Intuitively, a system is complex when it is composed of multiple branches (although something with these characteristics is not necessarily complex and complicated, since when broken down into parts it can be relatively easy to understand). Two criteria allow us to characterize this notion in a finer and more concrete way: the number of parts, and the independence of the parts.

In the case of living beings, complexity emerges in stages. Two major principles seem to intervene repetitively in this process: the "juxtaposition" of similar or identical entities, and then the "integration" of them into more complex entities, where they constitute their parts. Georges Chapouthier") proposed the term "living mosaic" for these composite sets. In art, a mosaic is a set that integrates small elements, the "tiles", which, despite retaining their individual characteristics of shape and color, when integrated into the whole, take on another meaning. In a "living mosaic", the "whole" is made up of layers or divisions (cell, organism, community...) in which a certain autonomy of functioning is left to those parts. A similar conception in "mosaic" was proposed by the linguist Stéphane Robert&action=edit&redlink=1 "Stéphane Robert (linguist) (not yet written)") regarding the complexity of language.

The phenomenon of education in the context of information societies as proposed by UNESCO in 2005.[16] Towards knowledge societies, it is a complex phenomenon because not only pedagogical and technological factors intervene but also social, political, economic and cultural factors. Therefore, in order to understand this phenomenon, it is necessary to approach it from complexity as proposed by Morin[11]​ in The 7 Necessary Knowledge for the Education of the Future.[8]​ However, there are other currents of study on complexity and education that are based on experimental projects on cognition and learning (Jacobson and Wilensky).[17]​ and emerging pedagogies[18]​ that have been applied from basic to higher education, with the purpose of proposing a new epistemology as pointed out by Luis Fernando Quiroga.[19]​.

From this perspective, we must point out the works of Landis, Anastasio and Slivka,[20]​ which point out that the first works on complexity and education date back to the 1960s as entities with their own structures and dynamics; later Ackoff[21]​ refers to the conditions in which educational entities adapt. Mason[22]​ determines the importance of emergent properties in education; Lemke and Sabelli[23]​ have worked on topics on hierarchical multi-scale organization, emergent patterns, agent-based modeling, dynamic attractors and repulsors, information flows and constraints, system-environment interaction, development trajectories, interaction across time scales; Davies and Sumara[24]​ talk about students as complex units, while authors such as Brusilovsky and Peylo,[25]​ and Bozhilov, Stefanov and Stoyanov[26]​ developed work on adaptive learning and the student.

Un sistema complejo es un sistema compuesto de partes interrelacionadas que como un conjunto exhiben propiedades y comportamientos no evidentes a partir de la suma de las partes individuales. Las características de los sistemas complejos (como la interdependencia, la diversidad y la adaptabilidad de los agentes, etc.), desafían los supuestos básicos de las teorías tradicionales.[4]​.

The number and independence of the parties

A complex system is made up of a large number of parts. Taking this definition strictly, in reality all material systems would be complex, except possibly subatomic particles, atoms, ions, and molecules. But a system can have a large number of parts without presenting very complicated or far-fetched characteristics, if it is the case, for example, that the movement is studied, and it is found that all its parts move in unison, that is, in solidarity. The independence of the parties precisely excludes the aforementioned case, although the corresponding concept is difficult to define precisely.

To the extent that we consider a solid as a perfectly rigid body, its parts are obviously not independent of each other, and with only some figures, with only some state variables, we can completely characterize the state of motion "Motion (physics)") of the solid: position of the center of inertia, speed of translation, speed of rotation"), etc., and with this information, the movement of each of the particles of the solid is perfectly determined. On the contrary, if it is considered that the body is not completely rigid, it could be studied the vibrations, and by the way, the resulting movements of the particles would then be much more complicated. Something similar could be stated about a fluid, although obviously here a distinction should be made between the stationary movement of the fluid and the turbulent movement.

To describe the movements of a body with parts independent of each other, naturally many more state variables are required, in theory an infinite number. And in this context, stating that its parts are independent does not imply that they do not interact with each other, but only that knowledge of the state of one of its parts provides very little or no information regarding the state of the other parts.

As can be seen, to a large extent there is subjectivity and ambiguity in the appreciation of this concept of independence, and from there arise the great difficulties encountered in defining this concept in good terms. A poorly known system may seem very complex, since in that framework it is revealed to be inexplicable, although it could seem very simple if only superficial observations and descriptions are taken into account.

