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Simon B. Kochen
Simon Bernhard Kochen (; born 14 August 1934, Antwerp) is a Canadian mathematician, working in the fields of model theory, number theory and quantum mechanics. Biography Kochen received his Ph.D. (''Ultrafiltered Products and Arithmetical Extensions'') from Princeton University in 1958 under the direction of Alonzo Church. Since 1967 he has been a member of Princeton's Department of Mathematics. He chaired the department from 1989 to 1992 and became the Henry Burchard Fine Professor in mathematics in 1994. During 1966–1967 and 1978–1979, Kochen was at the Institute for Advanced Study. In 1967 he was awarded, together with James Ax, the seventh Frank Nelson Cole Prize in Number Theory for a series of three joint papers on Diophantine problems involving p-adic techniques. Kochen and Ax also co-authored the Ax–Kochen theorem, an application of model theory to algebra. In 1967 Kochen and Ernst Specker proved the Kochen–Specker theorem in quantum mechanics and quantum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antwerp
Antwerp (; nl, Antwerpen ; french: Anvers ; es, Amberes) is the largest city in Belgium by area at and the capital of Antwerp Province in the Flemish Region. With a population of 520,504,Statistics Belgium; ''Loop van de bevolking per gemeente'' (Excel file) Population of all municipalities in Belgium, . Retrieved 1 November 2017. it is the most populous municipality in Belgium, and with a metropolitan population of around 1,200,000 people, it is the second-largest metrop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables (commonly represented by Roman letters) as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given, mostly in education, to the study of algebraic structures such as groups, rings, and fields (the term is no more in common use outside educational context). Linear algebra, which deals with linear equations and linear mappings, is used for modern presentations of geometry, and has many practical applications (in weather forecasting, for example). There are many areas of mathematics that belong to algebra, some having "algebra" in their name, such as commutative algebra, and some not, such as Galois theory. The word ''algebra'' is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1934 Births
Events January–February * January 1 – The International Telecommunication Union, a specialist agency of the League of Nations, is established. * January 15 – The 8.0 Nepal–Bihar earthquake strikes Nepal and Bihar with a maximum Mercalli intensity of XI (''Extreme''), killing an estimated 6,000–10,700 people. * January 26 – A 10-year German–Polish declaration of non-aggression is signed by Nazi Germany and the Second Polish Republic. * January 30 ** In Nazi Germany, the political power of federal states such as Prussia is substantially abolished, by the "Law on the Reconstruction of the Reich" (''Gesetz über den Neuaufbau des Reiches''). ** Franklin D. Roosevelt, President of the United States, signs the Gold Reserve Act: all gold held in the Federal Reserve is to be surrendered to the United States Department of the Treasury; immediately following, the President raises the statutory gold price from US$20.67 per ounce to $35. * February 6 – F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Theorists
A model is an informative representation of an object, person or system. The term originally denoted the Plan_(drawing), plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. Models can be divided into physical models (e.g. a model plane) and abstract models (e.g. mathematical expressions describing behavioural patterns). Abstract or conceptual models are central to philosophy of science, as almost every scientific theory effectively embeds some kind of model of the universe, physical or human condition, human sphere. In commerce, "model" can refer to a specific design of a product as displayed in a catalogue or show room (e.g. Ford Model T), and by extension to the sold product itself. Types of models include: Physical model A physical model (most commonly referred to simply as a model but in this context distinguished from a conceptual model) is a smaller or larger physical copy of an physical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Will Theorem
The free will theorem of John H. Conway and Simon B. Kochen states that if we have a free will in the sense that our choices are not a function of the past, then, subject to certain assumptions, so must some elementary particles. Conway and Kochen's paper was published in ''Foundations of Physics'' in 2006. In 2009, the authors published a stronger version of the theorem in the ''Notices of the American Mathematical Society''. Later, in 2017, Kochen elaborated some details. Axioms The proof of the theorem as originally formulated relies on three axioms, which Conway and Kochen call "fin", "spin", and "twin". The spin and twin axioms can be verified experimentally. # Fin: There is a maximal speed for propagation of information (not necessarily the speed of light). This assumption rests upon causality. # Spin: The squared spin component of certain elementary particles of spin one, taken in three orthogonal directions, will be a permutation of (1,1,0). # Twin: It is possible to "entangl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Particles
