Agarwal (2000), Ravi P., and Maria Meehan, Donal O'Regan, Fixed Point Theory and Applications, Cambridge University Press 2009 'This book provides a clear exposition of the flourishing field of fixed point theory. Starting form the basics of Banach's contraction theorem, most main results and techniques are ceveloped. . . . The theory is applied to many areas of current interest in analysis. . . . ' 
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Ashby (1964), W Ross, An Introduction to Cybernetics, Methuen 1956, 1964 'This book is intended to provide [an introduction to cybernetics]. It starts from common-place and well understood concepts, and proceeds step by step to show how these concepts can be made exact, and how they can be developed until they lead into such subjects as feedback, stability, regulation, ultrastability, information, coding, noise and other cybernetic topics.' 
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Augustine (419, 1991), Saint, and Edmond Hill (Introduction, translation and notes), and John E Rotelle (editor), The Trinity, New City Press 399-419, 1991 Written 399 - 419: De Trinitate is a radical restatement, defence and development of the Christian doctrine of the Trinity. Augustine's book has served as a foundation for most subsequent work, particularly that of Thomas Aquinas.  
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Auyang (1995), Sunny Y., How is Quantum Field Theory Possible?, Oxford University Press 1995 Jacket: 'Quantum field theory (QFT) combines quantum mechanics with Einstein's special theory of relativity and underlies elementary particle physics. This book presents a philosophical analysis of QFT. It is the first treatise in which the philosophies of space-time, quantum phenomena and particle interactions are encompassed in a unified framework.' 
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Barrow (1996), John D., and Frank J. Tipler, The Anthropic Cosmological Principle, Oxford University Press 1986, 1996 'This wide-ranging and detailed book explores the many ramifications of the Anthropic Cosmological Principle, covering the whole spectrum of human inquiry from Aristotle to Z bosons. Bringing a unique combination of skills and knowledge to the subject, John D. Barrow and Frank J. Tipler - two of the world's leading cosmologists - cover the definition and nature of life, the search for extraterrestrial intelligence, and the interpretation of the quantum theory in relation to the existence of observers.' 
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Bastin (1995), Ted, and C W Kilmister, Combinatorial Physics, World Scientific 1995 About this book (World Scientific) 'The authors aim to reinstate a spirit of philosophical enquiry in physics. They abandon the intuitive continuum concepts and build up constructively a combinatorial mathematics of process. This radical change alone makes it possible to calculate the coupling constants of the fundamental fields which — via high energy scattering — are the bridge from the combinatorial world into dynamics. The untenable distinction between what is ‘observed’, or measured, and what is not, upon which current quantum theory is based, is not needed. If we are to speak of mind, this has to be present — albeit in primitive form — at the most basic level, and not to be dragged in at one arbitrary point to avoid the difficulties about quantum observation. There is a growing literature on information-theoretic models for physics, but hitherto the two disciplines have gone in parallel. In this book they interact vitally.' 
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Brown (2018), Kevin, Reflections on Relativity, 2018 ' . . . general relativity teaches us that the principles of special relativity are applicable only over infinitesimal regions in the presence of gravitation, so in a sense the general theory restricts rather than generalizes the special theory. However, we can also regard special relativity as a theory of flat four-dimensional spacetime, characterized by the Minkowski metric (in suitable coordinates), and the general theory generalizes this by allowing the spacetime manifold to be curved, as represented by a wider class of metric tensors. It is remarkable that this generalization, which is so simple and natural from the geometrical standpoint, leads almost uniquely to a viable theory of gravitation.' (page 700) 
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Cantor, Georg, Contributions to the Founding of the Theory of Transfinite Numbers (Translated, with Introduction and Notes by Philip E B Jourdain), Dover 1895, 1897, 1955 Jacket: 'One of the greatest mathematical classics of all time, this work established a new field of mathematics which was to be of incalculable importance in topology, number theory, analysis, theory of functions, etc, as well as the entire field of modern logic.' 
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Cantor (1897, 1955), Georg, Contributions to the Founding of the Theory of Transfinite Numbers (Translated, with Introduction and Notes by Philip E B Jourdain), Dover 1895, 1897, 1955 Jacket: 'One of the greatest mathematical classics of all time, this work established a new field of mathematics which was to be of incalculable importance in topology, number theory, analysis, theory of functions, etc, as well as the entire field of modern logic.' 
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Casti (1996), John L, Five Golden Rules: Great Theories of 20th-Century Mathematics - and Why They Matter, John Wiley and Sons 1996 Preface: '[this book] is intended to tell the general reader about mathematics by showcasing five of the finest achievements of the mathematician's art in this [20th] century.' p ix. Treats the Minimax theorem (game theory), the Brouwer Fixed-Point theorem (topology), Morse's theorem (singularity theory), the Halting theorem (theory of computation) and the Simplex method (optimisation theory). 
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Cercignani (2006), Carlo, Ludwig Boltzmann: The Man Who Trusted Atoms, Oxford University Press, USA 2006 'Cercignani provides a stimulating biography of a great scientist. Boltzmann's greatness is difficult to state, but the fact that the author is still actively engaged in research into some of the finer, as yet unresolved issues provoked by Boltzmann's work is a measure of just how far ahead of his time Boltzmann was. It is also tragic to read of Boltzmann's persecution by his contemporaries, the energeticists, who regarded atoms as a convenient hypothesis, but not as having a definite existence. Boltzmann felt that atoms were real and this motivated much of his research. How Boltzmann would have laughed if he could have seen present-day scanning tunnelling microscopy images, which resolve the atomic structure at surfaces! If only all scientists would learn from Boltzmann's life story that it is bad for science to persecute someone whose views you do not share but cannot disprove. One surprising fact I learned from this book was how research into thermodynamics and statistical mechanics led to the beginnings of quantum theory (such as Planck's distribution law, and Einstein's theory of specific heat). Lecture notes by Boltzmann also seem to have influenced Einstein's construction of special relativity. Cercignani's familiarity with Boltzmann's work at the research level will probably set this above other biographies of Boltzmann for a very long time to come.' Dr David J Bottomley  
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Cohen (1980), Paul J, Set Theory and the Continuum Hypothesis, Benjamin/Cummings 1966-1980 Preface: 'The notes that follow are based on a course given at Harvard University, Spring 1965. The main objective was to give the proof of the independence of the continuum hypothesis [from the Zermelo-Fraenkel axioms for set theory with the axiom of choice included]. To keep the course as self contained as possible we included background materials in logic and axiomatic set theory as well as an account of Gödel's proof of the consistency of the continuum hypothesis. . . .'  
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Dauben (1990), Joseph Warren, Georg Cantor: His Mathematics and Philosophy of the Infinite, Princeton University Press 1990 Jacket: 'One of the greatest revolutions in mathematics occurred when Georg Cantor (1843-1918) promulgated his theory of transfinite sets. . . . Set theory has been widely adopted in mathematics and philosophy, but the controversy surrounding it at the turn of the century remains of great interest. Cantor's own faith in his theory was partly theological. His religious beliefs led him to expect paradox in any concept of the infinite, and he always retained his belief in the utter veracity of transfinite set theory. Later in his life, he was troubled by attacks of severe depression. Dauben shows that these played an integral part in his understanding and defense of set theory.' 
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Davies (1992), Paul, The Mind of God: Science and the Search for Ultimate Meaning, Penguin Books 1992 'Paul Davies' "The Mind of God: Science and the Search for Ultimate Meaning" explores how modern science is beginning to shed light on the mysteries of our existence. Is the universe - and our place in it - the result of random chance, or is there an ultimate meaning to existence? Where did the laws of nature come from? Were they created by a higher force, or can they be explained in some other way? How, for example, could a mechanism as complex as an eye have evolved without a creator? Paul Davies argues that the achievement of science and mathematics in unlocking the secrets of nature mean that there must be a deep and significant link between the human mind and the organization of the physical world. . . . ' 
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Deutsch (1997), David, The Fabric of Reality: The Science of Parallel Universes - and its Implications, Allen Lane Penguin Press 1997 Jacket: 'Quantum physics, evolution, computation and knowledge - these four strands of scientific theory and philosophy have, until now, remained incomplete explanations of the way the universe works. . . . Oxford scholar DD shows how they are so closely intertwined that we cannot properly understand any one of them without reference to the other three. . . .' 
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Dirac, P A M, The Principles of Quantum Mechanics (4th ed), Oxford UP/Clarendon 1983 Jacket: '[this] is the standard work in the fundamental principles of quantum mechanics, indispensible both to the advanced student and the mature research worker, who will always find it a fresh source of knowledge and stimulation.' (Nature)  
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Feynman (1965), Richard P, and Albert P Hibbs, Quantum Mechanics and Path Integrals, McGraw Hill 1965 Preface: 'The fundamental physical and mathematical concepts which underlie the path integral approach were first developed by R P Feynman in the course of his graduate studies at Princeton, ... . These early inquiries were involved with the problem of the infinite self-energy of the electron. In working on that problem, a "least action" principle was discovered [which] could deal successfully with the infinity arising in the application of classical electrodynamics.' As described in this book. Feynman, inspired by Dirac, went on the develop this insight into a fruitful source of solutions to many quantum mechanical problems.  
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Feynman (2002), Richard, Feynman Lectures on Gravitation, Westview Press 2002 Amazon Editorial Reviews Book Description 'The Feynman Lectures on Gravitation are based on notes prepared during a course on gravitational physics that Richard Feynman taught at Caltech during the 1962-63 academic year. For several years prior to these lectures, Feynman thought long and hard about the fundamental problems in gravitational physics, yet he published very little. . . .. Characteristically, Feynman took an untraditional non-geometric approach to gravitation and general relativity based on the underlying quantum aspects of gravity. Hence, these lectures contain a unique pedagogical account of the development of Einstein's general theory of relativity as the inevitable result of the demand for a self-consistent theory of a massless spin-2 field (the graviton) coupled to the energy-momentum tensor of matter. This approach also demonstrates the intimate and fundamental connection between gauge invariance and the principle of equivalence.' 
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Feynman (2005), Richard Phillips, Feynman's Thesis: A New Approach to Quantum Mechanics, World Scientific Publishing Company 2005 Amazon editorial review: 'Editorial Reviews Review 'The young Feynman revealed here was full of invention, verve, and ambition. His new approach to quantum mechanics, after simmering for decades beneath the surface of theoretical physics, burst into new prominence in the 1970s. Now its influence is pervasive, and still expanding. Feynman's original presentation is not only uniquely clear, but also contains insights and perspectives that are not widely known, and might well provide ammunition for another explosion or two.' Frank Wilczek 
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Fortun (1998), Mike, and Herbert J Bernstein, Muddling Through: Pursuing Science and Truths in the Twenty-First Century, Counterpoint 1998 Amazon editorial review: 'Does science discover truths or create them? Does dioxin cause cancer or not? Is corporate-sponsored research valid or not? Although these questions reflect the way we're used to thinking, maybe they're not the best way to approach science and its place in our culture. Physicist Herbert J. Bernstein and science historian Mike Fortun, both of the Institute for Science and Interdisciplinary Studies (ISIS), suggest a third way of seeing, beyond taking one side or another, in Muddling Through: Pursuing Science and Truths in the 21st Century. While they deal with weighty issues and encourage us to completely rethink our beliefs about science and truth, they do so with such grace and humor that we follow with ease discussions of toxic-waste disposal, the Human Genome Project, and retooling our language to better fit the way science is actually done.' 
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Hawking (1975), Steven W, and G F R Ellis, The Large Scale Structure of Space-Time, Cambridge UP 1975 Preface: Einstein's General Theory of Relativity . . . leads to two remarkable predictions about the universe: first that the final fate of massive stars is to collapse behind an event horizon to form a 'black hole' which will contain a singularity; and secondly that there is a singularity in our past which constitutes, in some sense, a beginning to our universe. Our discussion is principally aimed at developing these two results.' 
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Hodges (1983), Andrew, Alan Turing: The Enigma, Burnett 1983 Author's note: '. . . modern papers often employ the usage turing machine. Sinking without a capital letter into the collective mathematical consciousness (as with the abelian group, or the riemannian manifold) is probably the best that science can offer in the way of canonisation.' (530) 
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James (1912), Grace, Green Willow & Other Japanese Fairy Tales, Macmillan & Co, Senate Random House 1912, 1996 Jacket: ' Japanese Fairy Tales brings together a magnificent selection o dtories from all parts of the Land of the Rising Sun. Drawing on richly imaginative folk tradition, and set against the backdrop of Japan's mythic past, the tales are suffused with the essence of this magincal land. 
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Jech (1997), Thomas, Set Theory, Springer 1997 Jacket: 'This book covers major areas of modern set theory: cardinal arithmetic, constructible sets, forcing and Boolean-valued models, large cardinals and descriptive set theory. . . . It can be used as a textbook for a graduate course in set theory and can serve as a reference book.' 
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Joseph (2010), George Gheverghese, The Crest of the Peacock: Non-European Roots of Mathematics, Princeton University Press 2010 'From the Ishango Bone of central Africa and the Inca quipu of South America to the dawn of modern mathematics, The Crest of the Peacock makes it clear that human beings everywhere have been capable of advanced and innovative mathematical thinking. George Gheverghese Joseph takes us on a breathtaking multicultural tour of the roots and shoots of non-European mathematics. He shows us the deep influence that the Egyptians and Babylonians had on the Greeks, the Arabs' major creative contributions, and the astounding range of successes of the great civilizations of India and China.' 
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Kaku (1998), Michio, Introduction to Superstrings and M-Theory (Graduate Texts in Contemporary Physics), Springer 1998 ' Called by some "the theory of everything," superstrings may solve a problem which has eluded physicists for the past 50 years -- the final unification of the two great theories of the twentieth century, general relativity and quantum field theory. This is a course-tested comprehensive introductory graduate text on superstrings which stresses the most current areas of interest, not covered in other presentation, including: string field theory, multi loops, Teichmueller spaces, conformal field theory, and four-dimensional strings. The book begins with a simple discussion of point particle theory, and uses the Feynman path integral technique to unify the presentation of superstrings. Prerequisites are an aquaintance with quantum mechanics and relativity. This second edition has been revised and updated throughout.' 
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Kaku (2021), Michio, The God Equation: The Quest for a Theory of Everything , Doubleday 2021 ' This is the story of a quest: to find a Theory of Everything. Einstein dedicated his life to seeking this elusive Holy Grail, a single, revolutionary 'god equation' which would tie all the forces in the universe together, yet never found it. Some of the greatest minds in physics took up the search, from Stephen Hawking to Brian Greene. None have yet succeeded. In The God Equation, renowned theoretical physicist Michio Kaku takes the reader on a mind-bending ride through the twists and turns of this epic journey: a mystery that has fascinated him for most of his life. He guides us through the key debates in modern physics, from Newton's law of gravity via relativity and quantum mechanics to the latest developments in string theory.  
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Khinchin (1998), Aleksandr Yakovlevich, The Mathematical Foundations of Quantum Statistics, Dover 1998 'In the area of quantum statistics, I show that a rigorous mathematical basis of the computational formulas of statistical physics . . . may be obtained from an elementary application of the well-developed limit theorems of the theory of probability.' 
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Kolmogorov, Andrey Nikolaevich, and Nathan Morrison (Translator) (With an added bibliography by A T Bharucha-Reid), Foundations of the Theory of Probability, Chelsea 1956 Preface: 'The purpose of this monograph is to give an axiomatic foundation for the theory of probability. . . . This task would have been a rather hopeless one before the introduction of Lebesgue's theories of measure and integration. However, after Lebesgue's publication of his investigations, the analogies between measure of a set and mathematical expectation of a random variable became apparent. These analogies allowed of further extensions; thus, for example, various properties of independent random variables were seen to be in complete analogy with the corresponding properties of orthogonal functions . . .' 
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Kolmogorov (1956), Andrey Nikolaevich, and Nathan Morrison (Translator) (With an added bibliography by A T Bharucha-Reid), Foundations of the Theory of Probability, Chelsea 1956 Preface: 'The purpose of this monograph is to give an axiomatic foundation for the theory of probability. . . . This task would have been a rather hopeless one before the introduction of Lebesgue's theories of measure and integration. However, after Lebesgue's publication of his investigations, the analogies between measure of a set and mathematical expectation of a random variable became apparent. These analogies allowed of further extensions; thus, for example, various properties of independent random variables were seen to be in complete analogy with the corresponding properties of orthogonal functions . . .' 
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Kolmogorov (1956), Andrey Nikolaevich, and Nathan Morrison (Translator) (With an added bibliography by A T Bharucha-Reid), Foundations of the Theory of Probability, Chelsea 1956 Preface: 'The purpose of this monograph is to give an axiomatic foundation for the theory of probability. . . . This task would have been a rather hopeless one before the introduction of Lebesgue's theories of measure and integration. However, after Lebesgue's publication of his investigations, the analogies between measure of a set and mathematical expectation of a random variable became apparent. These analogies allowed of further extensions; thus, for example, various properties of independent random variables were seen to be in complete analogy with the corresponding properties of orthogonal functions . . .' 
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Kuhn (1996), Thomas S, The Structure of Scientific Revolutions, U of Chicago Press 1962, 1970, 1996 Introduction: 'a new theory, however special its range of application, is seldom just an increment to what is already known. Its assimilation requires the reconstruction of prior theory and the re-evaluation of prior fact, an intrinsically revolutionary process that is seldom completed by a single man, and never overnight.' [p 7]  
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Lonergan (1997), Bernard J F, and Robert M. Doran, Frederick E. Crowe (eds), Verbum : Word and Idea in Aquinas (Collected Works of Bernard Lonergan volume 2), University of Toronto Press 1997 Jacket: 'Verbum is a product of Lonergan's eleven years of study of the thought of Thomas Aquinas. The work is considered by many to be a breakthrough in the history of Lonergan's theology . . .. Here he interprets aspects in the writing of Aquinas relevant to trinitarian theory and, as in most of Lonergan's work, one of the principal aims is to assist the reader in the search to understand the workings of the human mind.' 
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Macmillan (2020), Margaret, War: How Conflict Shaped Us, Profile Books 2020 ' In War, Professor Margaret MacMillan explores the deep links between society and war and the questions they raise. We learn when war began - whether among early homo sapiens or later, as we began to organise ourselves into tribes and settle in communities. We see the ways in which war reflects changing societies and how war has brought change - for better and worse. Economies, science, technology, medicine, culture: all are instrumental in war and have been shaped by it - without conflict it we might not have had penicillin, female emancipation, radar or rockets. Throughout history, writers, artists, film-makers, playwrights, and composers have been inspired by war - whether to condemn, exalt or simply puzzle about it. If we are never to be rid of war, how should we think about it and what does that mean for peace? 
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Newton (1972), Isaac, Philosophiae Naturalis Principia Mathematica , Harvard University Press 1972 One of the most important contributions to human knowledge. First translated from the Latin by Andrew Motte in 1729,  
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Nielsen, Michael A, and Isaac L Chuang, Quantum Computation and Quantum Information, Cambridge University Press 2000 Review: A rigorous, comprehensive text on quantum information is timely. The study of quantum information and computation represents a particularly direct route to understanding quantum mechanics. Unlike the traditional route to quantum mechanics via Schroedinger's equation and the hydrogen atom, the study of quantum information requires no calculus, merely a knowledge of complex numbers and matrix multiplication. In addition, quantum information processing gives direct access to the traditionally advanced topics of measurement of quantum systems and decoherence.' Seth Lloyd, Department of Quantum Mechanical Engineering, MIT, Nature 6876: vol 416 page 19, 7 March 2002. 
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Nielsen (2000), Michael A, and Isaac L Chuang, Quantum Computation and Quantum Information, Cambridge University Press 2000 Review: A rigorous, comprehensive text on quantum information is timely. The study of quantum information and computation represents a particularly direct route to understanding quantum mechanics. Unlike the traditional route to quantum mechanics via Schroedinger's equation and the hydrogen atom, the study of quantum information requires no calculus, merely a knowledge of complex numbers and matrix multiplication. In addition, quantum information processing gives direct access to the traditionally advanced topics of measurement of quantum systems and decoherence.' Seth Lloyd, Department of Quantum Mechanical Engineering, MIT, Nature 6876: vol 416 page 19, 7 March 2002. 
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Pais (1982), Abraham, 'Subtle is the Lord...': The Science and Life of Albert Einstein, Oxford UP 1982 Jacket: In this . . . major work Abraham Pais, himself an eminent physicist who worked alongside Einstein in the post-war years, traces the development of Einstein's entire ouvre. . . . Running through the book is a completely non-scientific biography . . . including many letters which appear in English for the first time, as well as other information not published before.' [Raffiniert ist der Herr Gott, aber boshaft is er nicht] 
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Polya, George, and Gordon Latta, Complex Variables, John Wiley & Sons Inc 1974 Preface: 'After having lectured for several decades on complex variables to prospective engineers and physicists, I have definite and, I hope, not unrealistic ideas about their requirements and preferences. . . .
I hope that this book is useful not only to future engineers and physicists, but also to future mathematicians. Mathematical concepts and facts gain in vividness and clarity if they are well connected with the world around us and with general ideas, and if we obtain them by our own work through successive stages instead of in one lump.' 
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Streater (2000), Raymond F, and Arthur S Wightman, PCT, Spin, Statistics and All That, Princeton University Press 2000 Amazon product description: 'PCT, Spin and Statistics, and All That is the classic summary of and introduction to the achievements of Axiomatic Quantum Field Theory. This theory gives precise mathematical responses to questions like: What is a quantized field? What are the physically indispensable attributes of a quantized field? Furthermore, Axiomatic Field Theory shows that a number of physically important predictions of quantum field theory are mathematical consequences of the axioms. Here Raymond Streater and Arthur Wightman treat only results that can be rigorously proved, and these are presented in an elegant style that makes them available to a broad range of physics and theoretical mathematics.' 
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Tanenbaum (1996), Andrew S, Computer Networks, Prentice Hall International 1996 Preface: 'The key to designing a computer network was first enunciated by Julius Caesar: Divide and Conquer. The idea is to design a network as a sequence of layers, or abstract machines, each one based upon the previous one. . . . This book uses a model in which networks are divided into seven layers. The structure of the book follows the structure of the model to a considerable extent.'  
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Tapsell (2014), Kieran, Potiphar's Wife: The Vatican's Secret and Child Sexual Abuse, ATF Press 2014 Back cover: 'For 1500 years the Catholic Church accepted that clergy who sexually abused children deserved to be stripped of their status as priests and then imprisoned. . . . That all changed in 1922 when Pope Pius XI issues his decree Crimen Sollicitationis that created a de facto 'privilege of clergy' by imposing the 'secret of the Holy Ofice' on all information obtained through the Church's canonical investigations. If the State did not know about these crimes, then there would be no State trials, and the matter could be treated as a purely canonical crime to be dealt with in secret in the Church courts.' 
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Veltman, Martinus, Facts and Mysteries in Elementary Particle Physics, World Scientific 2003 'Introduction: The twentieth century has seen an enormous progress in physics. The fundamental physics of the first half of the century was dominated by the theory of relativity, Einstein's theory of gravitation and the theory of quantum mechanics. The second half of the century saw the rise of elementary particle physics. . . . Through this development there has been a subtle change in point of view. In Einstein's theory space and time play an overwhelming dominant role. . . . The view that we would like to defend can perhaps best be explaned by an analogy. To us, space-time and the laws of quantum mechanics are like the decor, the setting of a play. The elementary articles are the actors, and physics is what they do. . . . Thus in this book the elementary particles are the central objects.' 
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Veltman (1994), Martinus, Diagrammatica: The Path to the Feynman Rules, Cambridge University Press 1994 Jacket: 'This book provides an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics. The aim is to make clear what the physical foundations of present-day field theory are, to clarify the physical content of Feynman rules, and to outline their domain of applicability. ... The book includes valuable appendices that review some essential mathematics, including complex spaces, matrices, the CBH equation, traces and dimensional regularization. ...' 
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Veltman (2003), Martinus, Facts and Mysteries in Elementary Particle Physics, World Scientific 2003 'Introduction: The twentieth century has seen an enormous progress in physics. The fundamental physics of the first half of the century was dominated by the theory of relativity, Einstein's theory of gravitation and the theory of quantum mechanics. The second half of the century saw the rise of elementary particle physics. . . . Through this development there has been a subtle change in point of view. In Einstein's theory space and time play an overwhelming dominant role. . . . The view that we would like to defend can perhaps best be explaned by an analogy. To us, space-time and the laws of quantum mechanics are like the decor, the setting of a play. The elementary articles are the actors, and physics is what they do. . . . Thus in this book the elementary particles are the central objects.' 
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von Neumann, John, and Robert T Beyer (translator), Mathematical Foundations of Quantum Mechanics, Princeton University Press 1983 Jacket: '. . . a revolutionary book that caused a sea change in theoretical physics. . . . JvN begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which JvN regards as the definitive form of quantum mechanics. . . . Regarded as a tour de force at the time of its publication, this book is still indispensable for those interested in the fundamental issues of quantum mechanics.' 
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Weinberg (1995), Steven, The Quantum Theory of Fields Volume I: Foundations, Cambridge University Press 1995 Jacket: 'After a brief historical outline, the book begins anew with the principles about which we are most certain, relativity and quantum mechanics, and then the properties of particles that follow from these principles. Quantum field theory then emerges from this as a natural consequence. The classic calculations of quantum electrodynamics are presented in a thoroughly modern way, showing the use of path integrals and dimensional regularization. The account of renormalization theory reflects the changes in our view of quantum field theory since the advent of effective field theories. The book's scope extends beyond quantum elelctrodynamics to elementary partricle physics and nuclear physics. It contains much original material, and is peppered with examples and insights drawn from the author's experience as a leader of elementary particle research. Problems are included at the end of each chapter. ' 
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Weyl (1985), Hermann, Space Time Matter (translated by Henry L Brose), Dover 1985 Amazon customer review: ' The birth of gauge theory by its author: This book bewitched several generations of physicists and students. Hermann Weyl was one of the very great mathematicians of this century. He was also a great physicist and an artist with ideas and words. In this book you will find, at a deep level, the philosophy, mathematics and physics of space-time. It appeared soon after Einstein's famous paper on General Relativity, and is, in fact, a magnificent exposition of it, or, rather, of a tentative generalization of it. The mathematical part is of the highest class, striving to put geometry to the forefront. Actually, the book introduced a far-reaching generalization of the theory of connections, with respect to the Levi-Civita theory. It was not a generalization for itself, but motivated by the dream (Einstein's) of including gravitation and electromagnetism in the same (geometrical) theory. The result was gauge theory, which, slightly modified and applied to quantum mechanics resulted in the theory which dominates present particle physics. Weyl's unified theory was proved wrong by Einstein, and his criticism alone, accepted by Weyl and included in the book, would justify the reading. Though wrong, Weyl's theory is so beautiful that Paul Dirac stated that nature could not afford neglecting such perfection, and that the theory was probably only misplaced. Prophetic words! . . . ' Henrique Fleming 
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Whitehead (1910, 1962), Alfred North, and Bertrand Arthur Russell, Principia Mathematica (Cambridge Mathematical Library), Cambridge University Press 1910, 1962 The great three-volume Principia Mathematica is deservedly the most famous work ever written on the foundations of mathematics. Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premisses and primitive ideas, and so to prove that mathematics is a development of logic. Not long after it was published, Goedel showed that the project could not completely succeed, but that in any system, such as arithmetic, there were true propositions that could not be proved.  
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Wiener (1996), Norbert, Cybernetics or Control and Communication in the Animal and the Machine, MIT Press 1996 The classic founding text of cybernetics. 
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Wilczek (2008), Frank, The Lightness of Being: Mass, Ether, and the Unification of Forces, Basic Books 2008 ' In this excursion to the outer limits of particle physics, Wilczek explores what quarks and gluons, which compose protons and neutrons, reveal about the manifestation of mass and gravity. A corecipient of the 2004 Nobel Prize in Physics, Wilczek knows what he’s writing about; the question is, will general science readers? Happily, they know what the strong interaction is (the forces that bind the nucleus), and in Wilczek, they have a jovial guide who adheres to trade publishing’s belief that a successful physics title will not include too many equations. Despite this injunction (against which he lightly protests), Wilczek delivers an approachable verbal picture of what quarks and gluons are doing inside a proton that gives rise to mass and, hence, gravity. Casting the light-speed lives of quarks against “the Grid,” Wilczek’s term for the vacuum that theoretically seethes with quantum activity, Wilczek exudes a contagious excitement for discovery. A near-obligatory acquisition for circulating physics collections.' --Gilbert Taylor  
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Zee (2010), Anthony, Quantum Field Theory in a Nutshell, Princeton University Press 2010 ' Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. This expanded edition features several additional chapters, as well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading.' 
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Zemanian (1996), Armen H, Transfiniteness for Graphs, Electrical Newtorks and Random Walks, Springer Verlag 1996 'A substantial introduction is followed by chapters covering transfinite graphs; connectedness problems; finitely structured transfinite graphs; transfinite electrical networks; permissively finitely structured networks; and a theory for random walks on a finitely structured transfinite network. Appendices present brief surveys of ordinal and cardinal numbers; summable series; and irreducible and reversible Markov chains. Accessible to those familiar with basic ideas about graphs, Hilbert spaces, and resistive electrical networks. (Annotation copyright Book News, Inc. Portland, Or.)'  
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2019 redefinition of the SI base units - Wikipedia, 2019 redefinition of the SI base units - Wikipedia - the free encyclopedia, ' Effective 20 May 2019, the 144th anniversary of the Metre Convention, the SI base units were redefined in agreement with the International System of Quantities. In the redefinition, four of the seven SI base units – the kilogram, ampere, kelvin, and mole – were redefined by setting exact numerical values when expressed in SI units for the Planck constant (h), the elementary electric charge (e), the Boltzmann constant (kB), and the Avogadro constant (N_A), respectively. The second, metre, and candela were already defined by physical constants and were not subject to correction to their definitions.' back

