Polar Semiotics
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Polar Semiotics
Polar semiotics (or Polar semiology) is a concept in the field of semiotics, which is the science of signs. The most basic concept of polar semiotics can be traced in the thought of Roman Jakobson, when he conceptualized binary opposition as a relationship that necessarily implies some other relationship of conjunction and disjunction. A simple example is the binary symmetry between polar qualities that belong to a same category, such as high / low, in coordination with other types of categories, for example the presence or absence of a pitch. With further development, this same idea is represented in the so-called Greimasian square, attributed to Algirdas Julius Greimas, and which is an adaptation of Aristotle’s old logical square, used by classical philosophers such as Descartes and Spinoza, among others, to try to support empirical demonstrations. As Chandler (2017) states: “There is an apparently inbuilt dualism in our attempts to understand our perception and cognition ...
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Semiotics
Semiotics (also called semiotic studies) is the systematic study of sign processes ( semiosis) and meaning making. Semiosis is any activity, conduct, or process that involves signs, where a sign is defined as anything that communicates something, usually called a meaning, to the sign's interpreter. The meaning can be intentional such as a word uttered with a specific meaning, or unintentional, such as a symptom being a sign of a particular medical condition. Signs can also communicate feelings (which are usually not considered meanings) and may communicate internally (through thought itself) or through any of the senses: visual, auditory, tactile, olfactory, or gustatory (taste). Contemporary semiotics is a branch of science that studies meaning-making and various types of knowledge. The semiotic tradition explores the study of signs and symbols as a significant part of communications. Unlike linguistics, semiotics also studies non-linguistic sign systems. Semiotics includes th ...
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Categorization
Categorization is the ability and activity of recognizing shared features or similarities between the elements of the experience of the world (such as Object (philosophy), objects, events, or ideas), organizing and classifying experience by associating them to a more abstract group (that is, a category, class, or type), on the basis of their traits, features, similarities or other criteria that are Universal (metaphysics), universal to the group. Categorization is considered one of the most fundamental cognitive abilities, and as such it is studied particularly by psychology and cognitive linguistics. Categorization is sometimes considered synonymous with classification (cf., Classification (general theory)#Synonyms and near-synonyms, Classification synonyms). Categorization and classification allow humans to organize things, objects, and ideas that exist around them and simplify their understanding of the world. Categorization is something that humans and other organisms ''do ...
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Structuralism
In sociology, anthropology, archaeology, history, philosophy, and linguistics, structuralism is a general theory of culture and methodology that implies that elements of human culture must be understood by way of their relationship to a broader system. It works to uncover the structures that underlie all the things that humans do, think, perceive, and feel. Alternatively, as summarized by philosopher Simon Blackburn, structuralism is: Blackburn, Simon, ed. 2008. "Structuralism." In '' Oxford Dictionary of Philosophy'' (2nd rev. ed.). Oxford: Oxford University Press. . p. 353. e belief that phenomena of human life are not intelligible except through their interrelations. These relations constitute a structure, and behind local variations in the surface phenomena there are constant laws of abstract structure.Structuralism in Europe developed in the early 20th century, mainly in France and the Russian Empire, in the structural linguistics of Ferdinand de Saussure and the subsequ ...
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Code
In communications and information processing, code is a system of rules to convert information—such as a letter, word, sound, image, or gesture—into another form, sometimes shortened or secret, for communication through a communication channel or storage in a storage medium. An early example is an invention of language, which enabled a person, through speech, to communicate what they thought, saw, heard, or felt to others. But speech limits the range of communication to the distance a voice can carry and limits the audience to those present when the speech is uttered. The invention of writing, which converted spoken language into visual symbols, extended the range of communication across space and time. The process of encoding converts information from a source into symbols for communication or storage. Decoding is the reverse process, converting code symbols back into a form that the recipient understands, such as English or/and Spanish. One reason for coding is to ...
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Map (mathematics)
In mathematics, a map or mapping is a function in its general sense. These terms may have originated as from the process of making a geographical map: ''mapping'' the Earth surface to a sheet of paper. The term ''map'' may be used to distinguish some special types of functions, such as homomorphisms. For example, a linear map is a homomorphism of vector spaces, while the term linear function may have this meaning or it may mean a linear polynomial. In category theory, a map may refer to a morphism. The term ''transformation'' can be used interchangeably, but ''transformation'' often refers to a function from a set to itself. There are also a few less common uses in logic and graph theory. Maps as functions In many branches of mathematics, the term ''map'' is used to mean a function, sometimes with a specific property of particular importance to that branch. For instance, a "map" is a " continuous function" in topology, a "linear transformation" in linear algebra, etc. Some ...
