Purpose: Complexity is the real beast that baffles everybody. Though there are increasing inter-disciplinary discussions on it, yet it is scantly explored. The purpose of this paper is to bring a new and unique dimension to the discourse assimilating the important ideas of two towering scientists of their time, Newton and Heinz von Foerster. In the tradition of Foersterian second-order cybernetics the paper attempts to build a bridge from a cause-effect thinking to a thinking oriented towards “understanding understanding” and in the process presents a model of “Cybernetics of Simplification” indicating a path to simplicity from complexity. Design/methodology/approach – The design of research in the paper is exploratory and the paper takes a multidisciplinary approach. The model presented in the paper builds on analytics and systemics at the same time. Findings: Simplicity can be seen in complex systems or situations if one can construct the reality (be that the current one that is being experienced or perceived or the future one that is being desired or envisaged) through the Cybernetics of Simplification model, establishing the effect-cause-and-effect and simultaneously following the frame of iterate and infer as a circular feedback loop; in the tradition of cybernetics of cybernetics. Research limitations/implications – It is yet to be applied. Practical implications: The model in the paper seems to have far reaching implications for complex problem solving and enhancing understanding of complex situations and systems. Social implications – The paper has potential to provoke new ideas and new thinking among scholars of complexity. Originality/value – The paper presents an original idea in terms of Cybernetics of Simplification building on the cybernetics of the self-observing system. The value lies in the unique perspective that it brings to the cybernetics discussions on complexity and simplification.

Key words: causality, complexity, second-order cybernetics, cybernetics of simplification, self-observing system, simplification

The contemporary use of the term ‘complexity’ frequently indicates that it is considered a unified concept. This may lead to a neglect of the range of different theories that deal with the implications related to the notion of complexity. This paper, integrating both the English and the Latin traditions of research associated with this notion, suggests a more nuanced use of the term, thereby avoiding simplification of the concept to some of its dominant expressions only. The paper further explores the etymology of ‘complexity’ and offers a chronological presentation of three generations of theories that have shaped its uses; the epistemic and socio-cultural roots of these theories are also introduced. From an epistemological point of view, this reflection sheds light on the competing interpretations underlying the definition of what is considered as complex. Also, from an anthropological perspective it considers both the emancipatory as well as the alienating dimensions of complexity. Based on the highlighted ambiguities, the paper suggests in conclusion that contributions grounded in contemporary theories related to complexity, as well as critical appraisals of their epistemological and ethical legitimacy, need to follow the recursive feedback loops and dynamics that they constitute. In doing so, researchers and practitioners in education should consider their own practice as a learning process that does not require the reduction of the antagonisms and the complementarities that shape its own complexity.

“Enactive knowledge” is distributed across all the interactions between an organism and its environment. When a human subject interacts with a computerized virtual environment, his motor acts determine sensory feedback from the machine, giving rise to sensory-motor dynamics. The traces of these interactions, which are readily retrieved from the computer, complete information concerning the user’s activities. The analysis of traces makes it possible to describe the sensory-motor dynamics, and to characterize the variety of strategies employed by the users.

Purpose: Attention is drawn to a principle of “significance feedback” in neural nets that was devised in the encouraging ambience of the Biological Computer Laboratory and is arguably fundamental to much of the subsequent practical application of artificial neural nets. Design/methodology/approach – The background against which the innovation was made is reviewed, as well as subsequent developments. It is emphasised that Heinz von Foerster and BCL made important contributions prior to their focus on second-order cybernetics. Findings: The version of “significance feedback” denoted by “backpropagation of error” has found numerous applications, but in a restricted field, and the relevance to biology is uncertain. Practical implications: Ways in which the principle might be extended are discussed, including attention to structural changes in networks, and extension of the field of application to include conceptual processing. Originality/value – The original work was 40 years ago, but indications are given of questions that are still unanswered and avenues yet to be explored, some of them indicated by reference to intelligence as “fractal.”

Key words: cybernetics, neural nets, learning.