Action potential - Wikipedia, Action potential - Wikipedia, the free encyclopedia, ' In physiology, an action potential (AP) occurs when the membrane potential of a specific cell location rapidly rises and falls: this depolarization then causes adjacent locations to similarly depolarize. Action potentials occur in several types of animal cells, called excitable cells, which include neurons, muscle cells, endocrine cells and in some plant cells. ' back

Ad Gentes (Vatican II), Decree on the Mission Activity of the Church, 'Divinely sent to the nations of the world to be unto them "a universal sacrament of salvation," the Church, driven by the inner necessity of her own catholicity, and obeying the mandate of her Founder (cf. Mark 16:16), strives ever to proclaim the Gospel to all men. The Apostles themselves, on whom the Church was founded, following in the footsteps of Christ, "preached the word of truth and begot churches." It is the duty of their successors to make this task endure "so that the word of God may run and be glorified (2 Thess. 3:1) and the kingdom of God be proclaimed and established throughout the world.' back

Alan Turing, On Computable Numbers, with an application to the Entscheidungsproblem, 'The "computable" numbers may be described briefly as the real numbers whose expressions as a decimal are calculable by some finite means. Although the subject of this paper is ostensibly the computable numbers, it is almost equally easy to define and investigate computable functions of an integral variable of a real or computable variable, computable predicates and so forth. . . . ' back

Algebraic closure - Wikipedia, Algebraic closure - Wikipedia, the free encyclopedia, I'n mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed. It is one of many closures in mathematics. Using Zorn's lemma, it can be shown that every field has an algebraic closure, and that the algebraic closure of a field K is unique up to an isomorphism that fixes every member of K. Because of this essential uniqueness, we often speak of the algebraic closure of K, rather than an algebraic closure of K. . . . The fundamental theorem of algebra states that the algebraic closure of the field of real numbers is the field of complex numbers.' back

Allegory of the cave - Wikipedia, Allegory of the cave - Wikipedia, the free encyclopedia, 'Plato has Socrates describe a gathering of people who have lived chained to the wall of a cave all of their lives, facing a blank wall. The people watch shadows projected on the wall by things passing in front of a fire behind them, and begin to designate names to these shadows. The shadows are as close as the prisoners get to viewing reality. He then explains how the philosopher is like a prisoner who is freed from the cave and comes to understand that the shadows on the wall do not make up reality at all, as he can perceive the true form of reality rather than the mere shadows seen by the prisoners.' back

Analogue Computer - Wikipedia, Analogue Computer - Wikipedia, the free encyclopedia, ' An analog computer or analogue computer is a type of computer that uses the continuous variation aspect of physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved. In contrast, digital computers represent varying quantities symbolically and by discrete values of both time and amplitude.' back

Andrea Falcon (Stanford Encyclopedia of Philosophy), Aristotle on Causality, ' Each Aristotelian science consists in the causal investigation of a specific department of reality. If successful, such an investigation results in causal knowledge; that is, knowledge of the relevant or appropriate causes. The emphasis on the concept of cause explains why Aristotle developed a theory of causality which is commonly known as the doctrine of the four causes. For Aristotle, a firm grasp of what a cause is, and how many kinds of causes there are, is essential for a successful investigation of the world around us.' back

Anthropic principle - Wikipedia, Anthropic principle - Wikipedia, the free encyclopedia, 'The anthropic principle (from Greek anthropos, meaning "human") is the philosophical consideration that observations of the universe must be compatible with the conscious and sapient life that observes it. Some proponents of the anthropic principle reason that it explains why the universe has the age and the fundamental physical constants necessary to accommodate conscious life. As a result, they believe it is unremarkable that the universe's fundamental constants happen to fall within the narrow range thought to be compatible with life.' back

Apophatic theology - Wikipedia, Apophatic theology - Wikipedia, the free encyclopedia, 'Apophatic theology (from Greek ἀπόφασις from ἀπόφημι - apophēmi, "to deny")—also known as negative theology or via negativa (Latin for "negative way")—is a theology that attempts to describe God, the Divine Good, by negation, to speak only in terms of what may not be said about the perfect goodness that is God. It stands in contrast with cataphatic theology.' back

