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Autogram
An autogram ( grc, αὐτός = self, = letter) is a sentence that describes itself in the sense of providing an inventory of its own characters. They were invented by Lee Sallows, who also coined the word ''autogram''. An essential feature is the use of full cardinal number names such as "one", "two", etc., in recording character counts. Autograms are also called 'self-enumerating' or 'self-documenting' sentences. Often, letter counts only are recorded while punctuation signs are ignored, as in this example: The first autogram to be published was composed by Sallows in 1982 and appeared in Douglas Hofstadter's "Metamagical Themas" column in ''Scientific American''. The task of producing an autogram is perplexing because the object to be described cannot be known until its description is first complete. Self-enumerating pangrams A type of autogram that has attracted special interest is the autogramic pangram, a self-enumerating sentence in which every letter of the alphabet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lee Sallows
Lee Cecil Fletcher Sallows (born April 30, 1944) is a British electronics engineer known for his contributions to recreational mathematics. He is particularly noted as the inventor of golygons, self-enumerating sentences, and geomagic squares. Recreational mathematics Sallows is an expert on the theory of magic squares and has invented several variations on them, including alphamagic squares and geomagic squares. The latter invention caught the attention of mathematician Peter Cameron who has said that he believes that "an even deeper structure may lie hidden beyond geomagic squares" In "The lost theorem" published in 1997 he showed that every 3 × 3 magic square is associated with a unique parallelogram on the complex plane, a discovery that had escaped all previous researchers from ancient times down to the present day. In 2014 Sallows discovered a previously unnoticed result involving the medians of a triangle. A golygon is a polygon containing only right ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Douglas Hofstadter
Douglas Richard Hofstadter (born February 15, 1945) is an American scholar of cognitive science, physics, and comparative literature whose research includes concepts such as the sense of self in relation to the external world, consciousness, analogy-making, artistic creation, literary translation, and discovery in mathematics and physics. His 1979 book '' Gödel, Escher, Bach: An Eternal Golden Braid'' won both the Pulitzer Prize for general nonfiction"General Nonfiction" . ''Past winners and finalists by category''. The Pulitzer Prizes. Retrieved March 17, 2012. and a (at that time called The American Book Award) for Science. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metamagical Themas
''Metamagical Themas'' is an eclectic collection of articles that Douglas Hofstadter wrote for the popular science magazine ''Scientific American'' during the early 1980s. The anthology was published in 1985 by Basic Books. The volume is substantial in size and contains extensive notes concerning responses to the articles and other information relevant to their content. (One of the notes—page 65—suggested memetics for the study of memes.) Major themes include: self-reference in memes, language, art and logic; discussions of philosophical issues important in cognitive science/AI; analogies and what makes something similar to something else (specifically what makes, for example, an uppercase letter 'A' recognizable as such); and lengthy discussions of the work of Robert Axelrod on the prisoner's dilemma, as well as the idea of superrationality. The concept of superrationality, and its relevance to the Cold War, environmental issues and such, is accompanied by notes on exper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scientific American
''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it is the oldest continuously published magazine in the United States. ''Scientific American'' is owned by Springer Nature, which in turn is a subsidiary of Holtzbrinck Publishing Group. History ''Scientific American'' was founded by inventor and publisher Rufus Porter (painter), Rufus Porter in 1845 as a four-page weekly newspaper. The first issue of the large format newspaper was released August 28, 1845. Throughout its early years, much emphasis was placed on reports of what was going on at the United States Patent and Trademark Office, U.S. Patent Office. It also reported on a broad range of inventions including perpetual motion machines, an 1860 device for buoying vessels by Abraham Lincoln, and the universal joint which now can be found ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pangram
A pangram or holoalphabetic sentence is a sentence using every letter of a given alphabet at least once. Pangrams have been used to display typefaces, test equipment, and develop skills in handwriting, calligraphy, and keyboarding. Origins The best-known English pangram is "The quick brown fox jumps over the lazy dog". It has been used since at least the late 19th century, was used by Western Union to test Telex/ TWX data communication equipment for accuracy and reliability, and is now used by a number of computer programs to display computer fonts. Short pangrams Short pangrams in English are more difficult to devise and tend to use uncommon words and unnatural sentences. Longer pangrams afford more opportunity for humor, cleverness, or thoughtfulness. The following are examples of pangrams that are shorter than "The quick brown fox jumps over a lazy dog" (which has 33 letters) and use standard written English without abbreviations or proper nouns: *"Waltz, bad nymph, for qui ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rudy Kousbroek
