context and environment. This emergence of order corresponds to an attractor and it can be said, in another way, that the sociability of the system is considered as a sociobiological attractor.

Just as the notion of “interaction” is more important than that of “function” at the level of an agent, the emergence of a stable state or order takes precedence over the notion of predetermined order. In the first case, these are unpredictable events, and in the other case, these are calculable and predictable systems.

Thus, the concept of emergence is a fundamental part of the science of complexity and characterizes complex adaptive systems. This concept of the emergence and progressive and coherent organization of the parts of an interconnected system is based on two different approaches to the evolution of systems, the Platonicians and the Aristotelians:

• – for Aristotle’s followers, the approach is very mechanistic and deterministic. Living organisms, like interconnected systems, are “machines” whose behavior is explained solely by the laws of chemistry, physics and mechanics. In this approach, we will also classify the one advocated by Descartes and by determinists and reductionists. Even though many phenomena related to complex systems could be explained in this way, Aristotelians had to admit that there were fundamental differences between inanimate objects and living organisms: the physical organization of matter makes it possible to give living organism properties that inanimate things do not have;
• – for Plato’s followers, the approach is more open, vitalist and philosophical. Even though the components of the complex system obey the laws of physics, a life force animates the raw material and most of the properties that emerge from these organisms escape scientific analysis. Thus, Niels Bohr stated: “Knowledge of the fundamental characteristics in the functioning of living organisms is not sufficient to fully explain biological phenomena” [MCE 01].

However, in the life sciences, the proponents of each theory are opposed to the constitutive and emergent nature of phenomena related to complex systems. Indeed, thanks to molecular biology, the DNA of living organisms is observed in its smallest detail, genes are also isolated and attractive sites are identified. However, we are not yet able to explain, through the laws we know, how global properties emerge from such complex systems. Similarly, by focusing on the phenomena of organization and self-organization of organisms, we are still unable to explain certain points:

• – Is natural selection the only organizational cause of these complex systems? Does it have a direct impact on the organizational mechanisms of the interconnected system?
• – In the field of living organisms, does the gene have an influence on the intrinsic organization of organisms?
• – Is the configuration of a complex system directly and strongly correlated to the emerging global property and vice versa?

However, even though obscure points remain, everyone agrees that, in the phenomena of self-organization, if complex dynamic systems and living systems allow the emergence of structural patterns or stable forms, this is the result of the same mechanisms. Thus, the evolutionary models that have been developed by scientists are important to explain how orders are developed in Nature and in our industrial systems. Such models are fundamental to understanding the meaning of an organization, how a complex system is expressed and how global orders are organized, or to simulating the impact of a structural configuration on emerging orders and properties. However, they do not in any way allow us to understand and explain the profound meaning of emerging property, the meaning of life for example, but rather to understand and demystify the theory of self-organization.

2.1.5. The genesis and evolution of complex systems

Two possibilities are considered on how order emerges, on the genesis of biological or complex forms and on the theory of order and evolution:

• – Darwinism focuses on the organization of a social body, the architecture of an interconnected system, the structure of a living organism, or even the configuration of a product or process. It stipulates that any system is subject to disturbances, local disorders or random or environmentally oriented mutations (external stimuli). The reaction and adaptation of these new systems will be in a totally unpredictable direction because they are sensitive to the initial conditions (ownership of SIC). Natural selection will do the rest, and only the most appropriate configurations, forms or orders will be retained or survive;
• – according to physicists, all the systems around us are subject to the second principle of thermodynamics, which stipulates that the entropy of systems increases and that they tend towards disorder. This approach does not always correspond to reality since systems with deterministic chaos are alternately subjected to phases of apparent disorder and then to order phases (quantum leaps limited to a few stable states) as the control parameter increases. Thus, in the study of complex systems, some physical theories have the greatest difficulty in being applied.

This shows us that there are several ways to understand and envisage the evolution of a complex system, but that nothing should be neglected. In fact, the notions of self-organization, selection and evolution that we have described above are complementary and conclusive and this is what we do in everyday life:

• – In an industrial system, in a production plant, it is common to organize work meetings every morning to organize the team’s activities; similarly, in meetings to design and develop solutions. At some point, people exchange possibilities for changing the production program, choosing the least bad program and reconfiguring a production system to allocate resources differently, proposing “crazy ideas” about a product to meet a new demand, etc. These creative brainstorming sessions, followed by incubation periods and new brainstorming, etc., will initiate changes and elements of solutions. In short, disorder is created.
• – In a second phase, the modifications and solutions implemented will lead the system to enact a particular behavior: any stimulus applied to it is translated into a specific action or reaction of the system. This will lead to the generation of a form or the convergence of the system towards a new order that we always call an attractor. This source of self-organization is almost universal and has been shown in various works by Ulam and von Neumann [NEU 63], Wolfram [WOL 02] or even in Yingjiu Liu’s thesis [LIU 02]. The system organizes itself autonomously; it is subject to a whole series of actions and interactions that are propagated in the network and, after a certain number of steps, it will gradually stabilize in a stable state.
• – Finally, this situation to which we have converged will lead to a consolidation of the system’s structures, a strengthening of some of its components such as intrinsic functions at the level of agents or interactions. This phase of capitalization or adaptation will include activities such as configuration adjustment, learning, formalization of certain mechanisms, acquisition of know-how, etc. Thus, the second principle of thermodynamics is not enough if it is applied alone. Many complex systems tend towards order and not disorder. When a system is stable, an action can change it, destabilize it and turn it into disorder, but in fact such a system is placed on a new trajectory that converges towards a new order. In industry, this phase is called the structuring or self-organization phase. Thus, everything begins and ends with the organization.

