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Shannon Number
The Shannon number, named after the American mathematician Claude Shannon, is a conservative lower bound of the game-tree complexity of chess of 10120, based on an average of about 103 possibilities for a pair of moves consisting of a move for White followed by a move for Black, and a typical game lasting about 40 such pairs of moves. Shannon's calculation Shannon showed a calculation for the lower bound of the game-tree complexity of chess, resulting in about 10120 possible games, to demonstrate the impracticality of solving chess by brute force, in his 1950 paper "Programming a Computer for Playing Chess". (This influential paper introduced the field of computer chess.) Shannon also estimated the number of possible positions, "of the general order of \scriptstyle \frac, or roughly 1043". This includes some illegal positions (e.g., pawns on the first rank, both kings in check) and excludes legal positions following captures and promotions. After each player has mov ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Observable Universe
The observable universe is a ball-shaped region of the universe comprising all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time, because the electromagnetic radiation from these objects has had time to reach the Solar System and Earth since the beginning of the cosmological expansion. There may be 2 trillion galaxies in the observable universe, although that number was reduced in 2021 to only several hundred billion based on data from '' New Horizons''. Assuming the universe is isotropic, the distance to the edge of the observable universe is roughly the same in every direction. That is, the observable universe is a spherical region centered on the observer and is unique for every unique observational position. The word ''observable'' in this sense does not refer to the capability of modern technology to detect light or other information from an object, or whether there is anything to be detected. It refers to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Game Theory
Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Study has been largely confined to two-player games that have a ''position'' that the players take turns changing in defined ways or ''moves'' to achieve a defined winning condition. Combinatorial game theory has not traditionally studied games of chance or those that use imperfect or incomplete information, favoring games that offer perfect information in which the state of the game and the set of available moves is always known by both players. However, as mathematical techniques advance, the types of game that can be mathematically analyzed expands, thus the boundaries of the field are ever changing. Scholars will generally define what they mean by a "game" at the beginning of a paper, and these definitions often vary as they are specific to the game being analyzed and are not meant to represent the entire scope of the field. C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Large Integers
Large means of great size. Large may also refer to: Mathematics * Arbitrarily large, a phrase in mathematics * Large cardinal, a property of certain transfinite numbers * Large category, a category with a proper class of objects and morphisms (or both) * Large diffeomorphism, a diffeomorphism that cannot be continuously connected to the identity diffeomorphism in mathematics and physics * Large numbers, numbers significantly larger than those ordinarily used in everyday life * Large ordinal, a type of number in set theory * Large sieve, a method of analytic number theory ** Larger sieve, a heightening of the large sieve * Law of large numbers, a result in probability theory * Sufficiently large, a phrase in mathematics Other uses * ''Large'' (film), a 2001 comedy film * Large (surname), an English surname * LARGE, an enzyme * Large, a British English name for the maxima (music), a note length in mensural notation * Large, or G's, or grand, slang for $1,000 US dollars * Large, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Chess Problems
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Explosion
In mathematics, a combinatorial explosion is the rapid growth of the complexity of a problem due to how the combinatorics of the problem is affected by the input, constraints, and bounds of the problem. Combinatorial explosion is sometimes used to justify the intractability of certain problems.http://intelligence.worldofcomputing/combinatorial-explosion Combinatorial Explosion. Examples of such problems include certain mathematical functions, the analysis of some puzzles and games, and some pathological examples which can be modelled as the Acker ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Go And Mathematics
The game of Go is one of the most popular games in the world. As a result of its elegant and simple rules, the game has long been an inspiration for mathematical research. Shen Kuo, an 11th century Chinese scholar, estimated in his ''Dream Pool Essays'' that the number of possible board positions is around 10172. In more recent years, research of the game by John H. Conway led to the invention of the surreal numbers and contributed to development of combinatorial game theory (with Go Infinitesimals being a specific example of its use in Go). Computational complexity Generalized Go is played on ''n'' × ''n'' boards, and the computational complexity of determining the winner in a given position of generalized Go depends crucially on the ko rules. Go is “almost” in PSPACE, since in normal play, moves are not reversible, and it is only through capture that there is the possibility of the repeating patterns necessary for a harder complexity. Without ko Without ko, Go is PSPACE ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solving Chess