In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions (quarks, leptons, antiquarks, and antileptons, which generally are matter particles and antimatter particles), as well as the fundamental bosons (gauge bosons and the Higgs boson), which generally are force particles that mediate interactions among fermions. A particle containing two or more elementary particles is a composite particle. Ordinary matter is composed of atoms, once presumed to be elementary particles – ''atomos'' meaning "unable to be cut" in Greek – although the atom's existence remained controversial until about 1905, as some leading physicists regarded molecules as mathematical illusions, and matter as ultimately composed of energy. Subatomic constituents of the atom were first identified in the early 1930s; the electron and the proton, alon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Will
Free will is the capacity of agents to choose between different possible courses of action unimpeded. Free will is closely linked to the concepts of moral responsibility, praise, culpability, sin, and other judgements which apply only to actions that are freely chosen. It is also connected with the concepts of advice, persuasion, deliberation, and prohibition. Traditionally, only actions that are freely willed are seen as deserving credit or blame. Whether free will exists, what it is and the implications of whether it exists or not are some of the longest running debates of philosophy and religion. Some conceive of free will as the right to act outside of external influences or wishes. Some conceive free will to be the capacity to make choices undetermined by past events. Determinism suggests that only one course of events is possible, which is inconsistent with a libertarian model of free will. Ancient Greek philosophy identified this issue, which remains a major focus o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Will Theorem
The free will theorem of John H. Conway and Simon B. Kochen states that if we have a free will in the sense that our choices are not a function of the past, then, subject to certain assumptions, so must some elementary particles. Conway and Kochen's paper was published in ''Foundations of Physics'' in 2006. In 2009, the authors published a stronger version of the theorem in the ''Notices of the American Mathematical Society''. Later, in 2017, Kochen elaborated some details. Axioms The proof of the theorem as originally formulated relies on three axioms, which Conway and Kochen call "fin", "spin", and "twin". The spin and twin axioms can be verified experimentally. # Fin: There is a maximal speed for propagation of information (not necessarily the speed of light). This assumption rests upon causality. # Spin: The squared spin component of certain elementary particles of spin one, taken in three orthogonal directions, will be a permutation of (1,1,0). # Twin: It is possible to "entangl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Horton Conway
John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches of recreational mathematics, most notably the invention of the cellular automaton called the Game of Life. Born and raised in Liverpool, Conway spent the first half of his career at the University of Cambridge before moving to the United States, where he held the John von Neumann Professorship at Princeton University for the rest of his career. On 11 April 2020, at age 82, he died of complications from COVID-19. Early life and education Conway was born on 26 December 1937 in Liverpool, the son of Cyril Horton Conway and Agnes Boyce. He became interested in mathematics at a very early age. By the time he was 11, his ambition was to become a mathematician. After leaving sixth form, he studied mathematics at Gonville and Caius College, Camb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Contextuality
Quantum contextuality is a feature of the Phenomenology (physics), phenomenology of quantum mechanics whereby measurements of quantum observables cannot simply be thought of as revealing pre-existing values. Any attempt to do so in a realistic hidden-variable theory leads to values that are dependent upon the choice of the other (compatible) observables which are simultaneously measured (the measurement context). More formally, the measurement result (assumed pre-existing) of a quantum observable is dependent upon which other Commutative property, commuting observables are within the same measurement set. Contextuality was first demonstrated to be a feature of quantum phenomenology by the Kochen–Specker theorem, Bell–Kochen–Specker theorem. The study of contextuality has developed into a major topic of interest in quantum foundations as the phenomenon crystallises certain non-classical and counter-intuitive aspects of quantum theory. A number of powerful mathematical framewor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kochen–Specker Theorem
In quantum mechanics, the Kochen–Specker (KS) theorem, also known as the Bell–Kochen–Specker theorem, is a "no-go" theorem proved by John S. Bell in 1966 and by Simon B. Kochen and Ernst Specker in 1967. It places certain constraints on the permissible types of hidden-variable theories, which try to explain the predictions of quantum mechanics in a context-independent way. The version of the theorem proved by Kochen and Specker also gave an explicit example for this constraint in terms of a finite number of state vectors. The theorem is a complement to Bell's theorem (to be distinguished from the (Bell–)Kochen–Specker theorem of this article). While Bell's theorem established nonlocality to be a feature of any hidden variable theory that recovers the predictions of quantum mechanics, the KS theorem established contextuality to be an inevitable feature of such theories. The theorem proves that there is a contradiction between two basic assumptions of the hidden-vari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
