Alexandroff, P S, and (translated by Hazel Perfect and G M Petersen, An Introduction to the Theory of Groups, Blackie and Son Limited 1959-1963 back

Aquinas, Thomas, Summa Theologica (translated by Fathers of the English Dominican Province), Tabor Publishing 1981 'Brother Thomas raised new problems in his teaching, invented a new method, used new systems of proof. To hear him teach a new doctrine, with new arguments, one could not doubt that God, by the irradiation of this new light and by the novelty of this inspiration, gave him the power to teach, by the spoken and written word, new opinions and new knowledge.' (William of Tocco, T's first biographer) 
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Ashby, 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, 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, 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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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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Cercignani, 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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Hawking, 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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Hazewinkel, Michiel, Encyclopaedia of Mathematics (6 volumes), Kluwer Academic and Toppan 1995 'The Encyclopaedia of mathematics aims to be a reference work for all parts of mathematics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-85.' 
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Hazewinkel, Michiel, Encyclopaedia of Mathematics (6 volumes), Kluwer Academic and Toppan 1995 'The Encyclopaedia of mathematics aims to be a reference work for all parts of mathematics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-85.' 
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Huang, Kerson, Statistical Mechanics, John Wiley 1987 'Preface: ... The purpose of this book is to teach statistical mechanics as an integral part of theoretical physics, a discipline that aims to describe all natural phenomena on the basis of a single unifying theory. This theory, at present, is quantum mechanics. . . . Before the subject of statistical mechanics proper is presented, a brief but self contained discussion of thermodynamics and the classical kinetic theory of gases is given. The order of this development is imperative, from a pedagogical point of view, for two reasons. First, thermodynamics has successfully described a large part of macroscopic experience, which is the concern of statistical mechanics. It has done so not on the basis of molecular dynamics but on the basis of a few simple and intuitive postulates stated in everyday terms. If we first familiarize ourselves with thermodynamics, the task of statistical mechanics reduces to the explanation of thermodynamics. Second, the classical kinetic theory of gases is the only known special case in which thermodynamics can be derived nearly from first principles, ie, molecular dynamics. A study of this special case will help us to understand why statistical mechanics works.' 
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Neuenschwander, Dwight E, Emmy Noether's Wonderful Theorem, Johns Hopkins University Press 2011 Jacket: A beautiful piece of mathematics, Noether's therem touches on every aspect of physics. Emmy Noether proved her theorem in 1915 and published it in 1918. This profound concept demonstrates the connection between conservation laws and symmetries. For instance, the theorem shows that a system invariant under translations of time, space or rotation will obey the laws of conservation of energy, linear momentum or angular momentum respectively. This exciting result offers a rich unifying principle for all of physics.' 
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Peskin, Michael E, and Dan V Schroeder, An Introduction to Quantum Field Theory, Westview Press 1995 Amazon Product Description 'This book is a clear and comprehensive introduction to quantum field theory, one that develops the subject systematically from its beginnings. The book builds on calculation techniques toward an explanation of the physics of renormalization.'  
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Streater, Raymond F, and Arthur S Wightman, PCT, Spin, Statistics and All That, Princeton University Press 2005 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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Veltman, 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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Weinberg, 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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Zee, Anthony, Quantum Field Theory in a Nutshell, Princeton University Press 2003 Amazon book description: 'An esteemed researcher and acclaimed popular author takes up the challenge of providing a clear, relatively brief, and fully up-to-date introduction to one of the most vital but notoriously difficult subjects in theoretical physics. A quantum field theory text for the twenty-first century, this book makes the essential tool of modern theoretical physics available to any student who has completed a course on quantum mechanics and is eager to go on. Quantum field theory was invented to deal simultaneously with special relativity and quantum mechanics, the two greatest discoveries of early twentieth-century physics, but it has become increasingly important to many areas of physics. These days, physicists turn to quantum field theory to describe a multitude of phenomena. Stressing critical ideas and insights, Zee uses numerous examples to lead students to a true conceptual understanding of quantum field theory--what it means and what it can do. He covers an unusually diverse range of topics, including various contemporary developments,while guiding readers through thoughtfully designed problems. In contrast to previous texts, Zee incorporates gravity from the outset and discusses the innovative use of quantum field theory in modern condensed matter theory. Without a solid understanding of quantum field theory, no student can claim to have mastered contemporary theoretical physics. Offering a remarkably accessible conceptual introduction, this text will be widely welcomed and used.  
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Nowak, Martin A, Joshua B Plotkin and Vincent A A Jansen, "The evolution of syntactic communication", Nature, 404, 6777, 30 March 2000, page 495-498. Letters to Nature: '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 requisite for taking advantage of combinatorics, that is 'making infinite use of finite means'. ... Here we present a model for the population dynamics of language evolution, define the basic reproductive ratio of words and calculate the maximum size of a lexicon.'. back