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Self-organization
Self-organization, also called spontaneous order in the social sciences, is a process where some form of overall order arises from local interactions between parts of an initially disordered system. The process can be spontaneous when sufficient energy is available, not needing control by any external agent. It is often triggered by seemingly random fluctuations, amplified by positive feedback. The resulting organization is wholly decentralized, distributed over all the components of the system. As such, the organization is typically robust and able to survive or self-repair substantial perturbation. Chaos theory discusses self-organization in terms of islands of predictability in a sea of chaotic unpredictability. Self-organization occurs in many physical, chemical, biological, robotic, and cognitive systems. Examples of self-organization include crystallization, thermal convection of fluids, chemical oscillation, animal swarming, neural circuits, and black markets. ...
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Group Theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field (mathematics), fields, and vector spaces, can all be seen as groups endowed with additional operation (mathematics), operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom, and Standard Model, three of the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also ce ...
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Topological Space
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called points, along with an additional structure called a topology, which can be defined as a set of neighbourhoods for each point that satisfy some axioms formalizing the concept of closeness. There are several equivalent definitions of a topology, the most commonly used of which is the definition through open sets, which is easier than the others to manipulate. A topological space is the most general type of a mathematical space that allows for the definition of limits, continuity, and connectedness. Common types of topological spaces include Euclidean spaces, metric spaces and manifolds. Although very general, the concept of topological spaces is fundamental, and used in virtually every branch of modern mathematics. The study of topological spac ...
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Cohomology
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewed as a method of assigning richer algebraic invariants to a space than homology. Some versions of cohomology arise by dualizing the construction of homology. In other words, cochains are functions on the group of chains in homology theory. From its beginning in topology, this idea became a dominant method in the mathematics of the second half of the twentieth century. From the initial idea of homology as a method of constructing algebraic invariants of topological spaces, the range of applications of homology and cohomology theories has spread throughout geometry and algebra. The terminology tends to hide the fact that cohomology, a contravariant theory, is more natural than homology in many applications. At a basic level, this has to do ...
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Yoneda Lemma
In mathematics, the Yoneda lemma is arguably the most important result in category theory. It is an abstract result on functors of the type ''morphisms into a fixed object''. It is a vast generalisation of Cayley's theorem from group theory (viewing a group as a miniature category with just one object and only isomorphisms). It allows the embedding of any locally small category into a category of functors (contravariant set-valued functors) defined on that category. It also clarifies how the embedded category, of representable functors and their natural transformations, relates to the other objects in the larger functor category. It is an important tool that underlies several modern developments in algebraic geometry and representation theory. It is named after Nobuo Yoneda. Generalities The Yoneda lemma suggests that instead of studying the locally small category \mathcal , one should study the category of all functors of \mathcal into \mathbf (the category of sets with ...
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Artistic Language
An artistic language, or artlang, is a constructed language designed for aesthetic and phonetic pleasure. Language can be artistic to the extent that artists use it as a source of creativity in art, poetry, calligraphy or as a metaphor to address themes as cultural diversity and the vulnerability of the individual in a globalizing world. Unlike engineered languages or auxiliary languages, artistic languages often have irregular grammar systems, much like natural languages. Many are designed within the context of fictional worlds, such as J. R. R. Tolkien's Middle-earth. Others can represent fictional languages in a world not patently different from the real world, or have no particular fictional background attached. Genres Several different genres of constructed languages are classified as 'artistic'. An artistic language may fall into any one of the following groups, depending on the aim of its use. Similarly to philosophical languages, artlangs are created in accordance wit ...
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Natural Language
In neuropsychology, linguistics, and philosophy of language, a natural language or ordinary language is any language that has evolved naturally in humans through use and repetition without conscious planning or premeditation. Natural languages can take different forms, such as speech or signing. They are distinguished from constructed and formal languages such as those used to program computers or to study logic. Defining natural language Natural language can be broadly defined as different from * artificial and constructed languages, e.g. computer programming languages * constructed international auxiliary languages * non-human communication systems in nature such as whale and other marine mammal vocalizations or honey bees' waggle dance. All varieties of world languages are natural languages, including those that are associated with linguistic prescriptivism or language regulation. ( Nonstandard dialects can be viewed as a wild type in comparison with standard l ...
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