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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] |
Chess
Chess is a board game for two players, called White and Black, each controlling an army of chess pieces in their color, with the objective to checkmate the opponent's king. It is sometimes called international chess or Western chess to distinguish it from related games, such as xiangqi (Chinese chess) and shogi (Japanese chess). The recorded history of chess goes back at least to the emergence of a similar game, chaturanga, in seventh-century India. The rules of chess as we know them today emerged in Europe at the end of the 15th century, with standardization and universal acceptance by the end of the 19th century. Today, chess is one of the world's most popular games, played by millions of people worldwide. Chess is an abstract strategy game that involves no hidden information and no use of dice or cards. It is played on a chessboard with 64 squares arranged in an eight-by-eight grid. At the start, each player controls sixteen pieces: one king, one queen, two rooks, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chess Variant
A chess variant is a game related to, derived from, or inspired by chess. Such variants can differ from chess in many different ways. "International" or "Western" chess itself is one of a family of games which have related origins and could be considered variants of each other. Chess developed from '' chaturanga'', from which other members of this family, such as ''shatranj'', Tamerlane chess, '' shogi'', and ''xiangqi'' also evolved. Many chess variants are designed to be played with the equipment of regular chess. Most variants have a similar public-domain status as their parent game, but some have been made into commercial proprietary games. Just as in traditional chess, chess variants can be played over the board, by correspondence, or by computer. Some internet chess servers facilitate the play of some variants in addition to orthodox chess. In the context of chess problems, chess variants are called heterodox chess or fairy chess. Fairy chess variants tend to be created ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California At Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant university and the founding campus of the University of California system. Its fourteen colleges and schools offer over 350 degree programs and enroll some 31,800 undergraduate and 13,200 graduate students. Berkeley ranks among the world's top universities. A founding member of the Association of American Universities, Berkeley hosts many leading research institutes dedicated to science, engineering, and mathematics. The university founded and maintains close relationships with three national laboratories at Berkeley, Livermore and Los Alamos, and has played a prominent role in many scientific advances, from the Manhattan Project and the discovery of 16 chemical elements to breakthroughs in computer science and genomics. Berkeley is also k ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biophysics
Biophysics is an interdisciplinary science that applies approaches and methods traditionally used in physics to study biological phenomena. Biophysics covers all scales of biological organization, from molecular to organismic and populations. Biophysical research shares significant overlap with biochemistry, molecular biology, physical chemistry, physiology, nanotechnology, bioengineering, computational biology, biomechanics, developmental biology and systems biology. The term ''biophysics'' was originally introduced by Karl Pearson in 1892.Roland Glaser. Biophysics: An Introduction'. Springer; 23 April 2012. . The term ''biophysics'' is also regularly used in academia to indicate the study of the physical quantities (e.g. electric current, temperature, stress, entropy) in biological systems. Other biological sciences also perform research on the biophysical properties of living organisms including molecular biology, cell biology, chemical biology, and biochemistry. Overview ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
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] |
Hans-Joachim Bremermann
Hans-Joachim Bremermann (1926–1996) was a German-American mathematician and biophysicist. He worked on computer science and evolution, introducing ideas of how mating generates new gene combinations. Bremermann's limit, named after him, is the maximum computational speed of a self-contained system in the material universe. Early life Bremermann was born in Bremen, Germany, to Bernard Bremermann and Berta Wicke. Bremermann undertook doctoral studies at the University of Münster, completing his Staatsexamen in mathematics and physics in 1951. In the same year his doctoral dissertation ''Die Charakterisierung von Regularitätsgebieten durch pseudokonvexe Funktionen'' and was to become a specialist in complex analysis. This was a special case of the Levi problem. Career He came to the United States in 1952 to a research associate position at Stanford University. In 1953, he was appointed a research fellow at Harvard University. He returned to Munster for 1954–55. After ret ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Tree
In the context of Combinatorial game theory, which typically studies sequential games with perfect information, a game tree is a graph representing all possible game states within such a game. Such games include well-known ones such as chess, checkers, Go, and tic-tac-toe. This can be used to measure the complexity of a game, as it represents all the possible ways a game can pan out. Due to the large game trees of complex games such as chess, algorithms that are designed to play this class of games will use partial game trees, which makes computation feasible on modern computers. Various methods exist to solve game trees. If a complete game tree can be generated, a deterministic algorithm, such as backward induction or retrograde analysis can be used. Randomized algorithms and minimax algorithms such as MCTS can be used in cases where a complete game tree is not feasible. Understanding the game tree To better understand the game tree, it can be thought of as a technique for an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophical Magazine
The ''Philosophical Magazine'' is one of the oldest scientific journals published in English. It was established by Alexander Tilloch in 1798;John Burnett"Tilloch, Alexander (1759–1825)" Oxford Dictionary of National Biography, Oxford University Press, Sept 2004; online edn, May 2006, accessed 17 Feb 2010 in 1822 Richard Taylor became joint editor and it has been published continuously by Taylor & Francis ever since. Early history The name of the journal dates from a period when "natural philosophy" embraced all aspects of science. The very first paper published in the journal carried the title "Account of Mr Cartwright's Patent Steam Engine". Other articles in the first volume include "Methods of discovering whether Wine has been adulterated with any Metals prejudicial to Health" and "Description of the Apparatus used by Lavoisier to produce Water from its component Parts, Oxygen and Hydrogen". 19th century Early in the nineteenth century, classic papers by Humphry Davy, M ... [...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] |
Fifty-move Rule
The fifty-move rule in chess states that a player can claim a draw if no has been made and no pawn has been moved in the last fifty moves (for this purpose a "move" consists of a player completing a turn followed by the opponent completing a turn). The purpose of this rule is to prevent a player with no chance of winning from obstinately continuing to play indefinitely or seeking to win by tiring the opponent. Chess positions with only a few pieces can be " solved", that is, the outcome of best play for both sides can be determined by exhaustive analysis; and if the outcome is a win for one side or the other (rather than a draw), it is of interest to know whether the defending side can hold out long enough to invoke the fifty-move rule. The simplest common endings, called the basic checkmates, such as king and queen versus king, can all be won in well under 50 moves. However, in the 20th century it was discovered that certain endgame positions are winnable but require more than 5 ... [...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] |
Information Theory
Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. The field is at the intersection of probability theory, statistics, computer science, statistical mechanics, information engineering (field), information engineering, and electrical engineering. A key measure in information theory is information entropy, entropy. Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. For example, identifying the outcome of a fair coin flip (with two equally likely outcomes) provides less information (lower entropy) than specifying the outcome from a roll of a dice, die (with six equally likely outcomes). Some other important measures in information theory are mutual informat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