Shannon, Claude E, "The mathematical theory of communication", Bell System Technical Journal, 27, , July and October, 1948, page 379-423, 623-656. 'A Note on the Edition Claude Shannon's ``A mathematical theory of communication'' was first published in two parts in the July and October 1948 editions of the Bell System Technical Journal [1]. The paper has appeared in a number of republications since: • The original 1948 version was reproduced in the collection Key Papers in the Development of Information Theory [2]. The paper also appears in Claude Elwood Shannon: Collected Papers [3]. The text of the latter is a reproduction from the Bell Telephone System Technical Publications, a series of monographs by engineers and scientists of the Bell System published in the BSTJ and elsewhere. This version has correct section numbering (the BSTJ version has two sections numbered 21), and as far as we can tell, this is the only difference from the BSTJ version. • Prefaced by Warren Weaver's introduction, ``Recent contributions to the mathematical theory of communication,'' the paper was included in The Mathematical Theory of Communication, published by the University of Illinois Press in 1949 [4]. The text in this book differs from the original mainly in the following points: • the title is changed to ``The mathematical theory of communication'' and some sections have new headings, • Appendix 4 is rewritten, • the references to unpublished material have been updated to refer to the published material. The text we present here is based on the BSTJ version with a number of corrections.. back

Zurek, Wojciech Hubert, "Quantum origin of quantum jumps: Breaking of unitary symmetry induced by information transfer in the transition from quantum to classical", Physical Review A, 76, 5, 16 November 2007, page . Abstract: '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 a framework for 'wave-packet collapse', designating terminal points of quantum jumps and defining the measured observable by specifying its eigenstates. In quantum Darwinism, they are the progenitors of multiple copies spread throughout the environment &mdash the fittest quantum states that not only survive decoherence, but subvert the environment into carrying information about them &mdash into becoming a witness.'. back

Action (physics) - Wikipedia, Action (physics) - Wikipedia, the free encyclopedia, 'In physics, action is an attribute of the dynamics of a physical system from which the equations of motion of the system can be derived. It is a mathematical functional which takes the trajectory, also called path or history, of the system as its argument and has a real number as its result. Generally, the action takes different values for different paths. Action has the dimensions of energy.time or momentum.length], and its SI unit is joule-second.' back

Andrew Koppelman, Nonexistent & Irreplaceable: Keep the Religion in Religious Freedom, 'The singling out of religion for special legal treatment, I will argue here in response, is appropriate, and precisely because religion doesn’t correspond to any narrow category of morally salient thought or conduct; as such it is a concept flexible enough to be accommodated legally while keeping the state neutral about theological questions. Other, more specific categories are either too sectarian to be politically usable, too underinclusive, or too vague to be administrable.' back

Aquinas 160, Summa: I 27 1 Is there procession in God?, 'Our Lord says, "From God I proceeded" (Jn. 8:42).' back

Aquinas 92, I, 14, 13: Does God know future contingent things/, 'I answer that, Since as was shown above (Article 9), God knows all things; not only things actual but also things possible to Him and creature; and since some of these are future contingent to us, it follows that God knows future contingent things.' 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

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

Australian Magpie - Wikipedia, Australian Magpie - Wikipedia, 'The Australian Magpie (Cracticus tibicen) is a medium-sized black and white passerine bird of the family Artamidae native to Australia and southern New Guinea.' back