Aquinas Summa I, 3, 1 Proemium, Of the Simplicity of God, 'Cognito de aliquo an sit, inquirendum restat quomodo sit, ut sciatur de eo quid sit. Sed quia de Deo scire non possumus quid sit, sed quid non sit, non possumus considerare de Deo quomodo sit, sed potius quomodo non sit. . . . Potest autem ostendi de Deo quomodo non sit, removendo ab eo ea quae ei non conveniunt, utpote compositionem, motum, et alia huiusmodi. Primo ergo inquiratur de simplicitate ipsius, per quam removetur ab eo compositio.' back

Aquinas, Summa I, 15, 1, Are there ideas in God?, ' . . . in other agents (the form of the thing to be made pre-exists) according to intelligible being, as in those that act by the intellect; and thus the likeness of a house pre-exists in the mind of the builder. And this may be called the idea of the house, since the builder intends to build his house like to the form conceived in his mind. As then the world was not made by chance, but by God acting by His intellect, as will appear later, there must exist in the divine mind a form to the likeness of which the world was made. And in this the notion of an idea consists.' back

Aquinas, Summa I, 25, 3, Is God omnipotent?, '. . . God is called omnipotent because He can do all things that are possible absolutely; which is the second way of saying a thing is possible. For a thing is said to be possible or impossible absolutely, according to the relation in which the very terms stand to one another, possible if the predicate is not incompatible with the subject, as that Socrates sits; and absolutely impossible when the predicate is altogether incompatible with the subject, as, for instance, that a man is a donkey.' back

Aquinas, Summa, I, 1, 2, Is sacred doctrine is a science?, 'I answer that, Sacred doctrine is a science. We must bear in mind that there are two kinds of sciences. There are some which proceed from a principle known by the natural light of intelligence, such as arithmetic and geometry and the like. There are some which proceed from principles known by the light of a higher science: thus the science of perspective proceeds from principles established by geometry, and music from principles established by arithmetic. So it is that sacred doctrine is a science because it proceeds from principles established by the light of a higher science, namely, the science of God and the blessed.' back

Aquinas, Summa, I, 14, 8, Is the knowledge of God the cause of things?, 'Now it is manifest that God causes things by His intellect, since His being is His act of understanding; and hence His knowledge must be the cause of things, in so far as His will is joined to it. Hence the knowledge of God as the cause of things is usually called the "knowledge of approbation".' back

Aquinas, Summa, I, 27, 1, Is there procession in God?, 'As God is above all things, we should understand what is said of God, not according to the mode of the lowest creatures, namely bodies, but from the similitude of the highest creatures, the intellectual substances; while even the similitudes derived from these fall short in the representation of divine objects. Procession, therefore, is not to be understood from what it is in bodies, either according to local movement or by way of a cause proceeding forth to its exterior effect, as, for instance, like heat from the agent to the thing made hot. Rather it is to be understood by way of an intelligible emanation, for example, of the intelligible word which proceeds from the speaker, yet remains in him. In that sense the Catholic Faith understands procession as existing in God.' back

Aquinas, Summa, I, 3, 7, Is God altogether simple?, 'I answer that, The absolute simplicity of God may be shown in many ways. First, from the previous articles of this question. For there is neither composition of quantitative parts in God, since He is not a body; nor composition of matter and form; nor does His nature differ from His "suppositum"; nor His essence from His existence; neither is there in Him composition of genus and difference, nor of subject and accident. Therefore, it is clear that God is nowise composite, but is altogether simple. . . . ' back

Aquinas, Summa: I, 14, 1, Is there knowledge in God?, ' I answer that, In God there exists the most perfect knowledge. . . . it is clear that the immateriality of a thing is the reason why it is cognitive; and according to the mode of immateriality is the mode of knowledge. Hence it is said in De Anima ii that plants do not know, because they are wholly material. But sense is cognitive because it can receive images free from matter, and the intellect is still further cognitive, because it is more separated from matter and unmixed, as said in De Anima iii. Since therefore God is in the highest degree of immateriality as stated above (Question 7, Article 1), it follows that He occupies the highest place in knowledge.' back

Aquinas, Summa: I, 14, 1, Is there knowledge in God?, ' Respondeo dicendum quod in Deo perfectissime est scientia. Ad cuius evidentiam, considerandum est quod cognoscentia a non cognoscentibus in hoc distinguuntur, quia non cognoscentia nihil habent nisi formam suam tantum; sed cognoscens natum est habere formam etiam rei alterius, nam species cogniti est in cognoscente. Unde manifestum est quod natura rei non cognoscentis est magis coarctata et limitata, natura autem rerum cognoscentium habet maiorem amplitudinem et extensionem. Propter quod dicit philosophus, III de anima, quod anima est quodammodo omnia. Coarctatio autem formae est per materiam. Unde et supra diximus quod formae, secundum quod sunt magis immateriales, secundum hoc magis accedunt ad quandam infinitatem. Patet igitur quod immaterialitas alicuius rei est ratio quod sit cognoscitiva; et secundum modum immaterialitatis est modus cognitionis. Unde in II de anima dicitur quod plantae non cognoscunt, propter suam materialitatem. Sensus autem cognoscitivus est, quia receptivus est specierum sine materia, et intellectus adhuc magis cognoscitivus, quia magis separatus est a materia et immixtus, ut dicitur in III de anima. Unde, cum Deus sit in summo immaterialitatis, ut ex superioribus patet, sequitur quod ipse sit in summo cognitionis. back

Aquinas: Summa I, 1, 2, Is sacred doctrine a science?, 'I answer that, Sacred doctrine is a science. We must bear in mind that there are two kinds of sciences. There are some which proceed from a principle known by the natural light of intelligence, such as arithmetic and geometry and the like. There are some which proceed from principles known by the light of a higher science: thus the science of perspective proceeds from principles established by geometry, and music from principles established by arithmetic. So it is that sacred doctrine is a science because it proceeds from principles established by the light of a higher science, namely, the science of God and the blessed.' back

Archdiocese of Baltimore, Baltimore Cathechism No. 1, 'A Catechism of Christian Doctrine, Prepared and Enjoined by Order of the Third Council of Baltimore, or simply the Baltimore Catechism, is the official national catechism for children in the United States. It was the standard Catholic religion school text in the United States from 1885 to the late 1960s.' back

Aristotle, Aristotle, Metaphysics, ' All men naturally desire knowledge. An indication of this is our esteem for the senses; for apart from their use we esteem them for their own sake, and most of all the sense of sight. Not only with a view to action, but even when no action is contemplated, we prefer sight, generally speaking, to all the other senses.The reason of this is that of all the senses sight best helps us to know things, and reveals many distinctions.' back

Aristotle (continuity), Physics V, iii, 'A thing that is in succession and touches is 'contiguous'. The 'continuous' is a subdivision of the contiguous: things are called continuous when the touching limits of each become one and the same and are, as the word implies, contained in each other: continuity is impossible if these extremities are two. This definition makes it plain that continuity belongs to things that naturally in virtue of their mutual contact form a unity. And in whatever way that which holds them together is one, so too will the whole be one, e.g. by a rivet or glue or contact or organic union. ' 227a10 sqq back

Atlas Detector - CERN, Detector & Technology, ' The detector itself is a many-layered instrument designed to detect some of the tiniest yet most energetic particles ever created on earth. It consists of six different detecting subsystems wrapped concentrically in layers around the collision point to record the trajectory, momentum, and energy of particles, allowing them to be individually identified and measured. A huge magnet system bends the paths of the charged particles so that their momenta can be measured as precisely as possible.' back

Augustine of Hippo - Wikipedia, Augustine of Hippo - Wikipedia, ' Augustine of Hippo, Latin: Aurelius Augustinus Hipponensis; 13 November 354 – 28 August 430), also known as Saint Augustine, was a theologian and philosopher of Berber origin and the bishop of Hippo Regius in Numidia, Roman North Africa. His writings influenced the development of Western philosophy and Western Christianity, and he is viewed as one of the most important Church Fathers of the Latin Church in the Patristic Period. His many important works include The City of God, On Christian Doctrine, and Confessions.' back

Bernard d'Espagnat (1979), The Quantum Theory and Reality, 'The doctrine that the world is made up of objects whose existence is independent of human consciousness turns out to be in conflict with quantum mechanics and with facts established by experiment'
Bernard d'Espagnat, "Quantum theory and reality", Scientific American 241, (November 1979): 5, 128. back

Beta function (physics) - Wikipedia, Beta function (physics) - Wikipedia, the free encyclopedia, ' In theoretical physics, specifically quantum field theory, a beta function, β(g), encodes the dependence of a coupling parameter, g, on the energy scale, μ, of a given physical process described by quantum field theory. It is defined as
β (g ) = ∂g / ∂ log ⁡μ,
and, because of the underlying renormalization group, it has no explicit dependence on μ, so it only depends on μ implicitly through g. This dependence on the energy scale thus specified is known as the running of the coupling parameter, a fundamental feature of scale-dependence in quantum field theory, and its explicit computation is achievable through a variety of mathematical techniques. ' back

Big Bang - Wikipedia, Big Bang - Wikipedia, the free encyclopedia, ' The Big Bang theory is the prevailing cosmological model explaining the existence of the observable universe from the earliest known periods through its subsequent large-scale evolution. The model describes how the universe expanded from an initial state of high density and temperature, and offers a comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, and large-scale structure. ' back

Born rule - Wikipedia, Born rule - Wikipedia, the free encyclopedia, 'The Born rule (also called the Born law, Born's rule, or Born's law) is a law of quantum mechanics which gives the probability that a measurement on a quantum system will yield a given result. It is named after its originator, the physicist Max Born. The Born rule is one of the key principles of the Copenhagen interpretation of quantum mechanics. There have been many attempts to derive the Born rule from the other assumptions of quantum mechanics, with inconclusive results. . . . The Born rule states that if an observable corresponding to a Hermitian operator A with discrete spectrum is measured in a system with normalized wave function (see bra-ket notation), then the measured result will be one of the eigenvalues λ of A, and the probability of measuring a given eigenvalue λ_i will equal <ψ|P_i|ψ> where P_i is the projection onto the eigenspace of A corresponding to λ_i'. back

Bose-Einstein statistics - Wikipedia, Bose-Einstein statistics - Wikipedia, the free encyclopedia, 'In statistical mechanics, Bose–Einstein statistics (or more colloquially B–E statistics) determines the statistical distribution of identical indistinguishable bosons over the energy states in thermal equilibrium.' back

Boson - Wikipedia, Boson - Wikipedia, the free encyclopedia, 'In particle physics, bosons are particles with an integer spin, as opposed to fermions which have half-integer spin. From a behaviour point of view, fermions are particles that obey the Fermi-Dirac statistics while bosons are particles that obey the Bose-Einstein statistics. They may be either elementary, like the photon, or composite, as mesons. All force carrier particles are bosons. They are named after Satyendra Nath Bose. In contrast to fermions, several bosons can occupy the same quantum state. Thus, bosons with the same energy can occupy the same place in space.' back

Brain size - Wikipedia, Brain size - Wikipedia, the free encyclopedia, 'The size of the brain is a frequent topic of study within the fields of anatomy and evolution. Brain size is sometimes measured by weight and sometimes by volume (via MRI scans or by skull volume). Neuroimaging intelligence testing can be used to study the size of the brain in males and females. One question that has been frequently investigated is the relation of brain size to intelligence.' back

Brouwer fixed point theorem - Wikipedia, Brouwer fixed point theorem - Wikipedia, the free encyclopedia, ' Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after Luitzen Brouwer. It states that for any continuous function f with certain properties there is a point x₀ such that f(x₀) = x₀. The simplest form of Brouwer's theorem is for continuous functions f from a disk D to itself. A more general form is for continuous functions from a convex compact subset K of Euclidean space to itself.' back

Calculus of variations - Wikipedia, Calculus of variations - Wikipedia, the free encylopedia, ' The calculus of variations may be said to begin with Newton's minimal resistance problem in 1687, followed by the brachistochrone curve problem raised by Johann Bernoulli (1696). It immediately occupied the attention of Jakob Bernoulli and the Marquis de l'Hôpital, but Leonhard Euler first elaborated the subject, beginning in 1733. Lagrange was influenced by Euler's work to contribute significantly to the theory. After Euler saw the 1755 work of the 19-year-old Lagrange, Euler dropped his own partly geometric approach in favor of Lagrange's purely analytic approach and renamed the subject the calculus of variations in his 1756 lecture Elementa Calculi Variationum.' back

Cantor's theorem - Wikipedia, Cantor's theorem - Wikipedia, the free encyclopedia, ' In elementary set theory, Cantor's theorem is a fundamental result which states that, for any set A, the set of all subsets of A (the power set of A, denoted by P(A) ) has a strictly greater cardinality than A itself. For finite sets, Cantor's theorem can be seen to be true by simple enumeration of the number of subsets. Counting the empty set as a subset, a set with n members has a total of 2ⁿ subsets, so that if card (A) = n, then card (P(A)) = 2ⁿ, and the theorem holds because 2ⁿ > n for all non-negative integers.' back

Catherine & Johnathan Karoly, Heitor Villa-Lobos: The Jet Whistle, ' Villa-Lobos never forgot his “musical education” – the Rio street bands, the trips to the Amazon, and the music of the movie halls and theaters of his teen-age years. He fused these diverse influences into a powerfully nationalist musical voice. Villa-Lobos composed Assobio a Jato (The Jet Whistle) in New York in 1950. The composer named his work to describe the technique he calls on the flutist to use during its last movement. To produce the effect, the player blows directly and forcefully into the flute with his or her mouth almost covering the mouthpiece. Combined with a glissando, the resulting whistle sounds like a jet taking off.' back

Catholic Catechism: §§ 385-412, Satan, '391 Behind the disobedient choice of our first parents lurks a seductive voice, opposed to God, which makes them fall into death out of envy. Scripture and the Church's Tradition see in this being a fallen angel, called "Satan" or the "devil". The Church teaches that Satan was at first a good angel, made by God: "The devil and the other demons were indeed created naturally good by God, but they became evil by their own doing." ' back

Christianity - Wikipedia, Christianity - Wikipedia, the free encyclopedia, ' Christianity is an Abrahamic monotheistic religion based on the life and teachings of Jesus of Nazareth. Its adherents, known as Christians, believe that Jesus is the Christ, whose coming as the messiah was prophesied in the Hebrew Bible, called the Old Testament in Christianity, and chronicled in the New Testament. It is the world's largest religion, with about 2.4 billion followers.' back

Christopher Shields (Stanford Encyclopedia of Philosophy), The Active Mind of De Anima III 5 , ' After characterizing the mind (nous) and its activities in De Animaiii 4, Aristotle takes a surprising turn. In De Anima iii 5, he introduces an obscure and hotly disputed subject: the active mind or active intellect (nous poiêtikos). Controversy surrounds almost every aspect of De Anima iii 5, not least because in it Aristotle characterizes the active mind—a topic mentioned nowhere else in his entire corpus—as ‘separate and unaffected and unmixed, being in its essence actuality’ (chôristos kai apathês kai amigês, tê ousia energeia; DA iii 5, 430a17–18) and then also as ‘deathless and everlasting’ (athanaton kai aidion; DA iii 5, 430a23). This comes as no small surprise to readers of De Anima, because Aristotle had earlier in the same work treated the mind (nous) as but one faculty (dunamis) of the soul (psuchê), and he had contended that the soul as a whole is not separable from the body (DA ii 1, 413a3–5). back

Classical mechanics - Wikipedia, Classical mechanics - Wikipedia, the free encyclopedia, 'Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. It produces very accurate results within these domains, and is one of the oldest and largest subjects in science and technology.' back

Claude E Shannon, A Mathematical Theory of Communication, 'The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point. Frequently the messages have meaning; that is they refer to or are correlated according to some system with certain physical or conceptual entities. These semantic aspects of communication are irrelevant to the engineering problem. The significant aspect is that the actual message is one selected from a set of possible messages.' back

Claude Shannon (1949), Communication in the Presence of Noise, 'A method is developed for representing any communication system geometrically. Messages and the corresponding signals are points in two “function spaces,” and the modulation process is a mapping of one space into the other. Using this representation, a number of results in communication theory are deduced concerning expansion and compression of bandwidth and the threshold effect. Formulas are found for the maximum rate of transmission of binary digits over a system when the signal is perturbed by various types of noise. Some of the properties of “ideal” systems which transmit at this maximum rate are discussed. The equivalent number of binary digits per second for certain information sources is calculated.' [C. E. Shannon , “Communication in the presence of noise,” Proc. IRE, vol. 37, pp. 10–21, Jan. 1949.] back

Codec - Wikipedia, Codec - Wikipedia, the free encyclopedia, 'A codec is a device or computer program capable of encoding or decoding a digital data stream or signal. Codec is a portmanteau of coder-decoder or, less commonly, compressor-decompressor.' back