Some guidelines for studying complexity

In a first approximation, it can be said that complex systems are actually all systems, since complexity is the rule and simplicity the exception.

To apprehend or capture complexity in all its richness, it is necessary to bring into play different domains of knowledge and different approaches. Accounting for the complexity of the world obviously seems like a valid goal for researchers. And Edgar Morin, sociologist and philosopher, proposed an interesting approach to complexity in a conference he gave in France in 1993 ("Introduction à la complexité"[27]​).

As soon as the topic of complexity is analyzed, one can notice the capacity of this issue to put everything up for discussion and put everything into doubt. Complexity is notoriously the result of the intermingled effects of many parameters, which influence and enhance each other. Notwithstanding this, many of our approaches consist of simplifications that isolate effects, without putting them in relation to each other, which notoriously slows down and complicates the process of understanding the system studied as a whole. There is a reason why general systems theory is sometimes called systemic.

Redundancy should not be interpreted as a repetition under identical conditions, but rather the deployment of a multitude of different versions with the same scheme or motif (in English pattern).

Consequently, it is possible to model complexity in terms of functional redundancy, similar, for example, to what happens in a Chinese restaurant, where various functions are carried out in the same place in the structure, or in terms of structural redundancy, similar, for example, to what happens in a factory where the same function is carried out in several different places in a structure.

1 - Structural redundancy designates different structures to perform the same function, such as the double braking circuit of a car, or, for example, several different workshops where the same type of part or the same type of device is manufactured. Structural redundancy characterizes "complication." Structural redundancy is illustrated with the double braking circuit for greater driving safety in modern automobiles, as well as with the multiplicity of electrical, hydraulic, or pneumatic command circuits, installed in war vehicles, so that they function in extreme conditions after having suffered damage during combat.

2 - Functional redundancy is that which corresponds to a multiplicity of different functions executed at the same point in a structure, such as a craftsman's workshop, where different operations on different materials are regularly carried out. Functional redundancy characterizes “complexity” as well as Henry Atlan's condition of self-organization. It is neuropsychiatrist William Ross Ashby's concept of "variety" transferred to cybernetics.

Complex thinking is a notion used in philosophy and epistemology by authors such as Anthony Wilden") or Edgar Morin,[28] and is also applied in physics and biology (Henry Atlan"),[29] as well as in sociology, computer science, and other disciplines. The definition varies significantly depending on the area of ​​knowledge considered.[30]​.

However, the use of complex thinking in all these disciplines is the recognition that reality is complex: it cannot be contemplated from disjunctive, reductionist, simplifying and predominantly uncritical thinking. A holistic and integrated vision is required that glimpses the different perspectives of an object or situation. From a psychological perspective, this type of thinking is conceptualized as “that capable of critically delving into the essence of phenomena, playing with uncertainty and conceiving organization”[31]​.

For his part, Edgar Morin sees the world as an inseparable whole, and proposes a multidisciplinary and multi-referenced approach, so that the construction of thought can be achieved, opposing causality to face phenomena as an organic totality. Morin mentions a paradoxical situation: an incredible amount of knowledge has been acquired about the world, the universe, and the human being, obtained primarily with the scientific method: in the name of reason it was believed that myths and darkness were buried. And yet error, ignorance, blindness progress everywhere at the same time as knowledge (Morin, 2003).

Complex thinking allows us to contemplate different representations of a system, at the same time, (called metarepresentation by Heylighten [1990]), in order to have a more complete understanding of it.

In this situation, uncertainty arises about what is known. That is, if existing knowledge is restructured, we are capable of generating it, abandoning it and recovering it. In this regard, the vision of complex thinking is opposed to the paradigm of simplicity, to the fragmentation of knowledge, since.

The above triggers subjectivity and imbalance to become present, which implies that teachers must work with their students in the development of complex thinking, which allows them to contemplate reality epistemologically and holistically, being not only a passive observer, but also a participant and builder of it.[33]​[34]​.

Literature

-(2003), cited in Arancibia, Miriam Dolly, Pensamiento complex, in Fernández Labastida, Francisco – Mercado, Juan Andrés (editors), Philosophica: Online philosophical encyclopedia, URL: http://www.philosophica.info/archivo/2010/voces/pensamiento_complejo/Pensamiento_Complejo.html. Accessed April 27, 2013.

the Foundations of Physical and Cognitive Science, (Communication and Cognition, Gent), p. 200.