Big Bang - Wikipedia, Big Bang - Wikipedia, the free encyclopedia, 'The Big Bang theory is the prevailing cosmological model that explains the early development of the Universe. According to the Big Bang theory, the Universe was once in an extremely hot and dense state which expanded rapidly. This rapid expansion caused the young Universe to cool and resulted in its present continuously expanding state. According to the most recent measurements and observations, this original state existed approximately 13.7 billion years ago, which is considered the age of the Universe and the time the Big Bang occurred. ' back

Bohr model - Wikipedia, Bohr model - Wikipedia, the free encyclopedia, 'In atomic physics, the Rutherford–Bohr model or Bohr model, introduced by Niels Bohr in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with attraction provided by electrostatic forces rather than gravity' back

Boolean algebra - Wikipedia, Boolean algebra - Wikipedia, the free encyclopedia, 'In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively. Instead of elementary algebra where the values of the variables are numbers, and the main operations are addition and multiplication, the main operations of Boolean algebra are the conjunction and, denoted ∧, the disjunction or, denoted ∨, and the negation not, denoted ¬. It is thus a formalism for describing logical relations in the same way that ordinary algebra describes numeric relations.' 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

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)) = 2 ⁿ , and the theorem holds because 2ⁿ > n for all non-negative integers. ' back

Catholic Catechism 366, II. Body and Soul, but truly one, '366 The Church teaches that every spiritual soul is created immediately by God - it is not "produced" by the parents - and also that it is immortal: it does not perish when it separates from the body at death, and it will be reunited with the body at the final Resurrection.' back

Catholic Catechism p1, s2, c1, a1, p6, II. Body and soul, but truly one, '366 The Church teaches that every spiritual soul is created immediately by God - it is not "produced" by the parents - and also that it is immortal: it does not perish when it separates from the body at death, and it will be reunited with the body at the final Resurrection.' back

Cayley's theorem - Wikipedia, Cayley's theorem - Wikipedia, the free encyclopedia, 'In group theory, Cayley's theorem, named in honor of Arthur Cayley, states that every group G is isomorphic to a subgroup of the symmetric group on G. This can be understood as an example of the group action of G on the elements of G. A permutation of a set G is any bijective function taking G onto G; and the set of all such functions forms a group under function composition, called the symmetric group on G, and written as Sym(G). Cayley's theorem puts all groups on the same footing, by considering any group (including infinite groups such as (R,+)) as a permutation group of some underlying set. Thus, theorems which are true for permutation groups are true for groups in general.' back

Christopher Knaus, Magistrate condemns 'pernicious evil' of domestic violence while sentencing drunk wife-basher, '"That is, to classify the root cause of the defendant's aberrant behaviour towards the victim as being because of alcohol or drug misuse, or because of an issue with anger management, is simply wrong," she said. "He may in fact have those problems, but family violence is a pernicious evil – unfortunately prevalent in our society – that stems directly from the perpetrator's attitude to women, and from his attempt and desire to exert power and control over his partner.' back

Claire Wilson, Food science: should we believe anything we red about nutrition?, ' Out of the roughly 1 million papers that have been published on nutrition, only a tiny fraction, perhaps a few hundred, are large, good-quality randomised trials, says Ioannidis. The rest are mainly observational studies, small or poorly designed trials, opinion pieces, or reviews that summarise the results of other papers, with all their poten­tial flaws. Even national dietary guidelines are based on this kind of work.' back

Claude Shannon, 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

Claude Shannon - Wikipedia, Claude Shannon - Wikipedia, the free encyclopedia, 'Claude Elwood Shannon (April 30, 1916 – February 24, 2001), an American electrical engineer and mathematician, has been called "the father of information theory". Shannon is famous for having founded information theory and both digital computer and digital circuit design theory when he was 21 years-old by way of a master's thesis published in 1937, wherein he articulated that electrical application of Boolean algebra could construct and resolve any logical, numerical relationship. It has been claimed that this was the most important master's thesis of all time.' back

Code of Canon Law 331, The Roman Pontiff, '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

Conservation of energy - Wikipedia, Conservation of energy - Wikipedia, the free encyclopedia, 'In physics, the law of conservation of energy states that the total energy of an isolated system cannot change—it is said to be conserved over time. Energy can be neither created nor destroyed, but can change form, for instance chemical energy can be converted to kinetic energy in the explosion of a stick of dynamite. 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[which?], 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

