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Abstract Structure
An abstract structure is an abstraction that might be of the Euclidean space, geometric spaces or a set structure, or a hypostatic abstraction that is defined by a set of mathematical theorems and laws, properties and relationships in a way that is logically if not always historically independent However historical dependencies are partially considered in event theory as part of the combinatorics theory in Kolmogorov complexity and Wiener–Khinchin theorem, Kolmogorov-Khinchin equations of the structure of contingent experiences, for example, those involving physical objects. Abstract structures are studied not only in logic and mathematics but in the fields that apply them, as computer science and computer graphics, and in the studies that reflect on them, such as philosophy (especially the philosophy of mathematics). Indeed, modern mathematics has been defined in a very general sense as the study of abstract structures (by the Nicolas Bourbaki, Bourbaki group: see discussion there ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Space
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's Elements, Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension (mathematics), dimension, including the three-dimensional space and the ''Euclidean plane'' (dimension two). The qualifier "Euclidean" is used to distinguish Euclidean spaces from other spaces that were later considered in physics and modern mathematics. Ancient History of geometry#Greek geometry, Greek geometers introduced Euclidean space for modeling the physical space. Their work was collected by the Greek mathematics, ancient Greek mathematician Euclid in his ''Elements'', with the great innovation of ''mathematical proof, proving'' all properties of the space as theorems, by starting from a few fundamental properties, called ''postulates'', which either were considered as eviden ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Democracy
Democracy (From grc, δημοκρατία, dēmokratía, ''dēmos'' 'people' and ''kratos'' 'rule') is a form of government in which the people have the authority to deliberate and decide legislation (" direct democracy"), or to choose governing officials to do so ("representative democracy"). Who is considered part of "the people" and how authority is shared among or delegated by the people has changed over time and at different rates in different countries. Features of democracy often include freedom of assembly, association, property rights, freedom of religion and speech, inclusiveness and equality, citizenship, consent of the governed, voting rights, freedom from unwarranted governmental deprivation of the right to life and liberty, and minority rights. The notion of democracy has evolved over time considerably. Throughout history, one can find evidence of direct democracy, in which communities make decisions through popular assembly. Today, the dominant form of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstraction (mathematics)
Abstraction in mathematics is the process of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena. Two of the most highly abstract areas of modern mathematics are category theory and model theory. Description Many areas of mathematics began with the study of real world problems, before the underlying rules and concepts were identified and defined as abstract structures. For example, geometry has its origins in the calculation of distances and areas in the real world, and algebra started with methods of solving problems in arithmetic. Abstraction is an ongoing process in mathematics and the historical development of many mathematical topics exhibits a progression from the concrete to the abstract. For example, the first steps in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstraction
Abstraction in its main sense is a conceptual process wherein general rules and concepts are derived from the usage and classification of specific examples, literal ("real" or "concrete") signifiers, first principles, or other methods. "An abstraction" is the outcome of this process—a concept that acts as a common noun for all subordinate concepts and connects any related concepts as a ''group'', ''field'', or ''category''. Suzanne K. Langer (1953), ''Feeling and Form: a theory of art developed from Philosophy in a New Key'' p. 90: " Sculptural form is a powerful abstraction from actual objects and the three-dimensional space which we construe ... through touch and sight." Conceptual abstractions may be formed by filtering the information content of a concept or an observable phenomenon, selecting only those aspects which are relevant for a particular purpose. For example, abstracting a leather soccer ball to the more general idea of a ball selects only the information on gen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstraction (computer Science)
In software engineering and computer science, abstraction is: * The process of removing or generalizing physical, spatial, or temporal details or attributes in the study of objects or systems to focus attention on details of greater importance; it is similar in nature to the process of generalization; * the creation of abstract concept-objects by mirroring common features or attributes of various non-abstract objects or systems of study – the result of the process of abstraction. Abstraction, in general, is a fundamental concept in computer science and software development. The process of abstraction can also be referred to as modeling and is closely related to the concepts of ''theory'' and ''design''. Models can also be considered types of abstractions per their generalization of aspects of reality. Abstraction in computer science is closely related to abstraction in mathematics due to their common focus on building abstractions as objects, but is also related to other n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Language