Intuitively, a system is complex when it is composed of multiple branches (although something with these characteristics is not necessarily complex and complicated, since when broken down into parts it can be relatively easy to understand). Two criteria allow us to characterize this notion in a finer and more concrete way: the number of parts, and the independence of the parts.

In the case of living beings, complexity emerges in stages. Two major principles seem to intervene repetitively in this process: the "juxtaposition" of similar or identical entities, and then the "integration" of them into more complex entities, where they constitute their parts. Georges Chapouthier") proposed the term "living mosaic" for these composite sets. In art, a mosaic is a set that integrates small elements, the "tiles", which, despite retaining their individual characteristics of shape and color, when integrated into the whole, take on another meaning. In a "living mosaic", the "whole" is made up of layers or divisions (cell, organism, community...) in which a certain autonomy of functioning is left to those parts. A similar conception in "mosaic" was proposed by the linguist Stéphane Robert&action=edit&redlink=1 "Stéphane Robert (linguist) (not yet written)") regarding the complexity of language.

The phenomenon of education in the context of information societies as proposed by UNESCO in 2005.[16] Towards knowledge societies, it is a complex phenomenon because not only pedagogical and technological factors intervene but also social, political, economic and cultural factors. Therefore, in order to understand this phenomenon, it is necessary to approach it from complexity as proposed by Morin[11]​ in The 7 Necessary Knowledge for the Education of the Future.[8]​ However, there are other currents of study on complexity and education that are based on experimental projects on cognition and learning (Jacobson and Wilensky).[17]​ and emerging pedagogies[18]​ that have been applied from basic to higher education, with the purpose of proposing a new epistemology as pointed out by Luis Fernando Quiroga.[19]​.

From this perspective, we must point out the works of Landis, Anastasio and Slivka,[20]​ which point out that the first works on complexity and education date back to the 1960s as entities with their own structures and dynamics; later Ackoff[21]​ refers to the conditions in which educational entities adapt. Mason[22]​ determines the importance of emergent properties in education; Lemke and Sabelli[23]​ have worked on topics on hierarchical multi-scale organization, emergent patterns, agent-based modeling, dynamic attractors and repulsors, information flows and constraints, system-environment interaction, development trajectories, interaction across time scales; Davies and Sumara[24]​ talk about students as complex units, while authors such as Brusilovsky and Peylo,[25]​ and Bozhilov, Stefanov and Stoyanov[26]​ developed work on adaptive learning and the student.

Un sistema complejo es un sistema compuesto de partes interrelacionadas que como un conjunto exhiben propiedades y comportamientos no evidentes a partir de la suma de las partes individuales. Las características de los sistemas complejos (como la interdependencia, la diversidad y la adaptabilidad de los agentes, etc.), desafían los supuestos básicos de las teorías tradicionales.[4]​.

The number and independence of the parties

A complex system is made up of a large number of parts. Taking this definition strictly, in reality all material systems would be complex, except possibly subatomic particles, atoms, ions, and molecules. But a system can have a large number of parts without presenting very complicated or far-fetched characteristics, if it is the case, for example, that the movement is studied, and it is found that all its parts move in unison, that is, in solidarity. The independence of the parties precisely excludes the aforementioned case, although the corresponding concept is difficult to define precisely.

To the extent that we consider a solid as a perfectly rigid body, its parts are obviously not independent of each other, and with only some figures, with only some state variables, we can completely characterize the state of motion "Motion (physics)") of the solid: position of the center of inertia, speed of translation, speed of rotation"), etc., and with this information, the movement of each of the particles of the solid is perfectly determined. On the contrary, if it is considered that the body is not completely rigid, it could be studied the vibrations, and by the way, the resulting movements of the particles would then be much more complicated. Something similar could be stated about a fluid, although obviously here a distinction should be made between the stationary movement of the fluid and the turbulent movement.

To describe the movements of a body with parts independent of each other, naturally many more state variables are required, in theory an infinite number. And in this context, stating that its parts are independent does not imply that they do not interact with each other, but only that knowledge of the state of one of its parts provides very little or no information regarding the state of the other parts.

As can be seen, to a large extent there is subjectivity and ambiguity in the appreciation of this concept of independence, and from there arise the great difficulties encountered in defining this concept in good terms. A poorly known system may seem very complex, since in that framework it is revealed to be inexplicable, although it could seem very simple if only superficial observations and descriptions are taken into account.