CPT Symmetry - Wikipedia, CPT Symmetry - Wikipedia, the free encyclopedia, 'CPT symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity and time simultaneously.' back

D. Salart, A. Baas, C. Branciard, N. Gisin, & H. Zbinden, 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

Dark energy - Wikipedia, Dark energy - Wikipedia, the free encyclopedia, 'In physical cosmology and astronomy, dark energy is an unknown form of energy which is hypothesized to permeate all of space, tending to accelerate the expansion of the universe. Dark energy is the most accepted hypothesis to explain the observations since the 1990s indicating that the universe is expanding at an accelerating rate.' back

Dark matter - Wikipedia, Dark matter - Wikipedia, the free encyclopedia, 'Dark matter is an unidentified type of matter comprising approximately 27% of the mass and energy in the observable universe that is not accounted for by dark energy, baryonic matter (ordinary matter), and neutrinos. The name refers to the fact that it does not emit or interact with electromagnetic radiation, such as light, and is thus invisible to the entire electromagnetic spectrum.' 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

Differential geometry - Wikipedia, Differential geometry - Wikipedia,the free encyclopedia, 'Differential geometry is a mathematical discipline that uses the techniques of differential calculus and integral calculus, as well as linear algebra and multilinear algebra, to study problems in geometry. The theory of plane and space curves and of surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century. Since the late 19th century, differential geometry has grown into a field concerned more generally with the geometric structures on differentiable manifolds.' 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

Euler-Lagrange equation - Wikipedia, Euler-Lagrange equation - Wikipedia, the free encyclopedia, 'In calculus of variations, the Euler–Lagrange equation, Euler's equation, or Lagrange's equation although the latter name is ambiguous (see disambiguation page), is a differential equation whose solutions are the functions for which a given functional is stationary. It was developed by Swiss mathematician Leonhard Euler and Italian mathematician Joseph Louis Lagrange in the 1750s' back

Expansion of the universe - Wikipedia, Expansion of the universe - Wikipedia, the free encyclopedia, ' In 1912, Vesto Slipher discovered that light from remote galaxies was redshifted, which was later interpreted as galaxies receding from the Earth. In 1922, Alexander Friedmann used Einstein field equations to provide theoretical evidence that the universe is expanding. In 1927, Georges Lemaître independently reached a similar conclusion to Friedmann on a theoretical basis, and also presented the first observational evidence for a linear relationship between distance to galaxies and their recessional velocity. Edwin Hubble observationally confirmed Lemaître's findings two years later. Assuming the cosmological principle, these findings would imply that all galaxies are moving away from each other. Based on large quantities of experimental observation and theoretical work, the scientific consensus is that space itself is expanding, and that it expanded very rapidly within the first fraction of a second after the Big Bang. This kind of expansion is known as "metric expansion".' back

Felix Klein - Wikipedia, Felix Klein - Wikipedia, the free encyclopedia, 'Felix Christian Klein (25 April 1849 – 22 June 1925) was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory. His 1872 Erlangen Program, classifying geometries by their underlying symmetry groups, was a hugely influential synthesis of much of the mathematics of the day.' 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 diagram - Wikipedia, Feynman diagram - Wikipedia, the free encyclopedia, ' In theoretical physics, Feynman diagrams are pictorial representations of the mathematical expressions describing the behavior of subatomic particles. The scheme is named after its inventor, American physicist Richard Feynman, and was first introduced in 1948. The interaction of sub-atomic particles can be complex and difficult to understand intuitively. Feynman diagrams give a simple visualization of what would otherwise be an arcane and abstract formula. As David Kaiser writes, "since the middle of the 20th century, theoretical physicists have increasingly turned to this tool to help them undertake critical calculations", and so "Feynman diagrams have revolutionized nearly every aspect of theoretical physics".' 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

Hamilton's principle - Wikipedia, Hamilton's principle - Wikipedia, the free encyclopedia, 'In physics, Hamilton's principle is William Rowan Hamilton's formulation of the principle of stationary action . . . It states that the dynamics of a physical system is determined by a variational problem for a functional based on a single function, the Lagrangian, which contains all physical information concerning the system and the forces acting on it.' 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