In logic, mathematics, computer science, and linguistics, a formal language consists of words whose letters are taken from an alphabet and are well-formed according to a specific set of rules. The alphabet of a formal language consists of symbols, letters, or tokens that concatenate into strings of the language. Each string concatenated from symbols of this alphabet is called a word, and the words that belong to a particular formal language are sometimes called ''well-formed words'' or ''well-formed formulas''. A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar, which consists of its formation rules. In computer science, formal languages are used among others as the basis for defining the grammar of programming languages and formalized versions of subsets of natural languages in which the words of the language represent concepts that are associated with particular meanings or semantics. In computational complexity ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Earth
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surface is made up of the ocean, dwarfing Earth's polar ice, lakes, and rivers. The remaining 29% of Earth's surface is land, consisting of continents and islands. Earth's surface layer is formed of several slowly moving tectonic plates, which interact to produce mountain ranges, volcanoes, and earthquakes. Earth's liquid outer core generates the magnetic field that shapes the magnetosphere of the Earth, deflecting destructive solar winds. The atmosphere of the Earth consists mostly of nitrogen and oxygen. Greenhouse gases in the atmosphere like carbon dioxide (CO2) trap a part of the energy from the Sun close to the surface. Water vapor is widely present in the atmosphere and forms clouds that cover most of the planet. More solar e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continental Drift
Continental drift is the hypothesis that the Earth's continents have moved over geologic time relative to each other, thus appearing to have "drifted" across the ocean bed. The idea of continental drift has been subsumed into the science of plate tectonics, which studies the movement of the continents as they ride on plates of the Earth's lithosphere. The speculation that continents might have 'drifted' was first put forward by Abraham Ortelius in 1596. A pioneer of the modern view of mobilism was the Austrian geologist Otto Ampferer.Helmut W. Flügel: Die virtuelle Welt des Otto Ampferer und die Realität seiner Zeit'. In: Geo. Alp., Vol. 1, 2004. The concept was independently and more fully developed by Alfred Wegener in 1912, but the hypothesis was rejected by many for lack of any motive mechanism. The English geologist Arthur Holmes later proposed mantle convection for that mechanism. History Early history Abraham Ortelius , Theodor Christoph Lilienthal (1756), A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry: the ''Euclid's Elements, Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier,. Euclid was the first to organize these propositions into a logic, logical system in which each result is ''mathematical proof, proved'' from axioms and previously proved theorems. The ''Elements'' begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the ''Elements'' states results of what are now called algebra and number theory, explained in geometrical language. For more than two thousand years, the adjective " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orchestration
Orchestration is the study or practice of writing music for an orchestra (or, more loosely, for any musical ensemble, such as a concert band) or of adapting music composed for another medium for an orchestra. Also called "instrumentation", orchestration is the assignment of different instruments to play the different parts (e.g., melody, bassline, etc.) of a musical work. For example, a work for solo piano could be adapted and orchestrated so that an orchestra could perform the piece, or a concert band piece could be orchestrated for a symphony orchestra. In classical music, composers have historically orchestrated their own music. Only gradually over the course of music history did orchestration come to be regarded as a separate compositional art and profession in itself. In modern classical music, composers almost invariably orchestrate their own work. However, in musical theatre, film music and other commercial media, it is customary to use orchestrators and arrangers to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Melody
A melody (from Greek language, Greek μελῳδία, ''melōidía'', "singing, chanting"), also tune, voice or line, is a Linearity#Music, linear succession of musical tones that the listener perceives as a single entity. In its most literal sense, a melody is a combination of pitch (music), pitch and rhythm, while more figuratively, the term can include other musical elements such as Timbre, tonal color. It is the foreground to the background accompaniment. A line or part (music), part need not be a foreground melody. Melodies often consist of one or more musical Phrase (music), phrases or Motif (music), motifs, and are usually repeated throughout a musical composition, composition in various forms. Melodies may also be described by their melodic motion or the pitches or the interval (music), intervals between pitches (predominantly steps and skips, conjunct or disjunct or with further restrictions), pitch range, tension (music), tension and release, continuity and coheren ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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