Related papers: Concept and Definition of Complexity
Psychology has had difficulty accounting for the creative, context-sensitive manner in which concepts are used. We believe this stems from the view of concepts as identifiers rather than bridges between mind and world that participate in…
The concept of an angle is one that often causes difficulties in metrology. These are partly caused by a confusing mixture of several mathematical terms, partly by real mathematical difficulties and finally by imprecise terminology. The…
A definition of Artificial Intelligence was proposed in [1] but this definition was not absolutely formal at least because the word "Human" was used. In this paper we will formalize the definition from [1]. The biggest problem in this…
Aesthetics, among other criteria, can be statistically examined in terms of the complexity required for creating and decrypting a work of art. We propose three laws of aesthetic complexity. According to the first law of aesthetic…
We investigate the concept of symmetry and its role in problem solving. This paper first defines precisely the elements that constitute a "problem" and its "solution," and gives several examples to illustrate these definitions. Given…
In this article we revisit the concept of abstraction as it is used in visualization and put it on a solid formal footing. While the term \emph{abstraction} is utilized in many scientific disciplines, arts, as well as everyday life,…
Recently it has been argued that entropy can be a direct measure of complexity, where the smaller value of entropy indicates lower system complexity, while its larger value indicates higher system complexity. We dispute this view and…
We develop a general formalism for representing and understanding structure in complex systems. In our view, structure is the totality of relationships among a system's components, and these relationships can be quantified using information…
The difference between the terms additivity and extensivity, as well as their respective negations, is critically analyzed and illustrated with a few examples. The concepts of subadditivity, pseudo-additivity, and pseudo-extensivity are…
The quest for a scientific description of consciousness has given rise to new theoretical and empirical paradigms for the investigation of phenomenological contents as well as clinical disorders of consciousness. An outstanding challenge in…
Formal definitions of quantities, quantity spaces, dimensions and dimension groups are introduced. Based on these concepts, a theoretical framework and a practical algorithm for dimensional analysis are developed, and examples of…
The computational complexity of a quantum state quantifies how hard it is to make. `Complexity geometry', first proposed by Nielsen, is an approach to defining computational complexity using the tools of differential geometry. Here we…
Economic complexity reflects the amount of knowledge that is embedded in the productive structure of an economy. It resides on the premise of hidden capabilities - fundamental endowments underlying the productive structure. In general,…
The science of complexity is based on a new way of thinking that stands in sharp contrast to the philosophy underlying Newtonian science, which is based on reductionism, determinism, and objective knowledge. This paper reviews the…
Economic transformation -- change in what an economy produces -- is foundational to development and rising standards of living. Our understanding of this process has been propelled recently by two branches of work in the field of economic…
Persistence is an important characteristic of many complex systems in nature, related to how long the system remains at a certain state before changing to a different one. The study of complex systems' persistence involves different…
This chapter reviews the purpose and use of models from the field of complex systems and, in particular, the implications of trying to use models to understand or make decisions within complex situations, such as policy makers usually face.…
The human mind is known to be sensitive to complexity. For instance, the visual system reconstructs hidden parts of objects following a principle of maximum simplicity. We suggest here that higher cognitive processes, such as the selection…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
The notion of stiffness, which originated in several applications of a different nature, has dominated the activities related to the numerical treatment of differential problems for the last fifty years. Contrary to what usually happens in…