Human Rights Watch, Home | Human Rights Watch, 'Human Rights Watch is one of the world’s leading independent organizations dedicated to defending and protecting human rights. By focusing international attention where human rights are violated, we give voice to the oppressed and hold oppressors accountable for their crimes. Our rigorous, objective investigations and strategic, targeted advocacy build intense pressure for action and raise the cost of human rights abuse. For 30 years, Human Rights Watch has worked tenaciously to lay the legal and moral groundwork for deep-rooted change and has fought to bring greater justice and security to people around the world.' back

Human sacrifice - Wikipedia, Human sacrifice - Wikipedia, the free encyclopedia, 'Human sacrifice is the act of killing one or more human beings, usually as an offering to a deity, as part of a religious ritual. Its typology closely parallels the various practices of ritual slaughter of animals and of religious sacrifice in general.' back

Initial singularity - Wikipedia, Initial singularity - Wikipedia, the free encyclopedia, 'The initial singularity was the gravitational singularity of infinite density thought to have contained all of the mass and spacetime of the Universe before quantum fluctuations caused it to rapidly expand in the Big Bang and subsequent inflation, creating the present-day Universe.' back

Isaiah 1:18, Isaiah 1:18: Come now let us reason together . . . , 18"Come now, and let us reason together," Says the LORD, "Though your sins are as scarlet, They will be as white as snow; Though they are red like crimson, They will be like wool. back

Jeffrey Nicholls, Prolegomenon to Scientific Theology, ' This thesis is an attempt to carry speculative theology beyond the apogee it reached in the medieval work of Thomas Aquinas into the world of empirical science (Aquinas 2019). Since the time of Aquinas, our understanding of the Universe has increased enormously. The ancient theologians not only conceived a perfect God, but they also saw the world as a very imperfect place. Their reaction was to place God outside the world. I will argue that we live in a Universe which approaches infinity in size and complexity, is as perfect as can be, and fulfils all the roles traditionally attributed to God, creator, lawmaker and judge.' back

John Ashton, Open letter to Shell's Ben van Beurden from John Ashton, 'It is in truth not your fault that climate change is a hard problem. Though your industry must bear some responsibility for our failure so far to face it, that is not exclusively your fault either. But the choices of your generation of CEOs will be decisive, not only for you as corporations but for the eventual success or failure of our response to climate change. That is why you will be held relentlessly to account for those choices; why what you said in February invites forensic scrutiny.' back

John Paul II, Ordinatio Sacerdotalis, 22 May 1994, '4. Although the teaching that priestly ordination is to be reserved to men alone has been preserved by the constant and universal Tradition of the Church and firmly taught by the Magisterium in its more recent documents, at the present time in some places it is nonetheless considered still open to debate, or the Church's judgment that women are not to be admitted to ordination is considered to have a merely disciplinary force. Wherefore, in order that all doubt may be removed regarding a matter of great importance, a matter which pertains to the Church's divine constitution itself, in virtue of my ministry of confirming the brethren (cf. Lk 22:32) I declare that the Church has no authority whatsoever to confer priestly ordination on women and that this judgement is to be definitively held by all the Church's faithful.' back

Kookaburra - Wikipedia, Kookaburra - Wikipedia, the free encyclopedia, 'Kookaburras (genus Dacelo) are terrestrial tree kingfishers native to Australia and New Guinea, which grow to between 28–42 cm (11–17 in) in length. The name is a loanword from Wiradjuri guuguubarra, onomatopoeic of its call. . . . The kookaburra's loud call sounds like echoing human laughter. They are found in habitats ranging from humid forest to arid savanna, as well as in suburban areas with tall trees or near running water.' back

Lagrangian - Wikipedia, Lagrangian - Wikipedia, the free encyclopedia, 'The Lagrangian, L, of a dynamical system is a function that summarizes the dynamics of the system. It is named after Joseph Louis Lagrange. The concept of a Lagrangian was originally introduced in a reformulation of classical mechanics by Irish mathematician William Rowan Hamilton known as Lagrangian mechanics. In classical mechanics, the Lagrangian is defined as the kinetic energy, T, of the system minus its potential energy, V. In symbols, L = T - V. ' back