Complete theory - Wikipedia, Complete theory - Wikipedia - Wikipedia, the free encyclopedia, 'I In mathematical logic, a theory is complete if, for every closed formula in the theory's language, that formula or its negation is demonstrable. Recursively axiomatizable first-order theories that are consistent and rich enough to allow general mathematical reasoning to be formulated cannot be complete, as demonstrated by Gödel's first incompleteness theorem. This sense of complete is distinct from the notion of a complete logic, which asserts that for every theory that can be formulated in the logic, all semantically valid statements are provable theorems (for an appropriate sense of "semantically valid"). Gödel's completeness theorem is about this latter kind of completeness. ' back

Completeness of the real numbers - Wikipedia, Completeness of the real numbers - Wikipedia, the free encyclopedia, 'Intuitively, completeness implies that there are not any “gaps” (in Dedekind's terminology) or “missing points” in the real number line. . . . Depending on the construction of the real numbers used, completeness may take the form of an axiom (the completeness axiom), or may be a theorem proven from the construction. There are many equivalent forms of completeness, the most prominent being Dedekind completeness and Cauchy completeness (completeness as a metric space).' back

Complex number - Wikipedia, Complex number - Wikipedia, the free encyclopedia, 'IA complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, which satisfies the equation i² = −1. In this expression, a is the real part and b is the imaginary part of the complex number. Complex numbers extend the concept of the one-dimensional number line to the two-dimensional complex plane (also called Argand plane) by using the horizontal axis for the real part and the vertical axis for the imaginary part.' back

Complex plane - Wikipedia, Complex plane - Wikipedia, the free encuclopedia, ' In mathematics, the complex plane is a geometric representation of the complex numbers established by the real axis and the orthogonal imaginary axis. It can be thought of as a modified Cartesian plane, with the real part of a complex number represented by a displacement along the x-axis, and the imaginary part by a displacement along the y-axis.' back

Computability theory - Wikipedia, Computability theory - Wikipedia, the free encyclopedia, 'Computability theory, also called recursion theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown to include the study of generalized computability and definability. In these areas, recursion theory overlaps with proof theory and effective descriptive set theory. The basic questions addressed by recursion theory are "What does it mean for a function from the natural numbers to themselves to be computable?" and "How can noncomputable functions be classified into a hierarchy based on their level of noncomputability?". The answers to these questions have led to a rich theory that is still being actively researched.' back

Computer network - Wikipedia, Computer network - Wikipedia the free encyclopedia, 'A computer network, or simply a network, is a collection of computers and network hardware interconnected by communication channels that allow sharing of resources and information. . . . The best known computer network is the Internet. . . . Computer networking can be considered a branch of electrical engineering, telecommunications, computer science, information technology or computer engineering, since it relies upon the theoretical and practical application of the related disciplines.' back

Cosmological constant problem - Wikipedia, Cosmological constant problem - Wikipedia, the free encyclopedia, 'In cosmology, the cosmological constant problem or vacuum catastrophe is the disagreement between measured values of the vacuum energy density (the small value of the cosmological constant) and the zero-point energy suggested by quantum field theory. Depending on the assumptions, the discrepancy ranges from 40 to more than 100 orders of magnitude, a state of affairs described by Hobson et al. (2006) as "the worst theoretical prediction in the history of physics." ' back

Delay line memory - Wikipedia, Delay line memory - Wikipedia, the free encyclopedia, ' Delay line memory is a form of computer memory, now obsolete, that was used on some of the earliest digital computers. Like many modern forms of electronic computer memory, delay line memory was a refreshable memory, but as opposed to modern random-access memory, delay line memory was sequential-access.' back

Differentiable manifold - Wikipedia, Differentiable manifold - Wikipedia, the free encyclopedia, ' In mathematics, a differentiable manifold is a type of manifold that is locally similar enough to a linear space to allow one to do calculus. Any manifold can be described by a collection of charts, also known as an atlas. One may then apply ideas from calculus while working within the individual charts, since each chart lies within a linear space to which the usual rules of calculus apply. If the charts are suitably compatible (namely, the transition from one chart to another is differentiable), then computations done in one chart are valid in any other differentiable chart.' back

Double-slit experiment - Wikipedia, Double-slit experiment - Wikipedia, the free encyclopedia, 'In the double-slit experiment, light is shone at a solid thin plate that has two slits cut into it. A photographic plate is set up to record what comes through those slits. One or the other slit may be open, or both may be open. . . . The most baffling part of this experiment comes when only one photon at a time is fired at the barrier with both slits open. The pattern of interference remains the same as can be seen if many photons are emitted one at a time and recorded on the same sheet of photographic film. The clear implication is that something with a wavelike nature passes simultaneously through both slits and interferes with itself — even though there is only one photon present. (The experiment works with electrons, atoms, and even some molecules too.)' back

Eigenvalues and eigenvectors - Wikipedia, Eigenvalues and eigenvectors - Wikipedia, the free encyclopedia, ' In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by λ, is the factor by which the eigenvector is scaled. Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated. ' back

Einstein, Podolsky & Rosen (1935), Can the Quantum Mechanical Description of Physical Reality be Considered Complete?, A PDF of the classic paper. 'In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system. In quantum mechanics in the case of two physical quantities described by non-commuting operators, the knowledge of one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these two quantities cannot have simultaneous reality. Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that if (1) is false then (2) is also false, One is thus led to conclude that the description of reality given by the wave function is not complete.' back

Einstein, Podolsky and Rosen, Can the Quantum Mechanical Description of Physical Reality be Considered Complete?, A PDF of the classic paper. 'In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system. In quantum mechanics in the case of two physical quantities described by non-commuting operators, the knowledge of one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these two quantities cannot have simultaneous reality. Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that if (1) is false then (2) is also false, One is thus led to conclude that the description of reality given by the wave function is not complete.' back

Entropy - Wikipedia, Entropy - Wikipedia, the free encyclopedia, 'In statistical mechanics, entropy is an extensive property of a thermodynamic system. It is closely related to the number Ω of microscopic configurations (known as microstates) that are consistent with the macroscopic quantities that characterize the system (such as its volume, pressure and temperature). Under the assumption that each microstate is equally probable, the entropy S is the natural logarithm of the number of microstates, multiplied by the Boltzmann constant kB. Formally (assuming equiprobable microstates), S = k B ln ⁡ Ω . ' back

Entscheidungsproblem - Wikipedia, Entscheidungsproblem - Wikipedia, the free encyclopedia, 'In mathematics, the Entscheidungsproblem (. . . German for 'decision problem') is a challenge posed by David Hilbert in 1928. The Entscheidungsproblem asks for an algorithm that will take as input a description of a formal language and a mathematical statement in the language and produce as output either "True" or "False" according to whether the statement is true or false. . . . In 1936 and 1937 Alonzo Church and Alan Turing respectively, published independent papers showing that it is impossible to decide algorithmically whether statements in arithmetic are true or false, and thus a general solution to the Entscheidungsproblem is impossible. This result is now known as Church's Theorem or the Church–Turing Theorem (not to be confused with the Church–Turing thesis).' back

(ε, δ)-definition of limit - Wikipedia, (ε, δ)-definition of limit - Wikipedia, the free encyclopedia, 'In calculus, the (ε, δ)-definition of limit ("epsilon-delta definition of limit") is a formalization of the notion of limit. It was first given by Bernard Bolzano in 1817. Augustin-Louis Cauchy never gave an (ε, δ) definition of limit in his Cours d'Analyse, but occasionally used ε, δ arguments in proofs. The definitive modern statement was ultimately provided by Karl Weierstrass.' back

Eternity of the world - Wikipedia, Eternity of the world - Wikipedia, the free encyclopedia, ' The eternity of the world is the question of whether the world has a beginning in time or has existed from eternity. It was a concern for both ancient philosophers and the medieval theologians and medieval philosophers of the 13th century. The problem became a focus of a dispute in the 13th century, when some of the works of Aristotle, who believed in the eternity of the world, were rediscovered in the Latin West. This view conflicted with the view of the Catholic Church that the world had a beginning in time. The Aristotelian view was prohibited in the Condemnations of 1210–1277.' back

Euclidean geometry - Wikipedia, Euclidean geometry - Wikipedia, the free encyclopedia, ' Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions (theorems) from these. . . . The Elements begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of formal proof. It goes on to the solid geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, explained in geometrical language.' back

Euler's formula - Wikipedia, Euler's formula - Wikipedia, the free encyclopedia, 'Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Richard Feynman called Euler's formula "our jewel" and "the most remarkable formula in mathematics". (Feynman, Richard P. (1977). The Feynman Lectures on Physics, vol. I. Addison-Wesley, p. 22-10. ISBN 0-201-02010-6.) back

Evolution - Wikipedia, Evolution - Wikipedia, the free encyclopedia, '. . . Charles Darwin and Alfred Wallace were the first to formulate a scientific argument for the theory of evolution by means of natural selection. Evolution by natural selection is a process that is inferred from three facts about populations: 1) more offspring are produced than can possibly survive, 2) traits vary among individuals, leading to different rates of survival and reproduction, and 3) trait differences are heritable. . . . ' back

Fermi-Dirac statistics - Wikipedia, Fermi-Dirac statistics - Wikipedia, the fre encyclopedia, 'In statistical mechanics, Fermi-Dirac statistics is a particular case of particle statistics developed by Enrico Fermi and Paul Dirac that determines the statistical distribution of fermions over the energy states for a system in thermal equilibrium. In other words, it is the distribution of the probabilities that each possible energy levels is occupied by a fermion. back

Fermion - Wikipedia, Fermion - Wikipedia, the free encyclopedia, 'In particle physics, fermions are particles with a half-integer spin, such as protons and electrons. They obey the Fermi-Dirac statistics and are named after Enrico Fermi. In the Standard Model there are two types of elementary fermions: quarks and leptons. . . . In contrast to bosons, only one fermion can occupy a quantum state at a given time (they obey the Pauli Exclusion Principle). Thus, if more than one fermion occupies the same place in space, the properties of each fermion (e.g. its spin) must be different from the rest. Therefore fermions are usually related with matter while bosons are related with radiation, though the separation between the two is not clear in quantum physics. back

Feynman, Leighton & Sands FLP III:01, Chapter 1: Quantum Behaviour, 'The gradual accumulation of information about atomic and small-scale behavior during the first quarter of the 20th century, which gave some indications about how small things do behave, produced an increasing confusion which was finally resolved in 1926 and 1927 by Schrödinger, Heisenberg, and Born. They finally obtained a consistent description of the behavior of matter on a small scale. We take up the main features of that description in this chapter.' back

Feynman, Leighton & Sands FLP III:03, Chapter 3: Probability Amplitudes, 'We will begin in this chapter by dealing with some general quantum mechanical ideas. Some of the statements will be quite precise, others only partially precise. It will be hard to tell you as we go along which is which, but by the time you have finished the rest of the book, you will understand in looking back which parts hold up and which parts were only explained roughly. The chapters which follow this one will not be so imprecise. In fact, one of the reasons we have tried carefully to be precise in the succeeding chapters is so that we can show you one of the most beautiful things about quantum mechanics—how much can be deduced from so little.' back

Feynman, Leighton & Sands FLP III:08, Chapter 8: The Hamiltonian Matrix, 'One problem then in describing nature is to find a suitable representation for the base states. But that’s only the beginning. We still want to be able to say what “happens.” If we know the “condition” of the world at one moment, we would like to know the condition at a later moment. So we also have to find the laws that determine how things change with time. We now address ourselves to this second part of the framework of quantum mechanics—how states change with time.' back

Feynman, Leighton and Sands FLP II_02, Chapter 2: Differential Calculus of Vector Fields, ' Ideas such as the field lines, capacitance, resistance, and inductance are, for such purposes, very useful. So we will spend much of our time analyzing them. In this way we will get a feel as to what should happen in different electromagnetic situations. On the other hand, none of the heuristic models, such as field lines, is really adequate and accurate for all situations. There is only one precise way of presenting the laws, and that is by means of differential equations. They have the advantage of being fundamental and, so far as we know, precise. If you have learned the differential equations you can always go back to them. There is nothing to unlearn.' back

Form of the Good - Wikipedia, Form of the Good - Wikipedia, the free encyclopedia, ' "Form of the Good", or more literally "the idea of the good" (ἡ τοῦ ἀγαθοῦ ἰδέα) is a concept in the philosophy of Plato. It is described in Plato's dialogue the Republic (508e2–3), speaking through the character of Socrates. This form is the one that allows a philosopher-in-training to advance to a philosopher-king. It cannot be clearly seen or explained, but it is the form that allows one to realize all the other forms. The definition of the Good is a perfect, eternal, and changeless Form, existing outside space and time, in which particular good things share.' back

Formalism (mathematics) - Wikipedia, Formalism (mathematics) - Wikipedia, the free encyclopedia, ' In foundations of mathematics, philosophy of mathematics, and philosophy of logic, formalism is a theory that holds that statements of mathematics and logic can be thought of as statements about the consequences of certain string manipulation rules. For example, Euclidean geometry can be seen as a game whose play consists in moving around certain strings of symbols called axioms according to a set of rules called "rules of inference" to generate new strings. In playing this game one can "prove" that the Pythagorean theorem is valid because the string representing the Pythagorean theorem can be constructed using only the stated rules.' back

Frank Wilczek (1999), Quantum Field Theory, ' What are the essential features of quantum field theory? This question has no sharp answer. Theoretical physicists are very flexible in adapting their tools, and no axiomization can keep up with them. However I think it is fair to say that there are two characteristic, core ideas of quantum field theory. First: The basic dynamical degrees of freedom are operator functions of space and time – quantum fields, that obey appropriate commutation relations. Second: The interactions of these fields are local in space and time.' back

Gaussian curvature - Wikipedia, Gaussian curvature - Wikipedia, the free encyclopedia, ' In differential geometry, the Gaussian curvature or Gauss curvature of a point on a surface is the product of the principal curvatures, κ1 and κ2, of the given point. It is an intrinsic measure of curvature, i.e., its value depends only on how distances are measured on the surface, not on the way it is isometrically embedded in space. This result is the content of Gauss's Theorema egregium.' back

General relativity - Wikipedia, General relativity - Wikipedia, the free encyclopedia, 'General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics. General relativity generalises special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the four-momentum (mass-energy and linear momentum) of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations.' back

Genesis, Genesis, from the Holy Bible, King James Version, '1: In the beginning God created the heaven and the earth. 2: And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters. 3: And God said, Let there be light: and there was light.' back

Genesis, King James Version, ' In the beginning God created the heaven and the earth.
And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters.
And God said, Let there be light: and there was light.' back

Geodesics in general relativity - Wikipedia, Geodesics in general relativity - Wikipedia, the free encyclopedia, ' In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational force, is a particular type of geodesic. In other words, a freely moving or falling particle always moves along a geodesic.' back

Gödel's incompleteness theorems - Wikipedia, Gödel's incompleteness theorems - Wikipedia, 'Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results 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, giving a negative answer to Hilbert's second problem. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (i.e., any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency.' back

Gravitational-wave observatory - Wikipedia, Gravitational-wave observatory - Wikipedia, the free encyclopedia, 'A gravitational-wave detector (used in a gravitational-wave observatory) is any device designed to measure tiny distortions of spacetime called gravitational waves. Since the 1960s, various kinds of gravitational-wave detectors have been built and constantly improved. The present-day generation of laser interferometers has reached the necessary sensitivity to detect gravitational waves from astronomical sources, thus forming the primary tool of gravitational-wave astronomy.' back

Gregory J. Chaitin (1982), Gödel's Theorem and Information, 'Abstract: Gödel's theorem may be demonstrated using arguments having an information-theoretic flavor. In such an approach it is possible to argue that if a theorem contains more information than a given set of axioms, then it is impossible for the theorem to be derived from the axioms. In contrast with the traditional proof based on the paradox of the liar, this new viewpoint suggests that the incompleteness phenomenon discovered by Gödel is natural and widespread rather than pathological and unusual.'
International Journal of Theoretical Physics 21 (1982), pp. 941-954 back

Hamiltonian (quantum mechanics) - Wikipedia, Hamiltonian (quantum mechanics) - Wikipedia, the free encyclopedia, 'I In quantum mechanics, a Hamiltonian is an operator corresponding to the sum of the kinetic energies plus the potential energies for all the particles in the system (this addition is the total energy of the system in most of the cases under analysis). It is usually denoted by H . . .. Its spectrum is the set of possible outcomes when one measures the total energy of a system. Because of its close relation to the time-evolution of a system, it is of fundamental importance in most formulations of quantum theory. The Hamiltonian is named after William Rowan Hamilton, who created a revolutionary reformulation of Newtonian mechanics, now called Hamiltonian mechanics, which is also important in quantum physics. ' back

