Bierce, Ambrose Gwinnett, and David E Schults, S T Joshi (Editors), The Unabridged Devil's Dictionary, University of Georgia Press 2001 Amazon customer review: 'Ambrose Bierce, in this hilarious book, satirizes all aspects of human behavior. This lexicon that he has created provides often true insight in to the tacit meanings of otherwise benign words. For example, PRAY, v. To ask that the laws of the universe be annulled in behalf of a single petitioner confessedly unworthy. This book is a must-get.' Doshi 
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Dauben, 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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Deighton, Len, London Match, Ballantine Books 1997 Amazon Editorial Review From Publishers Weekly 'Winding up the tense story begun in Berlin Game and continued in Mexico Set, Deighton's new thriller follows British intelligence agent Bernard Samson as he careens between troubled spots in Berlin and London. Bernard's recent triumph is persuading the KGB's renowned spy Erich Stennis to defect to England but, since Samson's wife Fiona has gone over to the Russians, he isn't entirely trusted by his colleagues. Now suspicions that another mole has been planted among the operatives in London exacerbate Samson's fears, mostly for his small children, if he is accused. Determined to protect himself from his own fellow workers and the wily plots of Fiona and the KGB, Samson plunges into harrowing situations, climaxing in a bloody battle which both sides claim they've won. Actually, as Samson reveals, everybody loses in the deadly game of espionage.' Copyright 1985 Reed Business Information, Inc 
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Feynman, Richard P, and Robert B Leighton, Matthew Sands, The Feynman Lectures on Physics (volume 3) : Quantum Mechanics, Addison Wesley 1970 Foreword: 'This set of lectures tries to elucidate from the beginning those features of quantum mechanics which are the most basic and the most general. . . . In each instance the ideas are introduced together with a detailed discussion of some specific examples - to try to make the physical ideas as real as possible.' Matthew Sands 
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Graves, Robert, The Nazarene Gospel Restored, House of Stratus 2004 Amazon Book Description: 'Drawing upon Jewish scholarship and a vast knowledge of the ancient world, this extraordinary account attempts to reconstruct the historical Jesus by placing emphasis on the narrative of his life. Similar to The Da Vinci Code in mood, this revised edition untangles the distortions and age-old problems of the original texts to uncover the truth behind Jesus’s words and actions. It also includes a detailed account of the composition and reception of the book—when it first published, it was deemed controversial, its reviews were hostile, and its author was twice sued for libel.' 
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Hallett, Michael, Cantorian Set Theory and Limitation of Size, Oxford UP 1984 Jacket: 'This book will be of use to a wide audience, from beginning students of set theory (who can gain from it a sense of how the subject reached its present form), to mathematical set theorists (who will find an expert guide to the early literature), and for anyone concerned with the philosophy of mathematics (who will be interested by the extensive and perceptive discussion of the set concept).' Daniel Isaacson. 
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Istrastescu, Vasile I, Fixed Point Theory: An Introduction, Kluwer Academic 2002  
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Kolmogorov, A N, 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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Lide, David R, and (Editor-inChief), CRC Handbook of Chemistry and Physics: A Ready-Refrence Book of Chemical and Physical Datya, Taylor and Francis 2005-2006 Preface: 'Notwithstanding the new appearance of the pages, the overall philosophy of the Handbook remains the same, namely to provide a broad coverage of all types of data commonly encounted by physical scientists and engineers with as much depth as can be accommodated in a one-volume format. In spite of the growing popularity of Internet searching, which often turns up voluminous information of questionable quality, we feel there is still a need for a concise, reliable reference source spanning the full range of the physical sciences and focusing on key data that are frequently needed by R&D professionals, engineers and students. . . . '  