Lagrangian mechanics - Wikipedia, Lagrangian mechanics - Wikipedia, the free encyclopedia, 'Lagrangian mechanics is a re-formulation of classical mechanics that combines conservation of momentum with conservation of energy. It was introduced by Joseph Louis Lagrange in 1788. In Lagrangian mechanics, the trajectory of a system of particles is derived by solving Lagrange's equation, given herein, for each of the system's generalized coordinates. The fundamental lemma of calculus of variations shows that solving Lagrange's equation is equivalent to finding the path that minimizes the action functional, a quantity that is the integral of the Lagrangian over time.' back

Lorentz transformation - Wikipedia, Lorentz transformation - Wikipedia, the free encyclopedia, 'In physics, the Lorentz transformation or Lorentz-Fitzgerald transformation describes how, according to the theory of special relativity, two observers' varying measurements of space and time can be converted into each other's frames of reference. It is named after the Dutch physicist Hendrik Lorentz. It reflects the surprising fact that observers moving at different velocities may measure different distances, elapsed times, and even different orderings of events.' back

Louis de Broglie - Wikipedia, Louis de Broglie - Wikipedia, the free encyclopedia, 'Louis-Victor-Pierre-Raymond, 7th duc de Broglie . . . 15 August 1892 – 19 March 1987) was a French physicist who made groundbreaking contributions to quantum theory. In his 1924 PhD thesis he postulated the wave nature of electrons and suggested that all matter has wave properties. This concept is known as the de Broglie hypothesis, an example of wave-particle duality, and forms a central part of the theory of quantum mechanics.' back

Manley, D. B., & Taylor, C. S. (1996), Descartes Meditations - Trilingual Edition, ' The publication of this English-Latin-French edition of Descartes' Meditations on First Philosophy is quite simply an experiment in electronic scholarship. We decided to make this edition available and to encourage its free distribution for scholarly purposes. The idea behind the experiment is to see how others involved in electronic scholarship might put these texts to use. We have no predetermined ideas of what such use may be when transformed from this origin. The texts have no hypertext annotations except for those used for navigation. We invite others to download this edition and to create their own hypertext annotated editions and then to publish those additions on their own Web servers for everyone to use.' back

Mark Anderson, World Bank funding 'shrouded in darkness and riddled with abuse', 'The World Bank must “completely overhaul” a funding model built on heavy investment in financial companies that leaves the organisation with little control over where its money ends up, a group of NGOs has warned. The bank’s private sector arm, the International Finance Corporation (IFC), invested $36bn (£24.5bn) in financial companies including hedge funds, private equity firms and commercial banks between 2009 and 2013, according to a report released on Thursday. The study, prepared by NGOs including Oxfam, Global Witness and the Bretton Woods Project, said these funds would be better used to pursue development targets in areas such as education and public health. The report noted that, between 2009 and 2013, the IFC lent three times more to financial intermediaries than education programmes in the developing world. ' back

Measurement in quantum mechanics - Wikipedia, Measurement in quantum mechanics - Wikipedia, the free encyclopedia, 'The framework of quantum mechanics requires a careful definition of measurement. The issue of measurement lies at the heart of the problem of the interpretation of quantum mechanics, for which there is currently no consensus.' back

Micah Zenko, The Coronavirus Is the Worst Intelligence Failure in U.S. History, ' The White House detachment and nonchalance during the early stages of the coronavirus outbreak will be among the most costly decisions of any modern presidency. These officials were presented with a clear progression of warnings and crucial decision points far enough in advance that the country could have been far better prepared. But the way that they squandered the gifts of foresight and time should never be forgotten, nor should the reason they were squandered: Trump was initially wrong, so his inner circle promoted that wrongness rhetorically and with inadequate policies for far too long, and even today. Americans will now pay the price for decades.' 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