Hamiltonian mechanics - Wikipedia, Hamiltonian mechanics - Wikipedia, the free encyclopedia, ' Hamiltonian mechanics is a mathematically sophisticated formulation of classical mechanics. Historically, it contributed to the formulation of statistical mechanics and quantum mechanics. Hamiltonian mechanics was first formulated by William Rowan Hamilton in 1833, starting from Lagrangian mechanics, a previous reformulation of classical mechanics introduced by Joseph Louis Lagrange in 1788. Like Lagrangian mechanics, Hamiltonian mechanics is equivalent to Newton's laws of motion in the framework of classical mechanics. back

Hebrew Bible - Wikipedia, Hebrew Bible - Wikipedia, the free encyclopedia, The Hebrew Bible . . . is a term referring to the books of the Jewish Bible as originally written mostly in Biblical Hebrew with some Biblical Aramaic. The term closely corresponds to contents of the Jewish Tanakh and the Protestant Old Testament (see also Judeo-Christian) but does not include the deuterocanonical portions of the Roman Catholic or the Anagignoskomena portions of the Eastern Orthodox Old Testaments. The term does not imply naming, numbering or ordering of books, which varies (see also Biblical canon).' back

Hilbert's program - Wikipedia, Hilbert's program - Wikipedia, the free encyclopedia, ' In mathematics, Hilbert's program, formulated by German mathematician David Hilbert, was a proposed solution to the foundational crisis of mathematics, when early attempts to clarify the foundations of mathematics were found to suffer from paradoxes and inconsistencies. As a solution, Hilbert proposed to ground all existing theories to a finite, complete set of axioms, and provide a proof that these axioms were consistent. Hilbert proposed that the consistency of more complicated systems, such as real analysis, could be proven in terms of simpler systems. Ultimately, the consistency of all of mathematics could be reduced to basic arithmetic. back

Hindu - Wikipedia, Hindu - Wikipedia, the free encyclopedia, 'In 1995, while considering the question "who are Hindus and what are the broad features of Hindu religion", the Supreme Court of India highlighted Bal Gangadhar Tilak's formulation of Hinduism's defining features:
Acceptance of the Vedas with reverence; recognition of the fact that the means or ways to salvation are diverse; and the realization of the truth that the number of gods to be worshipped is large, that indeed is the distinguishing feature of Hindu religion.' back

History of the Internet - Wikipedia, History of the Internet - Wikipedia, the free encyclopedia, ' The history of the Internet begins with the development of electronic computers in the 1950s. Initial concepts of packet networking originated in several computer science laboratories in the United States, United Kingdom, and France. The US Department of Defense awarded contracts as early as the 1960s for packet network systems, including the development of the ARPANET (which would become the first network to use the Internet Protocol).' back

Human brain - Wikipedia, Human brain - Wikipedia, the free encyclopedia, 'The human brain is the central organ of the human nervous system, and with the spinal cord makes up the central nervous system. The brain consists of the cerebrum, the brainstem and the cerebellum. It controls most of the activities of the body, processing, integrating, and coordinating the information it receives from the sense organs, and making decisions as to the instructions sent to the rest of the body.' back

Human Genome Project - Wikipedia, Human Genome Project - Wikipedia, the free encyclopedia, ' The Human Genome Project (HGP) was an international scientific research project with the goal of determining the base pairs that make up human DNA, and of identifying and mapping all of the genes of the human genome from both a physical and a functional standpoint. . . . The Human Genome Project originally aimed to map the nucleotides contained in a human haploid reference genome (more than three billion). The "genome" of any given individual is unique; mapping the "human genome" involved sequencing a small number of individuals and then assembling these together to get a complete sequence for each chromosome. Therefore, the finished human genome is a mosaic, not representing any one individual.' back

Hylomorphism - Wikipedia, Hylomorphism - Wikipedia, the free encyclopedia, 'Hylomorphism (Greek ὑλο- hylo-, "wood, matter" + -morphism < Greek μορφή, morphē, "form") is a philosophical theory developed by Aristotle, which analyzes substance into matter and form. Substances are conceived of as compounds of form and matter.' back

On the Trinity - Wikipedia, On the Trinity - Wikipedia, the free encyclopedia, 'On the Trinity (Latin: De Trinitate) is a Latin book written by Augustine of Hippo to discuss the Trinity in context of the logos. Although not as well known as some of his other works, it is arguably his masterpiece and of more doctrinal importance than the Confessions or City of God. . . . Arthur West Haddan inferred from [the] evidence that it was written between 400, when he was forty-six years old and had been Bishop of Hippo about four years, and 428 at the latest; but it probably had been published ten or twelve years earlier, in around 417.' back

Inner product space - Wikipedia, Inner product space - Wikipedia, the free encyclopedia, 'In mathematics, an inner product space is a vector space of arbitrary (possibly infinite) dimension with additional structure, which, among other things, enables generalization of concepts from two or three-dimensional Euclidean geometry. The additional structure associates to each pair of vectors in the space a number which is called the inner product (also called a scalar product) of the vectors. Inner products allow the rigorous introduction of intuitive geometrical notions such as the angle between vectors or length of vectors in spaces of all dimensions. It also allows introduction of the concept of orthogonality between vectors. Inner product spaces generalize Euclidean spaces (with the dot product as the inner product) and are studied in functional analysis. An inner product space is sometimes also called a pre-Hilbert space, since its completion with respect to the metric induced by its inner product is a Hilbert space.' back

Internet protocol suite - Wikipedia, Internet protocol suite - Wikipedia, the freeencyclopedia, ' The Internet protocol suite is the conceptual model and set of communications protocols used in the Internet and similar computer networks. It is commonly known as TCP/IP because the foundational protocols in the suite are the Transmission Control Protocol (TCP) and the Internet Protocol (IP). . . .. The Internet protocol suite provides end-to-end data communication specifying how data should be packetized, addressed, transmitted, routed, and received. . . .. The technical standards underlying the Internet protocol suite and its constituent protocols are maintained by the Internet Engineering Task Force (IETF). The Internet protocol suite predates the OSI model, a more comprehensive reference framework for general networking systems. ' back

Isaac Newton, Method of Fluxions and Infinite Series with its Application to the Geometry of Curve-Lines, 'The method of fluxions and infinite series with its application to the geometry of curve-lines by the inventor Sir Isaac Newton ... ; translated from the author's Latin original not yet made publick. To which is subjoin'd, A perpetual comment upon the whole work, consisting of annotations, illustrations, and supplements, to make this treatise a compleat institution for the use of learners. back

Jeff Tollefson, US achieves laser-fusion record: what it means for nuclear-weapons research, ' Housed at Lawrence Livermore National Laboratory in California, the US$3.5-billion facility wasn’t designed to serve as a power-plant prototype, however, but rather to probe fusion reactions at the heart of thermonuclear weapons. After the United States banned underground nuclear testing at the end of the cold war in 1992, the energy department proposed the NIF as part of a larger science-based Stockpile Stewardship Program, designed to verify the reliability of the country’s nuclear weapons without detonating any of them.' back

Jeffrey Nicholls (1987), A theory of Peace, ' The argument: I began to think about peace in a very practical way during the Viet Nam war. I was the right age to be called up. I was exempted because I was a clergyman, but despite the terrors that war held for me, I think I would have gone. It was my first whiff of the force of patriotism. To my amazement, it was strong enough to make even me face death.
In the Church, I became embroiled in a deeper war. Not a war between goodies and baddies, but the war between good and evil that lies at the heart of all human consciousness. Existence is a struggle. We need all the help we can get. Religion is part of that help.' back

Jeffrey Nicholls (July 2019), Entropy and metaethics, ' I propose an answer [to the problematic search for modern ethics] in terms of what Einstein considered to be the most fundamental and irrefutable law of nature, the second law of thermodynamics, which expresses the fact that entropy almost never decreases. In a more morally relevant frame, this law expresses the fact that the universe is inherently creative. Human spirituality, whatever it may be, has emerged from the natural world. back

Jessica Haines, Two Stones Wave Patterns, back

Jim Branson, Eigenvalue Equations, 'The time independent Schrödinger Equation is an example of an Eigenvalue equation. ' back

John Palmer (Stanford Encyclopedia of Philosophy), Parmenides, ' Immediately after welcoming Parmenides to her abode, the goddess describes as follows the content of the revelation he is about to receive:
You must needs learn all things,/ both the unshaken heart of well-rounded reality/ and the notions of mortals, in which there is no genuine trustworthiness./ Nonetheless these things too will you learn, how what they resolved/ had actually to be, all through all pervading. (Fr. 1.28b-32) ' back

John Paul II (1983), Code of Canon Law: §331: Papal Power, ' Can. 331 The bishop of the Roman Church, in whom continues the office given by the Lord uniquely to Peter, the first of the Apostles, and to be transmitted to his successors, is the head of the college of bishops, the Vicar of Christ, and the pastor of the universal Church on earth. By virtue of his office he possesses supreme, full, immediate, and universal ordinary power in the Church, which he is always able to exercise freely.' back

John Paul II (1994), Ordinatio Sacerdotalis: Apostolic Letter to the Bishops of the Catholic Church on Reserving Priestly Ordination to Men Alone., 'When the question of the ordination of women arose in the Anglican Communion, Pope Paul VI, out of fidelity to his office of safeguarding the Apostolic Tradition, and also with a view to removing a new obstacle placed in the way of Christian unity, reminded Anglicans of the position of the Catholic Church: "She holds that it is not admissible to ordain women to the priesthood, for very fundamental reasons. These reasons include: the example recorded in the Sacred Scriptures of Christ choosing his Apostles only from among men; the constant practice of the Church, which has imitated Christ in choosing only men; and her living teaching authority which has consistently held that the exclusion of women from the priesthood is in accordance with God's plan for his Church".' back

John the Evangelist, The Gospel of John (KJV), ' In the beginning was the Word, and the Word was with God, and the Word was God. The same was in the beginning with God. All things were made by him; and without him was not any thing made that was made. In him was life; and the life was the light of men. And the light shineth in darkness; and the darkness comprehended it not.' back

John von Neumann (2014), Mathematical Foundations of Quantum Mechanics, ' Mathematical Foundations of Quantum Mechanics by John von Neumann translated from the German by Robert T. Beyer (New Edition) edited by Nicholas A. Wheeler. Princeton UP Princeton & Oxford. Preface: ' This book is the realization of my long-held intention to someday use the resources of TEX to produce a more easily read version of Robert T. Beyer’s authorized English translation (Princeton University Press, 1955) of John von Neumann’s classic Mathematische Grundlagen der Quantenmechanik (Springer, 1932).'This content downloaded from 129.127.145.240 on Sat, 30 May 2020 22:38:31 UTC back

Juan Yin et al, Lower Bound on the Speed of Nonlocal Correlations without Locality and Measurement Choice Loopholes , ' In their well-known paper, Einstein, Podolsky, and Rosen called the nonlocal correlation in quantum entanglement a “spooky action at a distance.” If the spooky action does exist, what is its speed? All previous experiments along this direction have locality and freedom-of-choice loopholes. Here, we strictly closed the loopholes by observing a 12 h continuous violation of the Bell inequality and concluded that the lower bound speed of spooky action was 4 orders of magnitude of the speed of light if Earth’s speed in any inertial reference frame was less than 10-3 time the speed of light. ' back

Kerson Huang (2013), A Critical History of Renormalization, ' The history of renormalization is reviewed with a critical eye,starting with Lorentz's theory of radiation damping, through perturbative QED with Dyson, Gell‐Mann & Low, and others, to Wilson's formulation and Polchinski's functional equation,and applications to "triviality", and dark energy in cosmology.' back

Lagrangian mechanics - Wikipedia, Lagrangian mechanics - Wikipedia, the free encyclopedia, ' Introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in 1788, Lagrangian mechanics is a formulation of classical mechanics and is founded on the stationary action principle. Given a system of point masses and a pair, t₁ and t₂ Lagrangian mechanics postulates that the system's trajectory (describing evolution of the system over time) . . . must be a stationary point of the action functional S = ∫ L dt. By convention, L = T − V, where T and V are the kinetic and potential energy of the system, respectively.' back

Laplace's demon - Wikipedia, Laplace's demon - Wikipedia, the free encyclopedia, ' We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.' A Philosophical Essay on Probabilities, Essai philosophique dur les probabilites introduction to the second edition of Theorie analytique des probabilites based on a lecture given in 1794. back

Lie Group - Wikipedia, Lie Group - Wikipedia, the free encyclopedia, 'In mathematics, a Lie group . . . is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups are named after Norwegian mathematician Sophus Lie, who laid the foundations of the theory of continuous transformation groups. Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. . . . One of the key ideas in the theory of Lie groups is to replace the global object, the group, with its local or linearized version, which Lie himself called its "infinitesimal group" and which has since become known as its Lie algebra.' back

Lumen Gentium (Vatican II), Dogmatic Constitution on the Church, 'THE MYSTERY OF THE CHURCH 1. Christ is the Light of nations. Because this is so, this Sacred Synod gathered together in the Holy Spirit eagerly desires, by proclaiming the Gospel to every creature, to bring the light of Christ to all men, a light brightly visible on the countenance of the Church. Since the Church is in Christ like a sacrament or as a sign and instrument both of a very closely knit union with God and of the unity of the whole human race, it desires now to unfold more fully to the faithful of the Church and to the whole world its own inner nature and universal mission.' back

Matrix mechanics - Wikipedia, Matrix mechanics - Wikipedia, the free encyclopedia, 'Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. Matrix mechanics was the first conceptually autonomous and logically consistent formulation of quantum mechanics. It extended the Bohr Model by describing how the quantum jumps occur. It did so by interpreting the physical properties of particles as matrices that evolve in time. It is equivalent to the Schrödinger wave formulation of quantum mechanics, and is the basis of Dirac's bra-ket notation for the wave function. back

Matthew Schmaltz, What is the Great Commission and why is it so controversial?, ' Converting others to Christianity raises a fundamental question about whether religious diversity is a reality to be celebrated or an obstacle to be overcome. Given the complex history of missionary activity, the meaning of the Great Commission will continue to be a subject of debate as Christianity confronts a rapidly changing world.' back

Max Planck, On the Law of Distribution of Energy in the Normal Spectrum, Annalen der Physik, vol. 4, p. 553 ff (1901) 'The recent spectral measurements made by O. Lummer and E. Pringsheim and even more notable those by H. Rubens and F. Kurlbaum which together confirmed an earlier result obtained by H. Beckmann show that the law of energy distribution in the normal spectrum, first derived by W. Wien from molecular-kinetic considerations and later by me from the theory of electromagnetic radiation, is not valid generally.' back

Maxwell's equations - Wikipedia, Maxwell's equations - Wikipedia, the free encyclopedia, ' Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. The equations provide a mathematical model for electric, optical and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc. Maxwell's equations describe how electric and magnetic fields are generated by charges, currents, and changes of the fields. One important consequence of the equations is that they demonstrate how fluctuating electric and magnetic fields propagate at the speed of light.' back

Measurement problem - Wikipedia, Measurement problem - Wikipedia, the free encyclopedia, 'The measurement problem in quantum mechanics is the problem of how (or whether) wave function collapse occurs. The inability to observe this process directly has given rise to different interpretations of quantum mechanics, and poses a key set of questions that each interpretation must answer. The wave function in quantum mechanics evolves deterministically according to the Schrödinger equation as a linear superposition of different states, but actual measurements always find the physical system in a definite state. Any future evolution is based on the state the system was discovered to be in when the measurement was made, meaning that the measurement "did something" to the system that is not obviously a consequence of Schrödinger evolution.' back

Measurement uncertainty - Wikipedia, Measurement uncertainty - Wikipedia, the free encyclopedia, 'In metrology, measurement uncertainty is a non-negative parameter characterizing the dispersion of the values attributed to a measured quantity. The uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity. All measurements are subject to uncertainty and a measured value is only complete if it is accompanied by a statement of the associated uncertainty.' back

Meinard Kuhlmann (Stanford Encyclopedia of Philosophy), Quantum Field Theory, ' Quantum Field Theory (QFT) is the mathematical and conceptual framework for contemporary elementary particle physics. In a rather informal sense QFT is the extension of quantum mechanics (QM), dealing with particles, over to fields, i.e. systems with an infinite number of degrees of freedom. (See the entry on quantum mechanics.) In the last few years QFT has become a more widely discussed topic in philosophy of science, with questions ranging from methodology and semantics to ontology. QFT taken seriously in its metaphysical implications seems to give a picture of the world which is at variance with central classical conceptions of particles and fields, and even with some features of QM.' back

Michelson and Morley, On the relative motion of the earth and the lumeniferous ether, The classic paper, 1887. They conclude that "It appears, from all that precedes, reasonably certain that if there be any relative motion between the earth and the luminiferous ether, it must be small; . . . " back

Middle term - Wikipedia, Middle term - Wikipedia, the free encyclopedia, 'In logic, a middle term is a term that appears (as a subject or predicate of a categorical proposition) in both premises but not in the conclusion of a categorical syllogism. The middle term (in bold below) must be distributed in at least one premise but not in the conclusion. The major term and the minor terms, also called the end terms, do appear in the conclusion.' back

Minkowski space - Wikipedia, Minkowski space - Wikipedia, the free encyclopedia, ' In mathematical physics, Minkowski space or Minkowski spacetime is a combination of Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Although initially developed by mathematician Hermann Minkowski for Maxwell's equations of electromagnetism, the mathematical structure of Minkowski spacetime was shown to be an immediate consequence of the postulates of special relativity.' back

Neuron - Wikipedia, Neuron - Wikipedia, the free encyclopedia, 'A neuron or nerve cell is an electrically excitable cell that communicates with other cells via specialized connections called synapses. It is the main component of nervous tissue in all animals except sponges and placozoa. Plants and fungi do not have nerve cells. . . . A typical neuron consists of a cell body (soma), dendrites, and a single axon. The soma is usually compact. The axon and dendrites are filaments that extrude from it. Dendrites typically branch profusely and extend a few hundred micrometers from the soma. The axon leaves the soma at a swelling called the axon hillock, and travels for as far as 1 meter in humans or more in other species.' back

New Testament - Wikipedia, New Testament - Wikipedia, the free encyclopedia, 'The New Testament (Koine Greek: Ἡ Καινὴ Διαθήκη, Hē Kainḕ Diathḗkē) is the second major division of the Christian biblical canon, the first such division being the much longer Old Testament.