Some guidelines for studying complexity

In a first approximation, it can be said that complex systems are actually all systems, since complexity is the rule and simplicity the exception.

To apprehend or capture complexity in all its richness, it is necessary to bring into play different domains of knowledge and different approaches. Accounting for the complexity of the world obviously seems like a valid goal for researchers. And Edgar Morin, sociologist and philosopher, proposed an interesting approach to complexity in a conference he gave in France in 1993 ("Introduction à la complexité"[27]​).

As soon as the topic of complexity is analyzed, one can notice the capacity of this issue to put everything up for discussion and put everything into doubt. Complexity is notoriously the result of the intermingled effects of many parameters, which influence and enhance each other. Notwithstanding this, many of our approaches consist of simplifications that isolate effects, without putting them in relation to each other, which notoriously slows down and complicates the process of understanding the system studied as a whole. There is a reason why general systems theory is sometimes called systemic.

Redundancy should not be interpreted as a repetition under identical conditions, but rather the deployment of a multitude of different versions with the same scheme or motif (in English pattern).

Consequently, it is possible to model complexity in terms of functional redundancy, similar, for example, to what happens in a Chinese restaurant, where various functions are carried out in the same place in the structure, or in terms of structural redundancy, similar, for example, to what happens in a factory where the same function is carried out in several different places in a structure.

1 - Structural redundancy designates different structures to perform the same function, such as the double braking circuit of a car, or, for example, several different workshops where the same type of part or the same type of device is manufactured. Structural redundancy characterizes "complication." Structural redundancy is illustrated with the double braking circuit for greater driving safety in modern automobiles, as well as with the multiplicity of electrical, hydraulic, or pneumatic command circuits, installed in war vehicles, so that they function in extreme conditions after having suffered damage during combat.

2 - Functional redundancy is that which corresponds to a multiplicity of different functions executed at the same point in a structure, such as a craftsman's workshop, where different operations on different materials are regularly carried out. Functional redundancy characterizes “complexity” as well as Henry Atlan's condition of self-organization. It is neuropsychiatrist William Ross Ashby's concept of "variety" transferred to cybernetics.

Complex thinking is a notion used in philosophy and epistemology by authors such as Anthony Wilden") or Edgar Morin,[28] and is also applied in physics and biology (Henry Atlan"),[29] as well as in sociology, computer science, and other disciplines. The definition varies significantly depending on the area of ​​knowledge considered.[30]​.

However, the use of complex thinking in all these disciplines is the recognition that reality is complex: it cannot be contemplated from disjunctive, reductionist, simplifying and predominantly uncritical thinking. A holistic and integrated vision is required that glimpses the different perspectives of an object or situation. From a psychological perspective, this type of thinking is conceptualized as “that capable of critically delving into the essence of phenomena, playing with uncertainty and conceiving organization”[31]​.

For his part, Edgar Morin sees the world as an inseparable whole, and proposes a multidisciplinary and multi-referenced approach, so that the construction of thought can be achieved, opposing causality to face phenomena as an organic totality. Morin mentions a paradoxical situation: an incredible amount of knowledge has been acquired about the world, the universe, and the human being, obtained primarily with the scientific method: in the name of reason it was believed that myths and darkness were buried. And yet error, ignorance, blindness progress everywhere at the same time as knowledge (Morin, 2003).

Complex thinking allows us to contemplate different representations of a system, at the same time, (called metarepresentation by Heylighten [1990]), in order to have a more complete understanding of it.

In this situation, uncertainty arises about what is known. That is, if existing knowledge is restructured, we are capable of generating it, abandoning it and recovering it. In this regard, the vision of complex thinking is opposed to the paradigm of simplicity, to the fragmentation of knowledge, since.

The above triggers subjectivity and imbalance to become present, which implies that teachers must work with their students in the development of complex thinking, which allows them to contemplate reality epistemologically and holistically, being not only a passive observer, but also a participant and builder of it.[33]​[34]​.

Literature

-(2003), cited in Arancibia, Miriam Dolly, Pensamiento complex, in Fernández Labastida, Francisco – Mercado, Juan Andrés (editors), Philosophica: Online philosophical encyclopedia, URL: http://www.philosophica.info/archivo/2010/voces/pensamiento_complejo/Pensamiento_Complejo.html. Accessed April 27, 2013.

the Foundations of Physical and Cognitive Science, (Communication and Cognition, Gent), p. 200.