Monika Scislowska, polish Composer, Conductor Krzysztof Penderecki Dies At 86, ' Warsaw, Poland (AP) -- Krzysztof Penderecki, an award-winning conductor and one of the world’s most popular contemporary classical music composers whose works have featured in Hollywood films like “The Shining” and “Shutter Island,” died Sunday. He was 86. . . . Penderecki was best known for his monumental compositions for orchestra and choir, like “St. Luke Passion" and “Seven Gates of Jerusalem,” though his range was much wider. Rock fans know him from his work with Radiohead’s Jonny Greenwood.' back

MSO Livestream, Rimsky-Korsakov's Scherezade, back

Niels Hendrik Abel - Wikipedia, Niels Hendrik Abel - Wikipedia, the free encyclopedia, "Niels Henrik Abel (August 5, 1802 – April 6, 1829) was a noted Norwegian mathematician[1] who proved the impossibility of solving the quintic equation in radicals.' back

Once Upon a Time in the West - Wikipedia, Once Upon a Time in the West - Wikipedia, the free encyclopedia, ' Once Upon a Time in the West . . . is a 1968 epic Spaghetti Western film directed by Sergio Leone, who co-wrote it with Sergio Donati based on a story by Dario Argento, Bernardo Bertolucci and Leone. It stars Henry Fonda, cast against type, as the villain, Charles Bronson as his nemesis, Claudia Cardinale as a newly widowed homesteader, and Jason Robards as a bandit. The widescreen cinematography was by Tonino Delli Colli, and the acclaimed film score was by Ennio Morricone. . . . In 2009, the film was selected for preservation in the United States National Film Registry by the Library of Congress as being "culturally, historically or aesthetically significant".' back

P. A. M. Dirac, The Lagragian in Quantum Mechanics, 'Quantum mechanics was built upon a foundation of analogy with the Hamiltonian theory of classical mechanics. . . . Now there is an alternative formulation for classical dynamics, provided by the Lagrangian. This requires one to work in terms of coordinates and velocities instead of coordinates and momenta. The two formulations are, of course, closely related, but there are reasons for believing that the Lagangian one is more fundamental.' 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. . . . Secodly the lagrangian method can easily be expressed relativitically, on account of the action function being a relativistic invariant; . . . ' 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

Paul Kugman, This Land of Denial and Death, ' Among advanced countries, the United States has long stood out as the land of denial and death. . . . About denial: Epidemiologists trying to get a handle on the coronavirus threat appear to have been caught off guard by the immediate politicization of their work, the claims that they were perpetrating a hoax designed to hurt Trump, or promote socialism, or something. But they should have expected that reaction, since climate scientists have faced the same accusations for years. . . . About death: . . .In fact, we have the lowest life expectancy among advanced countries, and the gap has been steadily widening for decades. This widening gap, in turn, surely reflects both America’s unique lack of universal health insurance and its equally unique surge in “deaths of despair” — deaths from drugs, alcohol and suicide — among working-class whites who have seen economic opportunities disappear.' 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

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

Publication of Darwin's theory - Wikipedia, Publication of Darwin's theory - Wikipedia, the free encyclopedia, 'The publication of Darwin's theory brought into the open Charles Darwin's ideas of evolution through natural selection, the culmination of more than twenty years of work.' back

Rachel Browne, 'Survivors have waited too long': 4000 institutions named in sex abuse royal commission, 'Data gleaned largely from private sessions found there were more than 4000 institutions where alleged abuse of children occurred. Religious institutions were most frequently named, with 60 per cent of survivors in private sessions reporting child abuse in a religious organisation. Just over one-third of survivors reported abuse in a government-managed institution. "It is remarkable that failures have occurred in so many institutions," Justice McClellan said.' 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

Richard J Cook, Physical time and physical space in general relativity, ''‘Now it came to me the independence of the gravitational acceleration from the nature of the falling substance, may be expressed as follows: In a gravitational field (of small spatial exten- sion) things behave as they do in space free of gravitation, . . . This happened in 1908. Why were another seven years required for the construction of the general theory of relativity? The main rea- son lies in the fact that it is not so easy to free oneself from the idea that coordinates must have an immediate metrical meaning.’’ Albert Einstein' [Misner, Thorne and Wheeler, Gravitation, page 5, from Schilp 1949 page 65-67] back

