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Infinity And The Mind
''Infinity and the Mind: The Science and Philosophy of the Infinite'' is a popular mathematics book by American mathematician, computer scientist, and science fiction writer Rudy Rucker. Synopsis The book contains accessible popular expositions on the mathematical theory of infinity, and a number of related topics. These include Gödel's incompleteness theorems and their relationship to concepts of artificial intelligence and the human mind, as well as the conceivability of some unconventional cosmological models. The material is approached from a variety of viewpoints, some more conventionally mathematical and others being nearly mystical. There is a brief account of the author's personal contact with Kurt Gödel. An appendix contains one of the few popular expositions on set theory research on what are known as "strong axioms of infinity." Reception Dave Langford reviewed ''Infinity and the Mind'' for ''White Dwarf'' #41, and stated that "a must for anyone who enjoyed Ho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rudy Rucker
Rudolf von Bitter Rucker (; born March 22, 1946) is an American mathematician, computer scientist, science fiction author, and one of the founders of the cyberpunk literary movement. The author of both fiction and non-fiction, he is best known for the novels in the Ware Tetralogy, the first two of which (''Software'' and '' Wetware'') both won Philip K. Dick Awards. Until its closure in 2014 he edited the science fiction webzine '' Flurb''. Early life Rucker was born and raised in Louisville, Kentucky, son of Embry Cobb Rucker Sr (October 1, 1914 - August 1, 1994), who ran a small furniture-manufacture company and later became an Episcopal priest and community activist, and Marianne (née von Bitter). The Rucker family were of Huguenot descent. Through his mother, he is a great-great-great-grandson of Georg Wilhelm Friedrich Hegel. Rucker attended St. Xavier High School before earning a BA in mathematics from Swarthmore College (1967) and MS (1969) and PhD (1973) degrees ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kurt Gödel
Kurt Friedrich Gödel ( , ; April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel had an immense effect upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell,For instance, in their "Principia Mathematica' (''Stanford Encyclopedia of Philosophy'' edition). Alfred North Whitehead, and David Hilbert were using logic and set theory to investigate the foundations of mathematics, building on earlier work by the likes of Richard Dedekind, Georg Cantor and Frege. Gödel published his first incompleteness theorem in 1931 when he was 25 years old, one year after finishing his doctorate at the University of Vienna. The first incompleteness theorem states that for any ω-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (for example P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Books By Rudy Rucker
A book is a medium for recording information in the form of writing or images, typically composed of many pages (made of papyrus, parchment, vellum, or paper) bound together and protected by a cover. The technical term for this physical arrangement is ''codex'' (plural, ''codices''). In the history of hand-held physical supports for extended written compositions or records, the codex replaces its predecessor, the scroll. A single sheet in a codex is a leaf and each side of a leaf is a page. As an intellectual object, a book is prototypically a composition of such great length that it takes a considerable investment of time to compose and still considered as an investment of time to read. In a restricted sense, a book is a self-sufficient section or part of a longer composition, a usage reflecting that, in antiquity, long works had to be written on several scrolls and each scroll had to be identified by the book it contained. Each part of Aristotle's ''Physics'' is called a bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1982 Non-fiction Books
__NOTOC__ Year 198 (CXCVIII) was a common year starting on Sunday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Sergius and Gallus (or, less frequently, year 951 ''Ab urbe condita''). The denomination 198 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire *January 28 **Publius Septimius Geta, son of Septimius Severus, receives the title of Caesar. **Caracalla, son of Septimius Severus, is given the title of Augustus. China *Winter – Battle of Xiapi: The allied armies led by Cao Cao and Liu Bei defeat Lü Bu; afterward Cao Cao has him executed. By topic Religion * Marcus I succeeds Olympianus as Patriarch of Constantinople (until 211). Births * Lu Kai (or Jingfeng), Chinese official and general (d. 269) * Quan Cong, Chinese general and advisor (d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Gardner
Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton.Martin (2010) He was also a leading authority on Lewis Carroll. ''The Annotated Alice'', which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies. He had a lifelong interest in magic and illusion and in 1999, MAGIC magazine named him as one of the "100 Most Influential Magicians of the Twentieth Century". He was considered the doyen of American puzzlers. He was a prolific and versatile author, publishing more than 100 books. Gardner was best known for creating and sustaining interest in recreational mathematicsand by extension, mathematics in generalthroughout the latter half of the 20th century, principally through his "Mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The New Yorker