The difficulty is therefore to know how an order is established in a complex structure. Everything depends of course on the behavior of nonlinear dynamic systems. Two theories are then evoked:

• – Catastrophe Theory: as previously mentioned, it was developed by the French mathematician René Thom. In the 1960s, Thom showed how some nonlinear systems could “catastrophically” switch from one state to another. It is actually a jump in the trajectory. However, this very attractive approach is very limited. Indeed, in practice, the mathematical models we had developed were too “reduced” and could never be applied in practice. This is an excellent qualitative approach that allows us to imagine and describe some complex behaviors, but not to predict them. Hence, a limited industrial interest.
• – Deterministic Chaos Theory: this is in fact very closely linked to and consistent with the catastrophe theory; it complements it with much greater success. Indeed, in industry, physics or biology, the description of the behavior of an elementary cell or agent can often depend on very few parameters which lead to models that are fairly close to reality, and in this case, it is possible to have a much more precise technique. This has allowed us to show, in the semiconductor manufacturing lines of the IBM Factory in Corbeil-Essonnes, how and when deterministic chaos could appear. And in the 1980s, we were able to develop innovative production management methods to better control its behavior, particularly in an area of low chaos.

2.1.6. How and where do structures emerge?

Complexity theory has a certain universality in that, in Nature, we are surrounded by complex systems with nonlinear functions and interactions. Such systems have the property of evolving in a divergent way, but in a limited space. For example, the number of states that a chaotic system can achieve may or may not be limited, but the extreme values are in a limited space. Similarly, a fractal structure has a dimension represented by a real number, but this is within certain limits. For example, a quasi-volume has a real dimension between integers 2 and 3.

In all complex systems, there is a powerful intrinsic dynamic. The objective is to migrate a system to the border of chaos to turn it upside down and acquire new properties, which we have also called orders. Indeed, these systems evolve according to an internal dynamic in an unpredictable way (because they cannot be calculated) and converge towards an emerging global structure. These considerations therefore lead us to define the following schema of principle in which two totally different approaches to complex system management are included.

These are in fact two visions of the world and two ways of understanding it:

• – on the left side of the figure, we find the Vitalist point of view, which is representative of the conventional approach to the processing of complex systems. A process is analyzed in a global and exhaustive way. By applying the principle of decomposition, the main, or global, tasks are divided into more elementary tasks and so on. The process is therefore modeled through a sequence of transformation functions. It is a static evolution model; by applying a stimulus, we observe and measure results. When the correct control parameters are adjusted, after a number of iterations or calculations, the real system can then be adjusted. We are in the old conception of a state of equilibrium dominated by the concept of action-reaction and predictability. In this static and top-down approach, we generally take the opportunity to simplify the so-called “complex” system or its process; it then becomes possible to automate it using computers. To solve a problem, many functions must be performed in parallel. The difficulty is only related to the performance of the calculation means, and it will always be possible, with appropriate time and investment, to find the right solution;
• – the right side of the figure represents the point of view of Mechanists and Connectionists. This is a dynamic, interaction-based approach, which we will call a bottom-up approach. Based on the principles just described, it is a question of generating a global function or of creating a structure or configuration based on the interactions existing in the interconnected network. This makes it possible to obtain a complex system (in the sense of behavior) from a great underlying simplicity (in terms of elementary functions and interactions). The implementation of such advanced concepts still raises many related problems nowadays, not to the performance of the calculation means, but to the overall performance of the emerging order (coherent with an overall objective). This requires an analysis of three points:
  • - the exploitation of instabilities and low chaos to achieve optimal flexibility and responsiveness,
  • - the definition of new associated methods for managing complex systems in order to better control them,
  • - the development of new approaches and simulation tools to validate action plans to be applied to complex systems.

In practice, it would be a mistake to apply only one of the approaches described above. These complement each other and highlight a feedback loop that operates accurately and continuously. The above diagram taken as a whole (right and left sides) forms a dynamic structural whole: one the left, being reductionist, the diversity of the system is reduced while defining strategies and tactics (optimal action plans), while one the right, concerning new forms, configurations and orders are generated. The dynamic is therefore intrinsic and comes from the internal evolution of the whole.