Unlike the Old Testament or Hebrew Bible, of which Christians hold different views, the contents of the New Testament deal explicitly with 1st century Christianity, although both the Old and New Testament are regarded, together, as Sacred Scripture. The New Testament has therefore (in whole or in part) frequently accompanied the spread of Christianity around the world, and both reflects and serves as a source for Christian theology.' back

Nic Hugget (Stanford Encyclopedia of Philosophy), Zeno's Paradoxes, ' Almost everything that we know about Zeno of Elea is to be found in the opening pages of Plato's Parmenides. There we learn that Zeno was nearly 40 years old when Socrates was a young man, say 20. Since Socrates was born in 469 BC we can estimate a birth date for Zeno around 490 BC. Beyond this, really all we know is that he was close to Parmenides (Plato reports the gossip that they were lovers when Zeno was young), and that he wrote a book of paradoxes defending Parmenides' philosophy. Sadly this book has not survived, and what we know of his arguments is second-hand, principally through Aristotle and his commentators (here I have drawn particularly on Simplicius, who, though writing a thousand years after Zeno, apparently possessed at least some of his book).' back

Nicene Creed - Wikipedia, Nicene Creed - Wikipedia, the free encyclopedia, ' The Nicene Creed (Greek: Σύμβολον τῆς Νίκαιας, Latin: Symbolum Nicaenum) is the profession of faith or creed that is most widely used in Christian liturgy. It forms the mainstream definition of Christianity for most Christians. It is called Nicene because, in its original form, it was adopted in the city of Nicaea (present day Iznik in Turkey) by the first ecumenical council, which met there in the year 325. The Nicene Creed has been normative for the Catholic Church, the Eastern Orthodox Church, the Church of the East, the Oriental Orthodox churches, the Anglican Communion, and the great majority of Protestant denominations.' back

NIST, Kilogram, Mass and Planck's Constant, ' For many observers, the connection between mass on the scale of a liter of water and a constant deriving from the very earliest days of quantum mechanics may not be immediately obvious. The scientific context for that connection is suggested by a deep underlying relationship between two of the most celebrated formulations in physics. One is Einstein's famous E =mc2, where E is energy, m is mass and c is the speed of light. The other expression, less well known to the general public but fundamental to modern science, is E = hν, the first "quantum" expression in history, stated by Max Planck in 1900. Here, E is energy, ν is frequency (the ν is not a “v” but instead the lowercase Greek letter nu), and h is what is now known as the Planck constant.' back

No-cloning theorem - Wikipedia, No-cloning theorem - Wikipedia, the free encyclopedia, ' In physics, the no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state, a statement which has profound implications in the field of quantum computing among others. The theorem is an evolution of the 1970 no-go theorem authored by James Park, in which he demonstrates that a non-disturbing measurement scheme which is both simple and perfect cannot exist . . .. The aforementioned theorems do not preclude the state of one system becoming entangled with the state of another as cloning specifically refers to the creation of a separable state with identical factors.' back

Nobelprize.org, The Nobel prize in Physics 1921: Albert Einstein, 'The Nobel Prize in Physics 1921 was awarded to Albert Einstein "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect".' back

Noether's theorem - Wikipedia, Noether's theorem - Wikipedia, the free encyclopedia, 'Noether's (first) theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proved by German mathematician Emmy Noether in 1915 and published in 1918. The action of a physical system is the integral over time of a Lagrangian function (which may or may not be an integral over space of a Lagrangian density function), from which the system's behavior can be determined by the principle of least action.' back

Nowak, Plotkin & Jansen (2000), The evolution of syntacic communication, 'Animal communication is typically non-syntactic, which means that signals refer to whole situations. Human language is syntactic, and signals consist of discrete components that have their own meaning. Syntax is a prerequisite for taking advantage of combinatorics, that is, "making infinite use of finite means''. The vast expressive power of human language would be impossible without syntax, and the transition from non-syntactic to syntactic communication was an essential step in the evolutionof human language. . . . ' back

Observable - Wikipedia, Observable - Wikipedia, the free encyclopedia, ' In physics, an observable is a physical quantity that can be measured. Examples include position and momentum. In systems governed by classical mechanics, it is a real-valued "function" on the set of all possible system states. In quantum physics, it is an operator, or gauge, where the property of the quantum state can be determined by some sequence of operations. . . . Physically meaningful observables must also satisfy transformation laws which relate observations performed by different observers in different frames of reference. These transformation laws are automorphisms of the state space, that is bijective transformations which preserve certain mathematical properties of the space in question. ' back

On shell and off shell - Wikipedia, On shell and off shell - Wikipedia, the free encyclopedia, ' In physics, particularly in quantum field theory, configurations of a physical system that satisfy classical equations of motion are called on shell, and those that do not are called off shell. In quantum field theory, virtual particles are termed off shell because they do not satisfy the energy–momentum relation; real exchange particles do satisfy this relation and are termed on shell (mass shell). In classical mechanics for instance, in the action formulation, extremal solutions to the variational principle are on shell and the Euler–Lagrange equations give the on-shell equations. Noether's theorem regarding differentiable symmetries of physical action and conservation laws is another on-shell theorem.' back

Original sin - Wikipedia, Original sin - Wikipedia, the free encyclopedia, 'Original sin, sometimes called ancestral sin, is, according to a doctrine proposed in Christian theology, humanity's state of sin resulting from the Fall of Man. This condition has been characterized in many ways, ranging from something as insignificant as a slight deficiency, or a tendency toward sin yet without collective guilt, referred to as a "sin nature," to something as drastic as total depravity or automatic guilt by all humans through collective guilt. Those who uphold this doctrine look to the teaching of Paul the Apostle in Romans 5:12-21 and 1 Corinthians 15:22 for its scriptural base, and see it as perhaps implied in an Old Testament passage Psalm 51:5.' back

Orthonormal basis - Wikipedia, Orthonormal basis - Wikipedia, the free encyclopedia, 'In mathematics, an orthonormal basis of an inner product space V (i.e., a vector space with an inner product), or in particular of a Hilbert space H, is a set of elements whose span is dense in the space, in which the elements are mutually orthogonal and of magnitude 1. Elements in an orthogonal basis do not have to have a magnitude of 1 but must be mutually perpendicular. It is easy to change the vectors in an orthogonal basis by scalar multiples to get an orthonormal basis, and indeed this is a typical way that an orthonormal basis is constructed.' back

OSI model - Wikipedia, OSI model - Wikipedia, the free encyclopedia, 'The Open Systems Interconnection model (OSI model) is a conceptual model that characterizes and standardizes the communication functions of a telecommunication or computing system without regard to its underlying internal structure and technology. Its goal is the interoperability of diverse communication systems with standard protocols. The model partitions a communication system into abstraction layers. The original version of the model defined seven layers.' back

P. A. M. Dirac (1933), The Lagrangian in Quantum Mechanics, ' . . . there is an alternative formulation [to the Hamiltonian] in classical dynamics, provided by the Lagrangian. This requires one to work in terms of coordinates and velocities instead of coordinates and momenta. The two formulation are closely related but there are reasons for believing that the Lagrangian one is more fundamental. . . . Secondly the lagrangian method can easily be expressed relativistically, on account of the action function being a relativistic invariant; . . .. ' [This article was first published in Physikalische Zeitschrift der Sowjetunion, Band 3, Heft 1 (1933), pp. 64–72.] back

Pan, Bouwmeester, Daniell, Weinfurter & Zeilinger, Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement, ' Abstract Bell's theorem states that certain statistical correlations predicted by quantum physics for measurements on two-particle systems cannot be understood within a realistic picture based on local properties of each individual particle—even if the two particles are separated by large distances. Einstein, Podolsky and Rosen first recognized the fundamental significance of these quantum correlations (termed ‘entanglement’ by Schrödinger) and the two-particle quantum predictions have found ever-increasing experimental support. A more striking conflict between quantum mechanical and local realistic predictions (for perfect correlations) has been discovered; but experimental verification has been difficult, as it requires entanglement between at least three particles. Here we report experimental confirmation of this conflict, using our recently developed method to observe three-photon entanglement, or ‘Greenberger–Horne–Zeilinger’ (GHZ) states. The results of three specific experiments, involving measurements of polarization correlations between three photons, lead to predictions for a fourth experiment; quantum physical predictions are mutually contradictory with expectations based on local realism. We find the results of the fourth experiment to be in agreement with the quantum prediction and in striking conflict with local realism.' back

Papal supremacy - Wikipedia, Papal supremacy - Wikipedia, the free encyclopedia, 'Papal supremacy is the doctrine of the Roman Catholic Church that the pope, by reason of his office as Vicar of Christ and as pastor of the entire Christian Church, has full, supreme, and universal power over the whole Church, a power which he can always exercise unhindered: that, in brief, "the Pope enjoys, by divine institution, supreme, full, immediate, and universal power in the care of souls." (Code of Canon Law: Can. 331) The doctrine had the most significance in the relationship between the church and the temporal state, in matters such as ecclesiastic privileges, the actions of monarchs and even successions.' back

Particle physics and representation theory - Wikipedia, Particle physics and representation theory - Wikipedia, the free encyclopedia, ' There is a natural connection between particle physics and representation theory, as first noted in the 1930s by Eugene Wigner. It links the properties of elementary particles to the structure of Lie groups and Lie algebras. According to this connection, the different quantum states of an elementary particle give rise to an irreducible representation of the Poincaré group. Moreover, the properties of the various particles, including their spectra, can be related to representations of Lie algebras, corresponding to "approximate symmetries" of the universe.' back

Path integral formulation - Wikipedia, Path integral formulation - Wikipedia, the free encyclopedia, 'The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique trajectory for a system with a sum, or functional integral, over an infinity of possible trajectories to compute a quantum amplitude. . . . This formulation has proved crucial to the subsequent development of theoretical physics, since it provided the basis for the grand synthesis of the 1970s which unified quantum field theory with statistical mechanics. . . . ' back

Patricia Curd (Stanford Encyclopedia of Philosophy), Anaxagoras, ' Anaxagoras of Clazomenae (a major Greek city of Ionian Asia Minor), a Greek philosopher of the 5th century B.C.E. (born ca. 500–480), was the first of the Presocratic philosophers to live in Athens. He propounded a physical theory of “everything-in-everything,” and claimed that nous (intellect or mind) was the motive cause of the cosmos. He was the first to give a correct explanation of eclipses, and was both famous and notorious for his scientific theories, including the claims that the sun is a mass of red-hot metal, that the moon is earthy, and that the stars are fiery stones.' back

PDG - U of California, Particle Data Group, ' The 2020 PDG collaboration consists of 237 authors and 5 technical associates from 174 institutions in 26 countries. It is led by a coordination team based mostly at Lawrence Berkeley National Laboratory (LBNL), which has served as PDG's headquarters since inception. . . . In the over 60 years since PDG started with the publication of the first wallet cards (W.H. Barkas and A.H. Rosenfeld, UCRL-8030), the Review of Particle Physics has become the most-cited publication in particle physics.' back

Permutation group - Wikipedia, Permutation group - Wikipedia, the free encyclopedia, 'In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself). The group of all permutations of a set M is the symmetric group of M, often written as Sym(M). The term permutation group thus means a subgroup of the symmetric group. If M = {1,2,...,n} then, Sym(M), the symmetric group on n letters is usually denoted by S_n. The way in which the elements of a permutation group permute the elements of the set is called its group action. Group actions have applications in the study of symmetries, combinatorics and many other branches of mathematics, physics and chemistry.' back

Philosophiae Naturalis Principia Mathematica - Wikipedia, Philosophiae Naturalis Principia Mathematica - Wikipedia, the free encyclopedia, 'The Philosophiæ Naturalis Principia Mathematica (Latin: "mathematical principles of natural philosophy" often Principia or Principia Mathematica for short) is a three-volume work by Isaac Newton published on 5 July 1687. It contains the statement of Newton's laws of motion forming the foundation of classical mechanics, as well as his law of universal gravitation and a derivation of Kepler's laws for the motion of the planets (which were first obtained empirically). The Principia is widely regarded as one of the most important scientific works ever written.' back

Photon - Wikipedia, Photon - Wikipedia, the free encyclopedia, 'A photon is an elementary particle, the quantum of all forms of electromagnetic radiation including light. It is the force carrier for electromagnetic force, even when static via virtual photons. The photon has zero rest mass and as a result, the interactions of this force with matter at long distance are observable at the microscopic and macroscopic levels.' back

Planck constant - Wikipedia, Planck constant - Wikipedia, the free encyclopedia, ' Since energy and mass are equivalent, the Planck constant also relates mass to frequency. By 2017, the Planck constant had been measured with sufficient accuracy in terms of the SI base units, that it was central to replacing the metal cylinder, called the International Prototype of the Kilogram (IPK), that had defined the kilogram since 1889. . . . For this new definition of the kilogram, the Planck constant, as defined by the ISO standard, was set to 6.626 070 150 × 10-34 J⋅s exactly. ' back

Planck units - Wikipedia, Planck units - Wikipedia, the free encycloedia, ' In particle physics and physical cosmology, Planck units are a set of units of measurement defined exclusively in terms of four universal physical constants, in such a manner that these physical constants take on the numerical value of 1 when expressed in terms of these units. . Originally proposed in 1899 by German physicist Max Planck, these units are also known as natural units because the origin of their definition comes only from properties of nature and not from any human construct. Planck units are only one system of several systems of natural units, but Planck units are not based on properties of any prototype object or particle (that would be arbitrarily chosen), but rather on only the properties of free space.' back

Planck-Einstein relation - Wikipedia, Planck-Einstein relation - Wikipedia, the free encyclopedia, 'The Planck–Einstein relation. . . refers to a formula integral to quantum mechanics, which states that the energy of a photon (E) is proportional to its frequency (ν). E = hν. The constant of proportionality, h, is known as the Planck constant.' back

Pleroma - Wikipedia, Pleroma - Wikipedia, the free encyclopedia, 'Pleroma (Greek πλήρωμα) generally refers to the totality of divine powers. The word means fullness from πληρόω ("I fill") comparable to πλήρης which means "full", and is used in Christian theological contexts: both in Gnosticism generally, and by St. Paul the Apostle in Colossians 2:9 (the word is used 17 times in the NT).[2] Pleroma is also used in the general Greek language and is used by the Greek Orthodox Church in this general form since the word appears in the book of Colossians. Elaine Pagels of Princeton University, view the reference in Colossians as something that was to be interpreted in the Gnostic sense.' back

Pope John Paul II (1996), Truth Cannot Contradict Truth, Address to the Pontifical Academy of Sciences October 22, 1996 , 'Consideration of the method used in the various branches of knowledge makes it possible to reconcile two points of view which would seem irreconcilable. The sciences of observation describe and measure the multiple manifestations of life with increasing precision and correlate them with the time line. The moment of transition to the spiritual cannot be the object of this kind of observation, which nevertheless can discover at the experimental level a series of very valuable signs indicating what is specific to the human being.' back

Pope Paul III (1546), Council of Trent: Decree Concerning Original Sin, '1. If anyone does not confess that the first man, Adam, when he transgressed the commandment of God in paradise, immediately lost the holiness and justice in which he had been constituted, and through the offense of that prevarication incurred the wrath and indignation of God, and thus death with which God had previously threatened him, and, together with death, captivity under his power who thenceforth had the empire of death, that is to say, the devil, and that the entire Adam through that offense of prevarication was changed in body and soul for the worse, let him be anathema.' back

Pope Paul VI (1964), Dogmatic Constitution: Lumen Gentium Chapter 7, ' § 48: . . . Already the final age of the world has come upon us (242) and the renovation of the world is irrevocably decreed and is already anticipated in some kind of a real way; for the Church already on this earth is signed with a sanctity which is real although imperfect. However, until there shall be new heavens and a new earth in which justice dwells, the pilgrim Church in her sacraments and institutions, which pertain to this present time, has the appearance of this world which is passing and she herself dwells among creatures who groan and travail in pain until now and await the revelation of the sons of God.' back