S Matrix - Wikipedia, S Matrix - Wikipedia, the free encyclopedia, 'In physics, the Scattering matrix (S-matrix) relates the initial state and the final state for an interaction of particles. It is used in quantum mechanics, scattering theory and quantum field theory.' 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

Self-energy - Wikipedia, Self-energy - Wikipedia, the free encyclopedia, 'In most theoretical physics such as quantum field theory, a particle's self-energy Sigma represents the contribution to the particle's energy, or effective mass, due to interactions between the particle and the system it is part of. For example, in electrostatics the self-energy of a given charge distribution is the energy required to assemble the distribution by bringing in the constituent charges from infinity, where the electric force goes to zero.' back

Sophus Lie - Wikipedia, Sophus Lie - Wikipedia, 'Marius Sophus Lie (pronounced [liː], as "Lee") (17 December 1842 - 18 February 1899) was a Norwegian-born mathematician. He largely created the theory of continuous symmetry, and applied it to the study of geometry and differential equations. 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

Steven Lee Myers, China Created a Fail-Safe System to Track Contagions. It Failed., ' The alarm system was ready. Scarred by the SARS epidemic that erupted in 2002, China had created an infectious disease reporting system that officials said was world-class: fast, thorough and, just as important, immune from meddling. Hospitals could input patients’ details into a computer and instantly notify government health authorities in Beijing, where officers are trained to spot and smother contagious outbreaks before they spread. It didn’t work. After doctors in Wuhan began treating clusters of patients stricken with a mysterious pneumonia in December, the reporting was supposed to have been automatic. Instead, hospitals deferred to local health officials who, over a political aversion to sharing bad news, withheld information about cases from the national reporting system — keeping Beijing in the dark and delaying the response.' The central health authorities first learned about the outbreak not from the reporting system but after unknown whistle-blowers leaked two internal documents online. back

Tamara M. Davis and Chales H. Lineweaver, Expansion Confusion: common misconceptions of cosmologival horizons and superluminal expansion of the Universe, ' We use standard general relativity to illustrate and clarify several common misconceptions about the expansion of the Universe. To show the abundance of these misconceptions we cite numerous misleading, or easily misinterpreted, statements in the literature. In the context of the new standard Lambda-CDM cosmology we point out confusions regarding the particle horizon, the event horizon, the ``observable universe'' and the Hubble sphere (distance at which recession velocity = c). We show that we can observe galaxies that have, and always have had, recession velocities greater than the speed of light. We explain why this does not violate special relativity and we link these concepts to observational tests. Attempts to restrict recession velocities to less than the speed of light require a special relativistic interpretation of cosmological redshifts. We analyze apparent magnitudes of supernovae and observationally rule out the special relativistic Doppler interpretation of cosmological redshifts at a confidence level of 23 sigma.' back

Thomas Aquinas, Summa Theologica, Thomas Aquinas: The medieval theological classic online : 'Because the doctor of Catholic truth ought not only to teach the proficient, but also to instruct beginners (according to the Apostle: As unto little ones in Christ, I gave you milk to drink, not meat -- 1 Cor. 3:1-2), we purpose in this book to treat of whatever belongs to the Christian religion, in such a way as may tend to the instruction of beginners. We have considered that students in this doctrine have not seldom been hampered by what they have found written by other authors, partly on account of the multiplication of useless questions, articles, and arguments, partly also because those things that are needful for them to know are not taught according to the order of the subject matter, but according as the plan of the book might require, or the occasion of the argument offer, partly, too, because frequent repetition brought weariness and confusion to the minds of readers.' 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

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

William K Rashbaum, Benjamin Weiser & Katie Brenner, Venezuelan Leader Maduro Is Charged in the U.S. With Drug Trafficking, ' Mr. Maduro’s government is “plagued by criminality and corruption,” Attorney General William P. Barr said in announcing the charges at a news briefing along with the head of the Drug Enforcement Administration and the top federal prosecutors in Miami and Manhattan, where an indictment accused Mr. Maduro, 57, of importing hundreds of tons of cocaine into the United States. The Justice Department aimed to root out “the extensive corruption within the Venezuelan government — a system constructed and controlled to enrich those at the highest levels of the government,” Mr. Barr added.' 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 canceled 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