2.2.1. Emergence of self-organized patterns

A concrete structure corresponds to a system’s stable state, i.e. a particular organization. Self-organization allows the transition, in an autonomous and reactive way, from one stable structure to another. The stability of a system’s structure depends on how long it remains stable despite disruptions that tend to destabilize it. Self-organization sometimes highlights phenomena of convergence towards particular structures. In this sense, it uses the concepts of attractors and basins of attraction, as defined in the chaos theory. This can be illustrated as follows:

• – a social organization is highly dependent on the nature of the problem being solved; it is contextual. In other words, an organization may be adequate to solve one problem but may be inadequate for another. We consider that a system adapts if, in the face of a situation not foreseen by the designer of the final application, it does not block itself but reacts by being able to modify its functions and structure on its own initiative in order to achieve the desired purpose. In this context, we need systems that are adaptable and have a learning capacity. In other words, the system can change its behavior in response to changes in its environment without drawing lasting consequences. We consider that a multi-agent system learns if it modifies its protocol over time, as well as if each agent in this system can modify its skills, beliefs and social attitudes according to the current moment and past experience. The system that learns to organize itself according to past experience makes it possible to arrive more quickly at the optimum that is the best organization responding to the problem at hand. It belongs here to the class of systems that we will call “reactive”;
• – programmable networks have communication functions between the actual network processing nodes. These networks (often of the Hopfield type) have an evolution that tends to bring them closer to a stable state through successive iterations. This is dynamic relaxation; it depends on an energy function, similar to that of Ising’s spin glasses [WIL 83], decreasing towards a local minimum. It is then said that the system evolves in a basin of attraction and converges towards an attractor whose trajectory depends on the context and its environment. This analogy with statistical physics (genetic algorithm, with its particular case, among others, simulated annealing) makes it possible to recover certain results, and to solve many allocation and optimization problems;
• – in a distributed production system, we are not faced with a scheduling problem, but with a problem involving configuration and reconfiguration of means and resources. The aim is therefore to highlight the self-organizing properties of these networks and to show how they converge towards stable, attractive states or orders in a given phase and state space. Thus, distributed production systems subject to disruptive conditions or moved to neighboring states will converge to the same stable state. This allows classifications to be made, for example, the automatic reconfiguration of a production system (allocation of resources and means) according to a context;
• – the same is true in logistics, with the possibility of organizing a round of distribution in terms of means of transport where the optimization of the route also requires these techniques;
• – in the field of Information Technology, IT systems can be dynamically reorganized to deal with problems that can evolve over time without the intervention of an external operator. Such a system could be adapted to the current context, and therefore to possible disruptions, through learning (supervised, unsupervised, reinforced, etc.).

In conclusion, a system with the capacity for self-organization has several states of equilibrium, i.e. particular organizations. Each particular organization is characterized by a set of different initial conditions that, when verified, converge the system to a corresponding stable organization. Most of the time, the self-organization system is between one or the other of its equilibrium states at the end of a time cycle that can be determined. It moves from one organizational state to another under the disorganizing pressure of its environment. The system that can adapt to changing circumstances by modifying the interaction structures between its components has the potential to achieve some consistency in environments with a high degree of uncertainty or change.

2.2.2. Best stability conditions: homeostasis

In a simple system, i.e. with a reduced number of elements, feedback loops ensure homeostasis. As a reminder, homeostasis is the property of a system to be able to stabilize around a given operating point. For example, a simple temperature sensor or detector, combined with a temperature controller, can act to keep the temperature of an enclosure between two limit values. The actual temperature value is then compared to a predefined threshold value and any excess is used to activate or deactivate the heating or cooling system.

More sophisticated and progressive approaches are also available, such as those used in the human body. The latter wishes to stabilize certain physiological constants at a given value, for example, to keep the temperature of the human body at a stable temperature of 37°C. Temperature sensors (neurons in the hypothalamus) can detect variations in the order of 0.01°C. Any excessive deviation makes it possible to activate compensation mechanisms that are not simply of the “go-no go” type but graduated according to the situation. Excessive body temperature triggers sweating and dilation of capillaries and certain blood vessels. Too low a temperature causes opposite effects, as well as shivering and an acceleration of the metabolism.

Many similar examples exist in chemistry, metabolism, the immune system, etc. where the system is able to regulate itself, i.e. to regulate its own functioning. In social systems, communication techniques between agents, based on game theory, make it possible to define very elaborate strategies whose evolutions and results are impossible to guess. Indeed, several elements specific to a complex system are taken into account:

• – there are many interactions in a given neighborhood;
• – each element modifies not only its own state, but also that of its close neighbors, according to rules with a low visibility horizon;
• – the objectives are local, but they often overlap those of the neighborhood and are in conflict with others;
• – each element tries to improve a number of its own properties and reduce those that are less valuable or less effective in relation to a given criterion.