|
Jorge Luis Borges And Mathematics
Jorge Luis Borges and mathematics concerns several modern mathematical concepts found in certain essays and short stories of Argentinian author Jorge Luis Borges (1899–1986), including concepts such as set theory, recursion, chaos theory, and infinite sequences, although Borges' strongest links to mathematics are through Georg Cantor's theory of infinite sets, outlined in "The Doctrine of Cycles" (''La doctrina de los ciclos''). Some of Borges' most popular works such as "The Library of Babel" (''La Biblioteca de Babel''), " The Garden of Forking Paths" (''El Jardín de Senderos que se Bifurcan''), " The Aleph" (''El Aleph''), an allusion to Cantor's use of the Hebrew letter aleph (\aleph) to denote cardinality of transfinite sets, and "The Approach to Al-Mu'tasim" (''El acercamiento a Almotásim'') illustrate his use of mathematics. According to Argentinian mathematician Guillermo Martínez, Borges at least had a knowledge of mathematics at the level of first courses i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jorge Luis Borges
Jorge Francisco Isidoro Luis Borges Acevedo (; ; 24 August 1899 – 14 June 1986) was an Argentine short-story writer, essayist, poet and translator, as well as a key figure in Spanish-language and international literature. His best-known books, ''Ficciones'' (''Fictions'') and '' El Aleph'' (''The Aleph''), published in the 1940s, are collections of short stories exploring themes of dreams, labyrinths, chance, infinity, archives, mirrors, fictional writers and mythology. Borges' works have contributed to philosophical literature and the fantasy genre, and majorly influenced the magic realist movement in 20th century Latin American literature.Theo L. D'Haen (1995) "Magical Realism and Postmodernism: Decentering Privileged Centers", in: Louis P. Zamora and Wendy B. Faris, ''Magical Realism: Theory, History and Community''. Duhan and London, Duke University Press, pp. 191–208. Born in Buenos Aires, Borges later moved with his family to Switzerland in 1914, where he studied ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paradox
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. A paradox usually involves contradictory-yet-interrelated elements that exist simultaneously and persist over time. They result in "persistent contradiction between interdependent elements" leading to a lasting "unity of opposites". In logic, many paradoxes exist that are known to be invalid arguments, yet are nevertheless valuable in promoting critical thinking, while other paradoxes have revealed errors in definitions that were assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. One example is Russell's paradox, which questions whether a "list of all lists that do not contain themselves" would include itself, and showed that attempts to found set theory on the identification ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Historia De La Eternidad
''Historia de la eternidad'' (in English: ''A History of Eternity'') is the first essay book published by Argentine author Jorge Luis Borges, in 1936 (editio princeps). Content In the essay after which the book is titled, which is complemented by two others (''La doctrina de los ciclos'', in English: ''Cycles' doctrine'', and ''El tiempo circular'', in English: ''Circular time''), the author contemplates the issues of time and eternity, from platonic, Christian and nietzschean perspectives. As Borges himself states in the book's prologue, eternity In the essays titled ''Los Kenningar'' (in English: ''The Kenningars'') and ''La metáfora'' (in English: ''Metaphor''), Borges analyzes that poetic resource, particularly from the point of view of the ancient Germanic epics. By comparing metaphors present in the ancient Icelandic sagas with later ones, we can observe how the same ones are repeated from one culture to another: In ''Los traductores de Las Mil y Una Noches'' (in E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second Order Logic
In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of Propositional calculus, propositional logic. Second-order logic is in turn extended by higher-order logic and type theory. First-order logic Quantifier (logic), quantifies only variables that range over individuals (elements of the domain of discourse); second-order logic, in addition, also quantifies over Finitary relation, relations. For example, the second-order Sentence (mathematical logic), sentence \forall P\,\forall x (Px \lor \neg Px) says that for every well-formed formula, formula ''P'', and every individual ''x'', either ''Px'' is true or not(''Px'') is true (this is the law of excluded middle). Second-order logic also includes quantification over set (mathematics), sets, function (mathematics), functions, and other variables (see section #Syntax and fragments, below). Both first-order and second-order logic use the idea of a domain of discourse (often called ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinitesimal
In mathematics, an infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally referred to the " infinity- th" item in a sequence. Infinitesimals do not exist in the standard real number system, but they do exist in other number systems, such as the surreal number system and the hyperreal number system, which can be thought of as the real numbers augmented with both infinitesimal and infinite quantities; the augmentations are the reciprocals of one another. Infinitesimal numbers were introduced in the development of calculus, in which the derivative was first conceived as a ratio of two infinitesimal quantities. This definition was not rigorously formalized. As calculus developed further, infinitesimals were replaced by limits, which can be calculated using the standard real numbers. Infinitesimals regained popularit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Measure (mathematics)