Minimalism is a useful element in the constructivist arsenal against objectivism. By reducing actions and sensory feedback to a bare minimum, it becomes possible to obtain a complete description of the sensory-motor dynamics; and this in turn reveals that the object of perception does not pre-exist in itself, but is actually constituted during the process of observation. In this paper, this minimalist approach is deployed for the case of the recognition of “the Other.” It is shown that the perception of another intentional subject is based on properties that are intrinsic to the joint perceptual activity itself.

Key words: sensory-motor, dynamics, perception, minimalism

Constructivism is an important theory of learning that is used to guide the development of new teaching methods, particularly in science education. However, because it is a theory of learning and not of teaching, constructivism is often either misused or misunderstood. Here we describe the four essential features of constructivism: eliciting prior knowledge, creating cognitive dissonance, application of new knowledge with feedback, and reflection on learning. We then use the criteria we developed to evaluate five representative published articles that claim to describe and test constructivist teaching methods. Of these five articles, we demonstrate that three do not adhere to the constructivist criteria, whereas two provide strong examples of how constructivism can be employed as a teaching method. We suggest that application of the four essential criteria will be a useful tool for all professional educators who plan to implement or evaluate constructivist teaching methods.

Constructivism is an important theory of learning that is used to guide the development of new teaching methods, particularly in science education. However, because it is a theory of learning and not of teaching, constructivism is often either misused or misunderstood. Here we describe the four essential features of constructivism: eliciting prior knowledge, creating cognitive dissonance, application of new knowledge with feedback, and reflection on learning. We then use the criteria we developed to evaluate five representative published articles that claim to describe and test constructivist teaching methods. Of these five articles, we demonstrate that three do not adhere to the constructivist criteria, whereas two provide strong examples of how constructivism can be employed as a teaching method. We suggest that application of the four essential criteria will be a useful tool for all professional educators who plan to implement or evaluate constructivist teaching methods.

Within the context of mathematics education, the current view of evaluation is open to criticism first, in terms of the rather behavioristic classification of the learning outcomes it identifies, and second, with regards to the prevalent mode of obtaining information, the written test. A constructivist approach affects our perspective of both the learner’s and the teacher’s role in a didactical situation, and also that of the subject matter’. In such s perspective, the need for formative evaluation becomes crucial since in order to follow the student’s thinking, the teacher requires feedback from him. To this effect, we have developed a new tool, the mini-interview. This paper describes an experiment investigating the problems involved in training teachers in the use of this tool for formative purposes.

When confronted with issues dealing with first and second order cybernetics, it seems that the manner of defining the former has been somewhat caricatured. The second appears to sometimes give rise to conclusions which are almost opposite to those of Wiener by questioning the possibility of a control for a system. We find in Wiener’s research a prefiguration of the autonomy concept, which, in our opinion, could bring an explanation – and a solution – in cases where control elicits some perverse effect; an acceptance of positive feedback if it serves a desired purpose; the central importance held for him by ergodic theory that we use in an addendum on imbalanced strange attractors control; the idea of a knowledge which may be the fruit of the control; an interest for logical paradoxes he put in relation to communication in nervous system; and already the notion of dialogue in the core of the relation man/man or man/machine. Of course, Wiener did not accord an equal development to all his insights, but we have not yet finished scrutinizing his writings. First and second order cybernetics perhaps form an agonistic/antagonistic couple of which neither element could overshadow the other.

Key words: communications, control, cybernetics, systems theory

Biological regulation is what allows an organism to handle the effects of a perturbation, modulating its own constitutive dynamics in response to particular changes in internal and external conditions. With the central focus of analysis on the case of minimal living systems, we argue that regulation consists in a specific form of second-order control, exerted over the core (constitutive) regime of production and maintenance of the components that actually put together the organism. The main argument is that regulation requires a distinctive architecture of functional relationships, and specifically the action of a dedicated subsystem whose activity is dynamically decoupled from that of the constitutive regime. We distinguish between two major ways in which control mechanisms contribute to the maintenance of a biological organisation in response to internal and external perturbations: dynamic stability and regulation. Based on this distinction an explicit definition and a set of organisational requirements for regulation are provided, and thoroughly illustrated through the examples of bacterial chemotaxis and the lac-operon. The analysis enables us to mark out the differences between regulation and closely related concepts such as feedback, robustness and homeostasis.