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An abstract structure is a set of laws, properties and relationships that is defined independently of any physical objects. Abstract structures are studied in philosophy, computer science and mathematics. Indeed, modern mathematics has been defined in a very general sense as the study of abstract structures (by the Bourbaki group: see discussion there, at algebraic structure and also structure). The Philosopher (detail), by Rembrandt Philosophy is a study that includes diverse subfields such as aesthetics, epistemology, ethics, logic, and metaphysics. ...
Computer science is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ...
Euclid, detail from The School of Athens by Raphael. ...
Nicolas Bourbaki is the collective allonym under which a group of mainly French 20th-century mathematicians wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. ...
In abstract algebra, an algebraic structure consists of a set together with a collection of operations or relations defined on it which satisfy certain axioms. ...
In mathematics, progress often consists of recognising the same structure in different contexts - so that one method exploiting it has multiple applications. ...
An abstract structure may be represented (perhaps with some degree of approximation) by one or more physical objects - this is called an implementation or instantiation of the abstract structure. But the abstract structure itself is defined in a way that is not dependent on the properties of any particular implementation. In computer science, the object lifetime (or life cycle) of an object in object-oriented programming is the time between an objects creation (also known as instantiation or construction) till the object is no longer used, and is destructed or freed. ...
Example - the rules of chess The rules of chess are an abstract structure, because their definition is independent of any particular chess set or board or chess notation. In this abstract structure, the king, for example, is defined as a piece that can move one square in any direction (except that it may not move onto a square that is under attack by an enemy piece). The king is not defined as a tall piece with a small cross on top, because it could be represented instead by the letter K, a particular sound frequency, a computer icon, or a small figurine of Cerebus the Aardvark. Because chess is an abstract structure, it is possible (and not unusual among chess masters) to play a game of chess that is entirely mental. (This might seem to require an exceptional memory, but in fact an exceptionally good understanding of the game obviates that need.) Chess is an abstract strategy board game for two players. ...
The king (♔♚) is the most important piece in the game of chess. ...
Cerebus issues 112 and 113, from 1988. ...
The mind is the term most commonly used to describe the higher functions of the human brain, particularly those of which humans are subjectively conscious, such as personality, thought, reason, memory, intelligence and emotion. ...
Other board games such as draughts and go are also examples of abstract structures. Most sports, on the other hand, are not abstract structures because their rules depend on the physical properties of the pitch, ball or other playing equipment. starting position on a 10×10 draughts board Draughts, also known as checkers, is a group of mental sport board games between two players which involve diagonal moves of uniform pieces and mandatory captures by jumping over the enemys pieces. ...
Go, also known as Wéiqà in Mandarin Chinese (Traditional Chinese: åœæ£‹; Simplified Chinese: 围棋), is a strategic, deterministic two-player Chinese board game. ...
An abstract structure has a richer structure than a concept or an idea. An abstract structure must include precise rules of behaviour which can be used to determine whether a candidate implementation actually matches the abstract structure in question. Thus we may debate how well a particular government fits the concept of democracy, but there is no room for debate over whether a given sequence of moves is or is not a valid game of chess. A concept is an abstract, idea, notion, or entity that serves to designate a category or class of entities, events, phenomena or relations between them. ...
An idea (Greek: ιδÎα) is a specific thought which arises in the mind. ...
Other examples A sort algorithm is an abstract structure, but a recipe is not, because it depends on the properties and quantities of its ingredients. In computer science and mathematics, a sorting algorithm is an algorithm that puts elements of a list in a certain order. ...
An example recipe, printed from the Wikibooks Cookbook. ...
A simple melody is an abstract structure, but an orchestration is not, because it depends on the properties of particular instruments. Look up melody in Wiktionary, the free dictionary. ...
For the use of the term orchestration in computer science, see orchestration (computers) Orchestration is the study and practice of adapting music for an orchestra or musical ensemble. ...
Euclidean geometry is an abstract structure, but the theory of continental drift is not, because it depends on the geology of the Earth. Euclid Euclidean geometry is a mathematical system due to the Hellenistic mathematician Euclid of Egypt. ...
Portrayal of shifting continents The concept of continental drift was first proposed by Alfred Wegener. ...
Earth is the third planet in the Solar system. ...
A formal language is an abstract structure, but a natural language is not, because its rules of grammar and syntax are open to debate and interpretation. In mathematics, logic and computer science, a formal language is a set of finite-length words (i. ...
The term natural language is used to distinguish languages spoken and signed (by hand signals and facial expressions) by humans for general-purpose communication from constructs such as writing, computer-programming languages or the languages used in the study of formal logic, especially mathematical logic. ...
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