''The New Yorker'' is an American weekly magazine featuring journalism, commentary, criticism, essays, fiction, satire, cartoons, and poetry. Founded as a weekly in 1925, the magazine is published 47 times annually, with five of these issues covering two-week spans. Although its reviews and events listings often focus on the Culture of New York City, cultural life of New York City, ''The New Yorker'' has a wide audience outside New York and is read internationally. It is well known for its illustrated and often topical covers, its commentaries on popular culture and eccentric American culture, its attention to modern fiction by the inclusion of Short story, short stories and literary reviews, its rigorous Fact-checking, fact checking and copy editing, its journalism on politics and social issues, and its single-panel cartoons sprinkled throughout each issue. Overview and history ''The New Yorker'' was founded by Harold Ross and his wife Jane Grant, a ''The New York Times, N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Games Workshop
Games Workshop Group (often abbreviated as GW) is a British manufacturer of miniature wargames, based in Nottingham, England. Its best-known products are ''Warhammer Age of Sigmar'' and ''Warhammer 40,000''. Founded in 1975 by John Peake (game designer), John Peake, Ian Livingstone and Steve Jackson (UK), Steve Jackson, Games Workshop was originally a manufacturer of wooden boards for games including backgammon, mancala, nine men's morris and Go (board game), Go. It later became an importer of the U.S. role-playing game ''Dungeons & Dragons'', and then a publisher of wargames and role-playing games in its own right, expanding from a bedroom mail-order company in the process. It expanded into Europe, the US, Canada, and Australia in the early 1990s. All UK-based operations were relocated to the current headquarters in Lenton, Nottingham in 1997. It started promoting games associated with The Lord of the Rings (film series), ''The Lord of the Rings'' film trilogy in 2001. It al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
White Dwarf (magazine)
''White Dwarf'' is a magazine published by British games manufacturer Games Workshop, which has long served as a promotions and advertising platform for Games Workshop and Citadel Miniatures products. During the first ten years of its publication, it covered a wide variety of fantasy and science-fiction role-playing games (RPGs) and board games, particularly the role playing games ''Advanced Dungeons & Dragons'' (''AD&D''), '' Call of Cthulhu'', ''RuneQuest'' and '' Traveller''. These games were all published by other games companies and distributed in the United Kingdom by Games Workshop stores. The magazine underwent a major change in style and content in the late 1980s. It is now dedicated exclusively to the miniature wargames produced by Games Workshop. History 1975: ''Owl and Weasel'' to ''White Dwarf'' Steve Jackson and Ian Livingstone initially produced a newsletter called ''Owl and Weasel'', which ran for twenty-five issues from February 1975 before it evolved into '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Langford
David Rowland Langford (born 10 April 1953) is a British author, editor, and critic, largely active within the science fiction field. He publishes the science fiction fanzine and newsletter ''Ansible'', and holds the all-time record for most Hugo Awards, with a total of 29 wins. Personal background David Langford was born and grew up in Newport, Monmouthshire, Wales before studying for a degree in Physics at Brasenose College, Oxford, where he first became involved in science fiction fandom. Langford is married to Hazel and is the brother of the musician and artist Jon Langford. His first job was as a weapons physicist at the Atomic Weapons Research Establishment at Aldermaston, Berkshire from 1975 to 1980. In 1985 he set up a "tiny and informally run software company" with science fiction writer Christopher Priest, called Ansible Information after Langford's news-sheet. The company has ceased trading. Increasing hearing difficulties have reduced Langford's participation i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Artificial Intelligence
Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech recognition, computer vision, translation between (natural) languages, as well as other mappings of inputs. The ''Oxford English Dictionary'' of Oxford University Press defines artificial intelligence as: the theory and development of computer systems able to perform tasks that normally require human intelligence, such as visual perception, speech recognition, decision-making, and translation between languages. AI applications include advanced web search engines (e.g., Google), recommendation systems (used by YouTube, Amazon and Netflix), understanding human speech (such as Siri and Alexa), self-driving cars (e.g., Tesla), automated decision-making and competing at the highest level in strategic game systems (such as chess and Go). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinity
Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol . Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions among philosophers. In the 17th century, with the introduction of the infinity symbol and the infinitesimal calculus, mathematicians began to work with infinite series and what some mathematicians (including l'Hôpital and Bernoulli) regarded as infinitely small quantities, but infinity continued to be associated with endless processes. As mathematicians struggled with the foundation of calculus, it remained unclear whether infinity could be considered as a number or magnitude and, if so, how this could be done. At the end of the 19th century, Georg Cantor enlarged the mathematical study of infinity by studying infinite sets and infinite numbers, showing that they can be of various sizes. For example, if a line is viewed as the set of all o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gödel's Incompleteness Theorems
Gödel's incompleteness theorems are two theorems of mathematical logic Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ... that are concerned with the limits of in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible. The first incompleteness theorem states that no consistency, consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