Portal: Mind and Brain - Wikipedia, Portal: Mind and Brain - Wikipedia, the free encyclopedia, 'Welcome to the Mind and Brain Portal. This is an interdisciplinary point of entry to such related fields as cognitive psychology, philosophy of mind, neuroscience, and linguistics.' back

Potential energy - Wikipedia, Potential energy - Wikipedia, the free encyclopedia, 'In physics, potential energy is the energy of an object or a system due to the position of the body or the arrangement of the particles of the system. The SI unit for measuring work and energy is the joule (symbol J). The term potential energy was coined by the 19th century Scottish engineer and physicist William Rankine although it has links to Greek philosopher Aristotle's concept of potentiality. Potential energy is associated with a set of forces that act on a body in a way that depends only on the body's position in space.' back

Potentiality and actuality - Wikipedia, Potentiality and actuality - Wikipedia, the free encyclopedia, 'In philosophy, Potentiality and Actuality are principles of a dichotomy which Aristotle used to analyze motion, causality, ethics, and physiology in his Physics, Metaphysics, Ethics and De Anima (which is about the human psyche). The concept of potentiality, in this context, generally refers to any "possibility" that a thing can be said to have. Aristotle did not consider all possibilities the same, and emphasized the importance of those that become real of their own accord when conditions are right and nothing stops them. Actuality, in contrast to potentiality, is the motion, change or activity that represents an exercise or fulfillment of a possibility, when a possibility becomes real in the fullest sense. back

Projective Hilbert space - Wikipedia, Projective Hilbert space - Wikipedia, the free encyclopedia, ' In mathematics and the foundations of quantum mechanics, the projective Hilbert space P(H) of a complex Hilbert space H is the set of equivalence classes of non-zero vectors v in H , for the relation ∼ on H given by w ∼ v if and only if v = λ w for some non-zero complex number λ . The equivalence classes of v for the relation ∼ \sim } are also called rays or projective rays. This is the usual construction of projectivization, applied to a complex Hilbert space.' back

Pseudo-Dionysius the Areopagite - Wikipedia, Pseudo-Dionysius the Areopagite - Wikipedia, the free encyclopedia, 'Pseudo-Dionysius the Areopagite (Greek: Διονύσιος ὁ Ἀρεοπαγίτης), also known as Pseudo-Denys, was a Christian theologian and philosopher of the late 5th to early 6th century (writing before 532), probably Syrian, the author of the set of works commonly referred to as the Corpus Areopagiticum or Corpus Dionysiacum. The author pseudonymously identifies himself in the corpus as "Dionysios", portraying himself as the figure of Dionysius the Areopagite, the Athenian convert of St. Paul mentioned in Acts 17:34 This false attribution resulted in the work being given great authority in subsequent theological writing in both East and West, with its influence only decreasing in the West with the fifteenth century demonstration of its later dating.' back

Psychophysical parallelism - Wikipedia, Psychophysical parallelism - Wikipedia, the free encyclopedia, ' In the philosophy of mind, psychophysical parallelism (or simply parallelism) is the theory that mental and bodily events are perfectly coordinated, without any causal interaction between them. As such, it affirms the correlation of mental and bodily events (since it accepts that when a mental event occurs, a corresponding physical effect occurs as well), but denies a direct cause and effect relation between mind and body.[1] This coordination of mental and bodily events has been postulated to occur either in advance by means of God (as per Gottfried Leibniz's idea of pre-established harmony) or at the time of the event (as in the occasionalism of Nicolas Malebranche) or, finally, according to Baruch Spinoza's Ethics, mind and matter are two of infinite attributes of the only Substance-God, which go as one without interacting with each other. On this view, mental and bodily phenomena are independent yet inseparable, like two sides of a coin.' back

Pythagorean theorem - Wikipedia, Pythagorean theorem - Wikipedia, the free encyclopedia, 'In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle). This is usually summarized as: The square on the hypotenuse is equal to the sum of the squares on the other two sides.' back

Quantum entanglement - Wikipedia, Quantum entanglement - Wikipedia, the free encyclopedia, 'Quantum entanglement is a physical phenomenon which occurs when pairs or groups of particles are generated, interact, or share spatial proximity in ways such that the quantum state of each particle cannot be described independently of the state of the other(s), even when the particles are separated by a large distance—instead, a quantum state must be described for the system as a whole. . . . Entanglement is considered fundamental to quantum mechanics, even though it wasn't recognized in the beginning. Quantum entanglement has been demonstrated experimentally with photons, neutrinos, electrons, molecules as large as buckyballs, and even small diamonds. The utilization of entanglement in communication and computation is a very active area of research.' back

Quantum harmonic oscillator - Wikipedia, Quantum harmonic oscillator - Wikipedia, the free encyclopedia, 'The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics. Furthermore, it is one of the few quantum-mechanical systems for which an exact, analytical solution is known.' back

Quantum nonlocality - Wikipedia, Quantum nonlocality - Wikipedia, the free encyclopedia, 'Quantum nonlocality is the phenomenon by which the measurements made at a microscopic level necessarily refute one or more notions (often referred to as local realism) that are regarded as intuitively true in classical mechanics. Rigorously, quantum nonlocality refers to quantum mechanical predictions of many-system measurement correlations that cannot be simulated by any local hidden variable theory. Many entangled quantum states produce such correlations when measured, as demonstrated by Bell's theorem.' back

Quantum state - Wikipedia, Quantum state - Wikipedia, the free encyclopedia, 'In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in time exhausts all that can be predicted about the system's behavior. A mixture of quantum states is again a quantum state. Quantum states that cannot be written as a mixture of other states are called pure quantum states, while all other states are called mixed quantum states. A pure quantum state can be represented by a ray in a Hilbert space over the complex numbers, while mixed states are represented by density matrices, which are positive semidefinite operators that act on Hilbert spaces.' back

Qubit - Wikipedia, Qubit - Wikipedia, the free encyclopedia, 'A quantum bit, or qubit . . . is a unit of quantum information. That information is described by a state vector in a two-level quantum mechanical system which is formally equivalent to a two-dimensional vector space over the complex numbers. Benjamin Schumacher discovered a way of interpreting quantum states as information. He came up with a way of compressing the information in a state, and storing the information on a smaller number of states. This is now known as Schumacher compression. In the acknowledgments of his paper (Phys. Rev. A 51, 2738), Schumacher states that the term qubit was invented in jest, during his conversations with Bill Wootters.' back

Renormalization - Wikipedia, Renormalization - Wikipedia, the free encyclopedia, ' Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of quantities to compensate for effects of their self-interactions. But even if it were the case that no infinities arose in loop diagrams in quantum field theory, it could be shown that renormalization of mass and fields appearing in the original Lagrangian is necessary.' back

Renormalization group - Wikipedia, Renormalization group - Wikipedia, the free encyclopedia, 'In theoretical physics, renormalization group (RG) refers to a mathematical apparatus that allows one to investigate the changes of a physical system as one views it at different distance scales. In particle physics it reflects the changes in the underlying force laws as one varies the energy scale at which physical processes occur. A change in scale is called a "scale transformation" or "conformal transformation." The renormalization group is intimately related to "conformal invariance" or "scale invariance," a symmetry by which the system appears the same at all scales (so-called self-similarity).' back

Ribosome - Wikipedia, Ribosome - Wikipedia, the free encyclopedia, ' Ribosomes are macromolecular machines, found within all living cells, that perform biological protein synthesis (mRNA translation). Ribosomes link amino acids together in the order specified by the codons of messenger RNA molecules to form polypeptide chains. Ribosomes consist of two major components: the small and large ribosomal subunits. Each subunit consists of one or more ribosomal RNA molecules and many ribosomal proteins.' back

Richard P. Feynman (1948), Space-Time Approach to Non-Relativistic Quantum Mechanics, ' Abstract Non-relativistic quantum mechanics is formulated here in a different way. It is, however, mathematically equivalent to the familiar formulation. In quantum mechanics the probability of an event which can happen in several different ways is the absolute square of a sum of complex contributions, one from each alternative way. The probability that a particle will be found to have a path x(t) lying somewhere within a region of space time is the square of a sum of contributions, one from each path in the region. The contribution from a single path is postulated to be an exponential whose (imaginary) phase is the classical action (in units of ℏ) for the path in question. The total contribution from all paths reaching x, t from the past is the wave function ψ(x, t). This is shown to satisfy Schroedinger's equation. The relation to matrix and operator algebra is discussed. Applications are indicated, in particular to eliminate the coordinates of the field oscillators from the equations of quantum electrodynamics.' back

Richard P. Feynman, Nobel Lecture: The Development of the Space-Time View of Quantum Electrodynamics, Nobel Lecture, December 11, 1965: We have a habit in writing articles published in scientific journals to make the work as finished as possible, to cover all the tracks, to not worry about the blind alleys or to describe how you had the wrong idea first, and so on. So there isn’t any place to publish, in a dignified manner, what you actually did in order to get to do the work, although, there has been in these days, some interest in this kind of thing. Since winning the prize is a personal thing, I thought I could be excused in this particular situation, if I were to talk personally about my relationship to quantum electrodynamics, rather than to discuss the subject itself in a refined and finished fashion. Furthermore, since there are three people who have won the prize in physics, if they are all going to be talking about quantum electrodynamics itself, one might become bored with the subject. So, what I would like to tell you about today are the sequence of events, really the sequence of ideas, which occurred, and by which I finally came out the other end with an unsolved problem for which I ultimately received a prize.' back

Robin Smith (Stanford Encyclopedia of Philosophy), Aristotle's Logic, 'Aristotle's logic, especially his theory of the syllogism, has had an unparalleled influence on the history of Western thought. It did not always hold this position: in the Hellenistic period, Stoic logic, and in particular the work of Chrysippus, took pride of place. However, in later antiquity, following the work of Aristotelian Commentators, Aristotle's logic became dominant, and Aristotelian logic was what was transmitted to the Arabic and the Latin medieval traditions, while the works of Chrysippus have not survived.' back

Rolf Landauer (1961), Irreversibility and Heat Generation in the Computing Process, 'Abstract: 'It is argued that computing machines inevitably involve devices which perform logical functions that do not have a single-valued inverse. The logical irreversibility is associated with physical irreversibility, and requires a minimum heat generation, per machine cycle, typically of the order of kT for each irreversible function. The dissipation serves the purpose of standardizing signals and making them independent of their exact logical history. Two simple, but representative, models of bistable devices are subjected to a more detailed analysis of switching kinetics to yield the relationship between speed and energy dissipation, and to estimate the effects of errors induced by thermal fluctuations.' back

Rolf Landauer (1999), Information is a Physical Entity, 'Abstract: This paper, associated with a broader conference talk on the fundamental physical limits of information handling, emphasizes the aspects still least appreciated. Information is not an abstract entity but exists only through a physical representation, thus tying it to all the restrictions and possibilities of our real physical universe. The mathematician's vision of an unlimited sequence of totally reliable operations is unlikely to be implementable in this real universe. Speculative remarks about the possible impact of that on the ultimate nature of the laws of physics are included.' back

Roulette - Wikipedia, Roulette - Wikipedia, the free encyclopedia, ' Roulette is a casino game named after the French word meaning little wheel which was likely developed from the Italian game Biribi. In the game, players may choose to place bets on either a single number, various groupings of numbers, . . . To determine the winning number, a croupier spins a wheel in one direction, then spins a ball in the opposite direction around a tilted circular track running around the outer edge of the wheel. The ball eventually loses momentum, passes through an area of deflectors, and falls onto the wheel and into one of [the] colored and numbered pockets on the wheel.' back

Russel Shorto, The Irish Affliction, 'Of the various crises the Catholic Church is facing around the world, the central one — wave after wave of accounts of systemic sexual abuse of children by priests and other church figures — has affected Ireland more strikingly than anywhere else. And no place has reacted so aggressively. The Irish responded to the publication in 2009 of two lengthy, damning reports — detailing thousands of cases of rape, sexual molestation and lurid beatings, spanning Ireland’s entire history as an independent country, and the efforts of church officials to protect the abusers rather than the victims — with anger, disgust, vocal assaults on priests in public and demands that the government and society disentangle themselves from the church.' back

Salart, Baas, Branciard, Gisin & Zbinden (2008), Testing the speed of 'spooky action at a distance', ' Abstract Correlations are generally described by one of two mechanisms: either a first event influences a second one by sending information encoded in bosons or other physical carriers, or the correlated events have some common causes in their shared history. Quantum physics predicts an entirely different kind of cause for some correlations, named entanglement. This reveals itself in correlations that violate Bell inequalities (implying that they cannot be described by common causes) between space-like separated events (implying that they cannot be described by classical communication). Many Bell tests have been performed, and loopholes related to locality and detection have been closed in several independent experiments. It is still possible that a first event could influence a second, but the speed of this hypothetical influence (Einstein’s ‘spooky action at a distance’) would need to be defined in some universal privileged reference frame and be greater than the speed of light. Here we put stringent experimental bounds on the speed of all such hypothetical influences. We performed a Bell test over more than 24 hours between two villages separated by 18 km and approximately east–west oriented, with the source located precisely in the middle. We continuously observed two-photon interferences well above the Bell inequality threshold. Taking advantage of the Earth’s rotation, the configuration of our experiment allowed us to determine, for any hypothetically privileged frame, a lower bound for the speed of the influence. For example, if such a privileged reference frame exists and is such that the Earth’s speed in this frame is less than 10^-3 times that of the speed of light, then the speed of the influence would have to exceed that of light by at least four orders of magnitude.' back

Salart, Baas, Branciard, Gisin, & Zbinden 2008, Testing spooky action at a distance, ' In science, one observes correlations and invents theoretical models that describe them. In all sciences, besides quantum physics, all correlations are described by either of two mechanisms. Either a first event influences a second one by sending some information encoded in bosons or molecules or other physical carriers, depending on the particular science. Or the correlated events have some common causes in their common past. Interestingly, quantum physics predicts an entirely different kind of cause for some correlations, named entanglement. This new kind of cause reveals itself, e.g., in correlations that violate Bell inequalities (hence cannot be described by common causes) between space-like separated events (hence cannot be described by classical communication). Einstein branded it as spooky action at a distance. A real spooky action at a distance would require a faster than light influence defined in some hypothetical universally privileged reference frame. Here we put stringent experimental bounds on the speed of all such hypothetical influences. We performed a Bell test during more than 24 hours between two villages separated by 18 km and approximately east-west oriented, with the source located precisely in the middle. We continuously observed 2-photon interferences well above the Bell inequality threshold. Taking advantage of the Earth's rotation, the configuration of our experiment allowed us to determine, for any hypothetically privileged frame, a lower bound for the speed of this spooky influence. For instance, if such a privileged reference frame exists and is such that the Earth's speed in this frame is less than 10^-3 that of the speed of light, then the speed of this spooky influence would have to exceed that of light by at least 4 orders of magnitude. back

Schrödinger equation - Wikipedia, Schrödinger equation - Wikipedia, the free encyclopedia, ' In quantum mechanics, the Schrödinger equation is a partial differential equation that describes how the quantum state of a quantum system changes with time. It was formulated in late 1925, and published in 1926, by the Austrian physicist Erwin Schrödinger. . . . In classical mechanics Newton's second law, (F = ma), is used to mathematically predict what a given system will do at any time after a known initial condition. In quantum mechanics, the analogue of Newton's law is Schrödinger's equation for a quantum system (usually atoms, molecules, and subatomic particles whether free, bound, or localized). It is not a simple algebraic equation, but in general a linear partial differential equation, describing the time-evolution of the system's wave function (also called a "state function").' back

Second law of thermodynamics - Wikipedia, Second law of thermodynamics - Wikipedia - The free encyclopedia, 'The second law of thermodynamics states that in a natural thermodynamic process, there is an increase in the sum of the entropies of the participating systems. The second law is an empirical finding that has been accepted as an axiom of thermodynamic theory. back

Sheffer stroke - Wikipedia, Sheffer stroke - Wikipedia, the free encyclopedia, 'In Boolean functions and propositional calculus, the Sheffer stroke, named after Henry M. Sheffer, written "|" . . . denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both". It is also called nand ("not and") or the alternative denial, since it says in effect that at least one of its operands is false.' back

Shelter Island Conference - Wikipedia, Shelter Island Conference - Wikipedia, the free encyclopedia, ' The first Shelter Island Conference on the Foundations of Quantum Mechanics was held from June 2–4, 1947 at the Ram's Head Inn in Shelter Island, New York. Shelter Island was the first major opportunity since Pearl Harbor and the Manhattan Project for the leaders of the American physics community to gather after the war. As Julian Schwinger would later recall, "It was the first time that people who had all this physics pent up in them for five years could talk to each other without somebody peering over their shoulders and saying, 'Is this cleared?'" ' back