Solving chess means finding an optimal strategy for the game of chess, that is, one by which one of the players ( White or Black) can always force a victory, or either can force a draw (see solved game). It also means more generally solving ''chess-like'' games (i.e. combinatorial games of perfect information), such as Capablanca chess and infinite chess. According to Zermelo's theorem, a determinable optimal strategy must exist for chess and chess-like games. In a weaker sense, ''solving chess'' may refer to proving which one of the three possible outcomes (White wins; Black wins; draw) is the result of two perfect players, without necessarily revealing the optimal strategy itself (see indirect proof). No complete solution for chess in either of the two senses is known, nor is it expected that chess will be solved in the near future. There is disagreement on whether the current exponential growth of computing power will continue long enough to someday allow for solving it by " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GitHub
GitHub, Inc. () is an Internet hosting service for software development and version control using Git. It provides the distributed version control of Git plus access control, bug tracking, software feature requests, task management, continuous integration, and wikis for every project. Headquartered in California, it has been a subsidiary of Microsoft since 2018. It is commonly used to host open source software development projects. As of June 2022, GitHub reported having over 83 million developers and more than 200 million repositories, including at least 28 million public repositories. It is the largest source code host . History GitHub.com Development of the GitHub.com platform began on October 19, 2007. The site was launched in April 2008 by Tom Preston-Werner, Chris Wanstrath, P. J. Hyett and Scott Chacon after it had been made available for a few months prior as a beta release. GitHub has an annual keynote called GitHub Universe. Organizational ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Tromp
John Tromp is a Dutch computer scientist. He formerly worked for Dutch Centre for Mathematics and Computer Science. Tromp discovered the number of legal states of the board game Go, and co-authored with Bill Taylor the Tromp-Taylor Rules, which they call "the logical rules of Go". He is also known for Binary combinatory logic (Binary lambda calculus). References External linksJohn Tromp's homepageat GitHub GitHub, Inc. () is an Internet hosting service for software development and version control using Git. It provides the distributed version control of Git plus access control, bug tracking, software feature requests, task management, continu ... {{DEFAULTSORT:Tromp, John Living people Dutch computer scientists Year of birth missing (living people) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Limburg
Maastricht University (abbreviated as UM; nl, Universiteit Maastricht) is a public research university in Maastricht, Netherlands. Founded in 1976, it is the second youngest of the thirteen Dutch universities. In 2021, 22,383 students studied at Maastricht University, 56% of whom were foreign students, with over 4,000 employees. About half of the bachelor's programmes are fully offered in English, while the other half is taught wholly or partly in Dutch. Most of the master's and doctoral programmes are in English. Besides traditional programmes, Maastricht University also has three honours liberal arts colleges: University College Maastricht and the Maastricht Science Programme in the same liberal arts tradition. The satellite University College Venlo opened in 2015. Maastricht University regularly ranks as one of Europe's leading universities. The university has been placed in the top 300 universities in the world by five major ranking tables. Maastricht University was at 88th p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Claude Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American people, American mathematician, electrical engineering, electrical engineer, and cryptography, cryptographer known as a "father of information theory". As a 21-year-old master's degree student at the Massachusetts Institute of Technology (MIT), he wrote A Symbolic Analysis of Relay and Switching Circuits, his thesis demonstrating that electrical applications of Boolean algebra could construct any logical numerical relationship. Shannon contributed to the field of cryptanalysis for national defense of the United States during World War II, including his fundamental work on codebreaking and secure telecommunications. Biography Childhood The Shannon family lived in Gaylord, Michigan, and Claude was born in a hospital in nearby Petoskey, Michigan, Petoskey. His father, Claude Sr. (1862–1934), was a businessman and for a while, a judge of probate in Gaylord. His mother, Mabel Wolf Shannon (1890–1945), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