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures ( length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many similarities and can often be treated together in a single mathematical context. Measures are foundational in probability theory, integration theory, and can be generalized to assume negative values, as with electrical charge. Far-reaching generalizations (such as spectral measures and projection-valued measures) of measure are widely used in quantum physics and physics in general. The intuition behind this concept dates back to ancient Greece, when Archimedes tried to calculate the area of a circle. But it was not until the late 19th and early 20th centuries that measure theory became a branch of mathematics. The foundations of modern measure theory were laid in the works of Émile Borel, Henri Lebesgue, Nikolai Luzin, Johann Radon, Const ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Book Of Sand (book)
''The Book of Sand'' ( es, El libro de arena, link=no) is a 1975 short story collection by Argentine writer Jorge Luis Borges. In the author's opinion, the collection, written in his last days — and while blind — is his best book. This opinion is not shared by most critics, many of whom prefer his other works such as those in ''Ficciones'' (1944). Referring to the collection, Borges said: The first edition, published in Buenos Aires by Emecé, contained 181 pages. In Madrid it was edited that year by Ultramar. Borges opts for an epilogue to this short story collection, different from the cases of his previous collections ''The Garden of Forking Paths'' (1941) and ''Artifices'' (1944) (later republished together in ''Ficciones''), which had a prologue. Regarding this, Borges begins ''The Book of Sand's'' epilogue by saying: "To prologue unread stories is an almost impossible work, as it demands the analysis of plots one should not anticipate. I prefer, thus, an epilogue." ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dense Set
In topology and related areas of mathematics, a subset ''A'' of a topological space ''X'' is said to be dense in ''X'' if every point of ''X'' either belongs to ''A'' or else is arbitrarily "close" to a member of ''A'' — for instance, the rational numbers are a dense subset of the real numbers because every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine approximation). Formally, A is dense in X if the smallest closed subset of X containing A is X itself. The of a topological space X is the least cardinality of a dense subset of X. Definition A subset A of a topological space X is said to be a of X if any of the following equivalent conditions are satisfied: The smallest closed subset of X containing A is X itself. The closure of A in X is equal to X. That is, \operatorname_X A = X. The interior of the complement of A is empty. That is, \operatorname_X (X \setminus A) = \varnothing. Every point in X either ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Book Of Sand
"The Book of Sand" ( es, El libro de arena, links=no) is a 1975 short story by Argentine writer Jorge Luis Borges about the discovery of a book with infinite pages. It has parallels to the same author's 1949 story " The Zahir" (revised in 1974), continuing the theme of self-reference and attempting to abandon the terribly infinite, and to his 1941 story "The Library of Babel" about an infinite library. Release The story was first published in 1975, in Spanish, as the last of 13 stories in a book of the same name. The first English translation—by Norman Thomas di Giovanni—was published in ''The New Yorker''. The entire volume ''The Book of Sand'' () first appeared in English in 1977. Plot summary An unnamed narrator is visited by a tall Scots Bible-seller, who presents him with a very old cloth-bound book that he bought in India from an Untouchable. The book is emblazoned with the title "Holy Writ," below which title is emblazoned "Bombay," but is said to be called "The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Periodic Function
A periodic function is a function that repeats its values at regular intervals. For example, the trigonometric functions, which repeat at intervals of 2\pi radians, are periodic functions. Periodic functions are used throughout science to describe oscillations, waves, and other phenomena that exhibit periodicity. Any function that is not periodic is called aperiodic. Definition A function is said to be periodic if, for some nonzero constant , it is the case that :f(x+P) = f(x) for all values of in the domain. A nonzero constant for which this is the case is called a period of the function. If there exists a least positive constant with this property, it is called the fundamental period (also primitive period, basic period, or prime period.) Often, "the" period of a function is used to mean its fundamental period. A function with period will repeat on intervals of length , and these intervals are sometimes also referred to as periods of the function. Geometrically, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation
In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set. Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set , namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). These are all the possible orderings of this three-element set. Anagrams of words whose letters are different are also permutations: the letters are already ordered in the original word, and the anagram is a reordering of the letters. The study of permutations of finite sets is an important topic in the fields of combinatorics and group theory. Permutations are used in almost every branch of mathematics, and in many other fields of scie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthography
An orthography is a set of conventions for writing a language, including norms of spelling, hyphenation, capitalization, word breaks, emphasis, and punctuation. Most transnational languages in the modern period have a writing system, and most of these systems have undergone substantial standardization, thus exhibiting less dialect variation than the spoken language. These processes can fossilize pronunciation patterns that are no longer routinely observed in speech (e.g., "would" and "should"); they can also reflect deliberate efforts to introduce variability for the sake of national identity, as seen in Noah Webster's efforts to introduce easily noticeable differences between American and British spelling (e.g., "honor" and "honour"). Some nations (e.g. France and Spain) have established language academies in an attempt to regulate orthography officially. For most languages (including English) however, there are no such authorities and a sense of 'correct' orthography evol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.svg "Click for more on -> Measure (mathematics)")