Singlet - Wikipedia, Singlet - Wikipedia, the free encyclopedia, 'In theoretical physics, a singlet usually refers to a one-dimensional representation (e.g. a particle with vanishing spin). It may also refer to two or more particles prepared in a correlated state, such that the total angular momentum of the state is zero. Singlets frequently occur in atomic physics as one of the two ways in which the spin of two electrons can be combined; the other being a triplet. A single electron has spin 1/2, and transforms as a doublet, that is, as the fundamental representation of the rotation group SU(2). The product of two doublet representations can be decomposed into the sum of the adjoint representation (the triplet) and the trivial representation, the singlet. More prosaically, a pair of electron spins can be combined to form a state of total spin 1 and a state of spin 0. The singlet state formed from a pair of electrons has many peculiar properties, and plays a fundamental role in the EPR paradox and quantum entanglement' back

Spacetime - Wikipedia, Spacetime - Wikipedia, the free encyclopedia, 'In physics, spacetime is any mathematical model that combines space and time into a single construct called the space-time continuum. Spacetime is usually interpreted with space being three-dimensional and time playing the role of the fourth dimension. According to Euclidean space perception, the universe has three dimensions of space, and one dimension of time. By combining space and time into a single manifold, physicists have significantly simplified a large amount of physical theory, as well as described in a more uniform way the workings of the universe at both the supergalactic and subatomic levels.' back

Special relativity - Wikipedia, Special relativity - Wikipedia, the free encyclopedia, ' Special relativity . . . is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein (after the considerable and independent contributions of Hendrik Lorentz, Henri Poincaré and others) in the paper "On the Electrodynamics of Moving Bodies". It generalizes Galileo's principle of relativity—that all uniform motion is relative, and that there is no absolute and well-defined state of rest (no privileged reference frames)—from mechanics to all the laws of physics, including both the laws of mechanics and of electrodynamics, whatever they may be. Special relativity incorporates the principle that the speed of light is the same for all inertial observers regardless of the state of motion of the source.' back

Standard model - Wikipedia, Standard model - Wikipedia, the free encyclopedia, 'The Standard Model of particle physics is a theory that describes three of the four known fundamental interactions between the elementary particles that make up all matter. It is a quantum field theory developed between 1970 and 1973 which is consistent with both quantum mechanics and special relativity. To date, almost all experimental tests of the three forces described by the Standard Model have agreed with its predictions. However, the Standard Model falls short of being a complete theory of fundamental interactions, primarily because of its lack of inclusion of gravity, the fourth known fundamental interaction, but also because of the large number of numerical parameters (such as masses and coupling constants) that must be put "by hand" into the theory (rather than being derived from first principles) . . . ' back

Symmetry - Wikipedia, Symmetry - Wikipedia, the free encyclopedia, 'Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, that an object is invariant to a transformation, such as reflection but including other transforms too. Although these two meanings of "symmetry" can sometimes be told apart, they are related, so they are here discussed together.' back

Telecommunications industry - Wikipedia, Telecommunications industry - Wikipedia, the free encyclopedia, ' The telecommunications industries within the sector of information and communication technology is made up of all telecommunications/telephone companies and internet service providers and plays the crucial role in the evolution of mobile communications and the information society. . . . Digital subscriber line (DSL) is the main broadband telecom technology. The fastest growth comes from (value-added) services delivered over mobile networks. . . . Think of telecommunications as the world's biggest machine. Strung together by complex networks, telephones, mobile phones and internet-linked PCs, the global system touches nearly all of us. [Investopedia]' back

Thomas Ainsworth (Stanford Encyclopedia of Philosophy), Form vs. Matter, 'Aristotle famously contends that every physical object is a compound of matter and form. This doctrine has been dubbed “hylomorphism”, a portmanteau of the Greek words for matter (hulê) and form (eidos or morphê). Highly influential in the development of Medieval philosophy, Aristotle’s hylomorphism has also enjoyed something of a renaissance in contemporary metaphysics.' back

Thomas Aquinas Summa Theologiae I, 1, 2, Is sacred doctrine is a science?, 'I answer that, Sacred doctrine is a science. We must bear in mind that there are two kinds of sciences. There are some which proceed from a principle known by the natural light of intelligence, such as arithmetic and geometry and the like. There are some which proceed from principles known by the light of a higher science: thus the science of perspective proceeds from principles established by geometry, and music from principles established by arithmetic. So it is that sacred doctrine is a science because it proceeds from principles established by the light of a higher science, namely, the science of God and the blessed.' back

Thomas Aquinas, Summa I, 3 Proemium (Latin), Summa I, 3: On the simplicity of God, ' Cognito de aliquo an sit, inquirendum restat quomodo sit, ut sciatur de eo quid sit. Sed quia de Deo scire non possumus quid sit, sed quid non sit, non possumus considerare de Deo quomodo sit, sed potius quomodo non sit. Primo ergo considerandum est quomodo non sit; . . . Potest autem ostendi de Deo quomodo non sit, removendo ab eo ea quae ei non conveniunt, utpote compositionem, motum, et alia huiusmodi. Primo ergo inquiratur de simplicitate ipsius, per quam removetur ab eo compositio. . . . Circa primum quaeruntur octo. Primo, utrum Deus sit corpus. Secundo, utrum sit in eo compositio formae et materiae. Tertio, utrum sit in eo compositio quidditatis, sive essentiae, vel naturae, et subiecti. Quarto, utrum sit in eo compositio quae est ex essentia et esse. Quinto, utrum sit in eo compositio generis et differentiae. Sexto, utrum sit in eo compositio subiecti et accidentis. Septimo, utrum sit quocumque modo compositus, vel totaliter simplex. Octavo, utrum veniat in compositionem cum aliis.' back

Thomas Aquinas, Summa, I, 2, 3, Does God exist?, 'I answer that, The existence of God can be proved in five ways. The first and more manifest way is the argument from motion. . . . ' back

Thomas Aquinas, Summa, I, 3, Introduction, ' When the existence of a thing has been ascertained there remains the further question of the manner of its existence, in order that we may know its essence. Now, because we cannot know what God is, but rather what He is not, we have no means for considering how God is, but rather how He is not. . . . ' back

Topology - Wikipedia, Topology - Wikipedia, the freeencyclopedia, 'In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing. . . . The motivating insight behind topology is that some geometric problems depend not on the exact shape of the objects involved, but rather on the way they are put together. For example, the square and the circle have many properties in common: they are both one dimensional objects (from a topological point of view) and both separate the plane into two parts, the part inside and the part outside.' back

Transfinite numbers - Wikipedia, Transfinite numbers - Wikipedia, the free encyclopedia, 'Transfinite numbers are cardinal numbers or ordinal numbers that are larger than all finite numbers, yet not necessarily absolutely infinite. The term transfinite was coined by Georg Cantor, who wished to avoid some of the implications of the word infinite in connection with these objects, which were nevertheless not finite. Few contemporary workers share these qualms; it is now accepted usage to refer to transfinite cardinals and ordinals as "infinite". However, the term "transfinite" also remains in use.' back

Tree of life (biology) - Wikipedia, Tree of life (biology) - Wikipedia, the free encyclopedia, 'The tree of life or universal tree of life is a metaphor used to describe the relationships between organisms, both living and extinct, as described in a famous passage in Charles Darwin's On the Origin of Species (1859).' back

Trinity - Wikipedia, Trinity - Wikipedia, the free encyclopedia, 'The Christian doctrine of the Trinity (from Latin trinitas "triad", from trinus "threefold") defines God as three consubstantial persons, expressions, or hypostases: the Father, the Son (Jesus Christ), and the Holy Spirit; "one God in three persons". The three persons are distinct, yet are one "substance, essence or nature" homoousios). In this context, a "nature" is what one is, while a "person" is who one is.' back

Triple-alpha process - Wikipedia, Triple-alpha process - Wikipedia, the free encyclopedia, 'The triple-alpha process is a set of nuclear fusion reactions by which three helium-4 nuclei (alpha particles) are transformed into carbon.' back

Truth table - Wikipedia, Truth table - Wikipedia, the free encyclopedia, ' A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables (Enderton, 2001). In particular, truth tables can be used to show whether a propositional expression is true for all legitimate input values, that is, logically valid.' back

Turing machine - Wikipedia, Turing machine - Wikipedia, the free encyclopedia, ' A Turing machine is a hypothetical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a computer. The "machine" was invented in 1936 by Alan Turingwho called it an "a-machine" (automatic machine). The Turing machine is not intended as practical computing technology, but rather as a hypothetical device representing a computing machine. Turing machines help computer scientists understand the limits of mechanical computation.' back

Turing's Proof - Wikipedia, Turing's Proof - Wikipedia, the free encyclopedia, 'Turing's proof is a proof by Alan Turing, first published in January 1937 with the title "On Computable Numbers, with an Application to the Entscheidungsproblem." It was the second proof of the assertion (Alonzo Church's proof was first) that some decision problems are "undecidable": there is no single algorithm that infallibly gives a correct "yes" or "no" answer to each instance of the problem. In his own words: "...what I shall prove is quite different from the well-known results of Gödel ... I shall now show that there is no general method which tells whether a given formula U is provable in K [Principia Mathematica]..." '. back

Ullin T. Place, Is Consciousness a Brain Process?, The thesis that consciousness is a process in brain is put forward as a reasonable scientific hypothesis, not to be dismissed on logical grounds alone. conditions under which two sets of observations are treated as observations of same process, rather than as observations of two independent correlated processes, are discussed. It is suggested that we can identify consciousness with a given pattern of brain activity, if we can explain subject's introspective observations by reference to brain processes with which they are correlated. It is argued that problem of providing a physiological explanation of introspective observations is made to seem more difficult than it really is by ‘phenomenological fallacy’, mistaken idea that descriptions of appearances of things are descriptions of actual state of affairs in a mysterious internal environment. back

Unitarity (physics) - Wikipedia, Unitarity (physics) - Wikipedia, the free encyclopedia, In quantum physics, unitarity means that the sum of probabilities of all possible outcome of any event is always 1. This is necessary for the theory to be consistent. This implies that the operator which describes the progress of a physical system in time must be a unitary operator. This operator is e^iHt where H is the Hamiltonian of the system and t is time. back

Unitary operator - Wikipedia, Unitary operator - Wikipedia, the free encyclopedia, ' In functional analysis, a branch of mathematics, a unitary operator . . . is a bounded linear operator U : H → H on a Hilbert space H satisfying UU* = U*U = I where U* is the adjoint of U, and I : H → H is the identity operator. This property is equivalent to the following: 1. U preserves the inner product ( , ) of the Hilbert space, ie for all vectors x and y in the Hilbert space, (Ux, Uy) = (x, y) and
2. U is surjective.' back

Unmoved mover - Wikipedia, Unmoved mover - Wikipedia, the free encyclopedia, ' The unmoved mover (Ancient Greek: ὃ οὐ κινούμενον κινεῖ, romanized: ho ou kinoúmenon kineî, lit. 'that which moves without being moved'] or prime mover (Latin: primum movens) is a concept advanced by Aristotle as a primary cause (or first uncaused cause) or "mover" of all the motion in the universe. As is implicit in the name, the unmoved mover moves other things, but is not itself moved by any prior action. In Book 12 (Greek: Λ) of his Metaphysics, Aristotle describes the unmoved mover as being perfectly beautiful, indivisible, and contemplating only the perfect contemplation: self-contemplation. He equates this concept also with the active intellect. This Aristotelian concept had its roots in cosmological speculations of the earliest Greek pre-Socratic philosophers and became highly influential and widely drawn upon in medieval philosophy and theology. St. Thomas Aquinas, for example, elaborated on the unmoved mover in the Quinque viae. ' back

URL - Wikipedia, URL - Wikipedia, the free encyclopedia, ' A Uniform Resource Locator (URL), colloquially termed a web address, is a reference to a web resource that specifies its location on a computer network and a mechanism for retrieving it. A URL is a specific type of Uniform Resource Identifier (URI) although many people use the two terms interchangeably. URLs occur most commonly to reference web pages (http), but are also used for file transfer (ftp), email (mailto), database access (JDBC), and many other applications.' back

USSG - Indiana University, ISO/OSI Network Model, 'The standard model for networking protocols and distributed applications is the International Standard Organization's Open System Interconnect (ISO/OSI) model. It defines seven network layers: Layer 1 - Physical ... Layer 2 - Data Link ... Layer 3 - Network ...Layer 4 - Transport ... :ayer 5 - Session ... Layer 6 - Presentation ... Layer 7 - Application back

W. F. McGrew et al, Atomic clock performance enabling geodesy below the centimetre level, ' The passage of time is tracked by counting oscillations of a frequency reference, such as Earth’s revolutions or swings of a pendulum. By referencing atomic transitions, frequency (and thus time) can be measured more precisely than any other physical quantity, with the current generation of optical atomic clocks reporting fractional performance below the 10⁻¹⁷ level. However, the theory of relativity prescribes that the passage of time is not absolute, but is affected by an observer’s reference frame. Consequently, clock measurements exhibit sensitivity to relative velocity, acceleration and gravity potential. Here we demonstrate local optical clock measurements that surpass the current ability to account for the gravitational distortion of space-time across the surface of Earth. In two independent ytterbium optical lattice clocks, we demonstrate unprecedented values of three fundamental benchmarks of clock performance. In units of the clock frequency, we report systematic uncertainty of 1.4 × 10⁻¹⁸, measurement instability of 3.2 × 10⁻¹⁹ and reproducibility characterized by ten blinded frequency comparisons, yielding a frequency difference of [−7 ± (5)stat ± (8)sys] × 10⁻¹⁹, where ‘stat’ and ‘sys’ indicate statistical and systematic uncertainty, respectively. Although sensitivity to differences in gravity potential could degrade the performance of the clocks as terrestrial standards of time, this same sensitivity can be used as a very sensitive probe of geopotential. Near the surface of Earth, clock comparisons at the 1 × 10⁻¹⁸ level provide a resolution of one centimetre along the direction of gravity, so the performance of these clocks should enable geodesy beyond the state-of-the-art level. These optical clocks could further be used to explore geophysical phenomena, detect gravitational waves, test general relativity and search for dark matter.' back

Werner Heisenberg, Quantum-theoretical re-interpretation of kinematic and mechanical relations, 'The present paper seeks to establish a basis for theoretical quantum mechanics founded exclusively upon relationships between quantities which in principle are observable.' back

Wigner's theorem - Wikipedia, Wigner's theorem - Wikipedia, the free encyclopedia, 'Wigner's theorem, proved by Eugene Wigner in 1931, is a cornerstone of the mathematical formulation of quantum mechanics. The theorem specifies how physical symmetries such as rotations, translations, and CPT are represented on the Hilbert space of states. According to the theorem, any symmetry transformation of ray space is represented by a linear and unitary or antilinear and antiunitary transformation of Hilbert space. The representation of a symmetry group on Hilbert space is either an ordinary representation or a projective representation. back

Wojciech Hubert Zurek (2008), Quantum origin of quantum jumps: breaking of unitary symmetry induced by information transfer and the transition from quantum to classical, 'Submitted on 17 Mar 2007 (v1), last revised 18 Mar 2008 (this version, v3)) Measurements transfer information about a system to the apparatus, and then further on – to observers and (often inadvertently) to the environment. I show that even imperfect copying essential in such situations restricts possible unperturbed outcomes to an orthogonal subset of all possible states of the system, thus breaking the unitary symmetry of its Hilbert space implied by the quantum superposition principle. Preferred outcome states emerge as a result. They provide framework for the “wavepacket collapse”, designating terminal points of quantum jumps, and defining the measured observable by specifying its eigenstates.' back

Zeno's paradoxes - Wikipedia, Zeno's paradoxes - Wikipedia, the free encyclopedia, 'Zeno's paradoxes are a set of problems generally thought to have been devised by Zeno of Elea to support Parmenides's doctrine that "all is one" and that, contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion.' back

Zero-energy universe - Wikipedia, Zero-energy universe - Wikipedia, the free encyclopedia, 'The zero-energy universe hypothesis proposes that the total amount of energy in the universe is exactly zero: its amount of positive energy in the form of matter is exactly cancelled out by its negative energy in the form of gravity. . . . The zero-energy universe theory originated in 1973, when Edward Tryon proposed in the journal Nature that the universe emerged from a large-scale quantum fluctuation of vacuum energy, resulting in its positive mass-energy being exactly balanced by its negative gravitational potential energy.' back

Zero-point energy - Wikipedia, Zero-point energy - Wikipedia, the free encyclopedia, ' Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly fluctuate in their lowest energy state as described by the Heisenberg uncertainty principle. As well as atoms and molecules, the empty space of the vacuum has these properties. According to quantum field theory, the universe can be thought of not as isolated particles but continuous fluctuating fields: matter fields, whose quanta are fermions (i.e. leptons and quarks), and force fields, whose quanta are bosons (e.g. photons and gluons). All these fields have zero-point energy. These fluctuating zero-point fields lead to a kind of reintroduction of an aether in physics, since some systems can detect the existence of this energy. However this aether cannot be thought of as a physical medium if it is to be Lorentz invariant such that there is no contradiction with Einstein's theory of special relativity.' back