Herman Rudolf "Rudy" Kousbroek (1 November 1929 – 4 April 2010) was a Dutch poet, translator, writer and first of all essayist. He was a prominent figure in Dutch cultural life between 1950 and 2010 and one of the most outspoken atheists in the Netherlands. In 1975 he was awarded the P.C. Hooft Prize for his essays. His principal work is the book ''Het Oostindisch kampsyndroom'' (The East Indian Camp Syndrome), a compilation of critical essays that are in one way or the other related to the Dutch East Indies and clearly show his admiration for Dutch Indo-Eurasian authors like E. du Perron, Tjalie Robinson, Beb Vuyk as well as Indonesian intellectual Sutan Sjahrir. Life Rudy Kousbroek was born in Pematang Siantar, on the isle of Sumatra, in the Dutch East Indies. The first sixteen years of his life he lived there. During the Japanese occupation he and his family were imprisoned in a Japanese concentration camp. After World War II his family repatriated to the Netherlands. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Futility Closet
Futility Closet is a blog, podcast, and database started in 2005 by editorial manager and publishing journalist Greg Ross. As of February 2021 the database totaled over 11,000 items. They range over the fields of history, literature, language, art, philosophy, and recreational mathematics. The associated ''Futility Closet Podcast'' was a weekly podcast hosted by Greg and his wife Sharon Ross. It presented curious and little-known events and people from history, and posed logical puzzles. History In January 2005, Greg Ross started the Futility Closet website, an online wunderkammer of trivia, quotations, mathematical curiosities, chess problems, and other diversions. The site has spawned two printed collections, and continues to be updated daily. Gary Antonick of the ''New York Times Numberplay blog described the first book as "the literary equivalent of Trader Joe's Tempting Trail Mix". Futility Closet has sometimes been a conduit or used to popularize results by John H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roman Numerals
Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, each letter with a fixed integer value, modern style uses only these seven: The use of Roman numerals continued long after the decline of the Roman Empire. From the 14th century on, Roman numerals began to be replaced by Arabic numerals; however, this process was gradual, and the use of Roman numerals persists in some applications to this day. One place they are often seen is on clock faces. For instance, on the clock of Big Ben (designed in 1852), the hours from 1 to 12 are written as: The notations and can be read as "one less than five" (4) and "one less than ten" (9), although there is a tradition favouring representation of "4" as "" on Roman numeral clocks. Other common uses include year numbers on monuments and buildings and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as ''decimal notation''. A ''decimal numeral'' (also often just ''decimal'' or, less correctly, ''decimal number''), refers generally to the notation of a number in the decimal numeral system. Decimals may sometimes be identified by a decimal separator (usually "." or "," as in or ). ''Decimal'' may also refer specifically to the digits after the decimal separator, such as in " is the approximation of to ''two decimals''". Zero-digits after a decimal separator serve the purpose of signifying the precision of a value. The numbers that may be represented in the decimal system are the decimal fractions. That is, fractions of the form , where is an integer, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
English Numerals
English number words include numerals and various words derived from them, as well as a large number of words borrowed from other languages. Cardinal numbers Cardinal numbers refer to the size of a group. In English, these words are numerals. If a number is in the range 21 to 99, and the second digit is not zero, the number is typically written as two words separated by a hyphen. In English, the hundreds are perfectly regular, except that the word ''hundred'' remains in its singular form regardless of the number preceding it. So too are the thousands, with the number of thousands followed by the word "thousand". For the number one thousand it may be written 1 000 or 1000 or 1,000, for larger numbers they are written for example 10 000 or 10,000 for ease of human reading. The use of the , as a separator is avoided in some languages as it is used for a decimal placement, for example with money. As a result some style guides recommend avoidance of the comma (,) as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quine (computing)
A quine is a computer program which takes no input and produces a copy of its own source code as its only output. The standard terms for these programs in the computability theory and computer science literature are "self-replicating programs", "self-reproducing programs", and "self-copying programs". A quine is a fixed point of an execution environment, when the execution environment is viewed as a function transforming programs into their outputs. Quines are possible in any Turing-complete programming language, as a direct consequence of Kleene's recursion theorem. For amusement, programmers sometimes attempt to develop the shortest possible quine in any given programming language. The name "quine" was coined by Douglas Hofstadter, in his popular science book ''Gödel, Escher, Bach'', in honor of philosopher Willard Van Orman Quine (1908–2000), who made an extensive study of indirect self-reference, and in particular for the following paradox-producing expression, known as Q ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diagonal Lemma
In mathematical logic, the diagonal lemma (also known as diagonalization lemma, self-reference lemma or fixed point theorem) establishes the existence of self-referential sentences in certain formal theories of the natural numbers—specifically those theories that are strong enough to represent all computable functions. The sentences whose existence is secured by the diagonal lemma can then, in turn, be used to prove fundamental limitative results such as Gödel's incompleteness theorems and Tarski's undefinability theorem. Background Let \mathbb be the set of natural numbers. A first-order theory T in the language of arithmetic ''represents'' the computable function f: \mathbb\rightarrow\mathbb if there exists a "graph" predicate \mathcal_f(x, y) in the language of T such that for each n \in \mathbb : \vdash_\,(\forall y) ^\circ f(n)=y) \Leftrightarrow \mathcal_f(^\circ n,\,y)/math> Here ^\circ n is the numeral corresponding to the natural number n, which is defined to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