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Monk, Ray, Bertrand Russell: The Ghost of Madness, Free Press 2016 ' In the second half of his life, Bertrand Russell transformed himself from a major philosopher, whose work was intelligible to a small elite, into a political activist and popular writer, known to millions throughout the world. Yet his life is the tragic story of a man who believed in a modern, rational approach to life and who, though his ideas guided popular opinion throughout the twentieth century, lost everything. Russell's views on marriage, religion, education, and politics attracted legions of devoted followers and, at the same time, provoked harsh attacks from every direction. On the one hand, he was stripped of his post at New York's City College because he was thought to be a bad influence on his students, and on the other, he was awarded the Order of Merit, the Nobel Prize in literature, and a lifetime Fellowship of Trinity College, Cambridge. He lived to be ninety-seven, and as he became older he became increasingly controversial. Monk quotes Russell's telegrams to Kennedy and Khrushchev during the Cuban missile crisis, an influence that Russell and his followers believed tipped the balance toward peace. Russell devoted his last years to a campaign organized by his secretary to lend support to Che Guevara's call for a globally coordinated revolutionary struggle against "U.S. imperialism." Until now, this last campaign has been misunderstood as a -- perhaps misguided, but nevertheless innocent -- plea for world peace. Monk reveals it was no such thing. Drawing on thousands of documents collected at the Russell archives in Canada, Monk steers through the turbulence of Russell's public activities, scrutinizing his sometimes paradoxical and often outrageous pronouncements. Monk's focus, however, is on the tragedy of Russell's personal life, and in revealing this inner drama Monk has relied heavily on the cooperation of Russell's surviving relatives and access to previously unexamined legal and private correspondence. A central player in Russell's life was his first son, John. Russell applied the methods of the new science of child psychology in his parenting, believing that a new generation of children could be reared to be "independent, fearless, and free." But instead of being a model of this new generation, John became anxious, withdrawn, and eventually schizophrenic. Nor was John's daughter Lucy (who was Russell's favorite grandchild) to be a model of the new generation; gradually she grew so emotionally disturbed that, at the age of twenty-six, she took her own life. The Ghost of Madness completes the most searching examination yet published of Bertrand Russell's unique life and work. Together with Ray Monk's highly praised first volume of the biography, The Spirit of Solitude, this is the classic account of an extraordinary man who championed the great ideas of the twentieth century and was all but destroyed by them. It is a portrait of the mind of a century.' 
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Whitehead, Alfred North , The Concept of Nature, CreateSpace 1930, 2016 ' Hailed as "one of the most valuable books on the relation of philosophy and science," Alfred North Whitehead's The Concept of Nature, first published in 1920, was an important contribution to the development of philosophic naturalism. Examining the fundamental problems of substance, space, and time, Whitehead assesses the impact of Einstein's theories as well as the then-recent findings of modern physics on the concept of nature.' 
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Lan, Shau-Yu, et al, "A Clock Directly Linking Time to a Particle's Mass", Science, 339, 6119, 1 February 2013, page 554-557. 'ABSTRACT Historically, time measurements have been based on oscillation frequencies in systems of particles, from the motion of celestial bodies to atomic transitions. Relativity and quantum mechanics show that even a single particle of mass m determines a Compton frequency ω₀ = mc²/ℏ, where c is the speed of light and ℏ is Planck's constant h divided by 2π. A clock referenced to ω₀ would enable high-precision mass measurements and a fundamental definition of the second. We demonstrate such a clock using an optical frequency comb to self-reference a Ramsey-Bordé atom interferometer and synchronize an oscillator at a subharmonic of ω0. This directly demonstrates the connection between time and mass. It allows measurement of microscopic masses with 4 × 10−9 accuracy in the proposed revision to SI units. Together with the Avogadro project, it yields calibrated kilograms.'. back

Atom - Wikipedia, Atom - Wikipedia, the free encyclopedia, 'The atom is a basic unit of matter that consists of a dense central nucleus surrounded by a cloud of negatively charged electrons. The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons (except in the case of hydrogen-1, which is the only stable nuclide with no neutrons). The electrons of an atom are bound to the nucleus by the electromagnetic force.' 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

Cantor's paradox - Wikipedia, Cantor's paradox - Wikipedia, the free encyclopedia, 'In set theory, Cantor's paradox is derivable from the theorem that there is no greatest cardinal number, so that the collection of "infinite sizes" is itself infinite. The difficulty is handled in axiomatic set theory by declaring that this collection is not a set but a proper class; in von Neumann–Bernays–Gödel set theory it follows from this and the axiom of limitation of size that this proper class must be in bijection with the class of all sets. Thus, not only are there infinitely many infinities, but this infinity is larger than any of the infinities it enumerates.' back

Cantor's theorem - Wikipedia, Cantor's theorem - Wikipedia, the free encyclopedia, 'In elementary set theory, Cantor's theorem states that, for any set A, the set of all subsets of A (the power set of A) has a strictly greater cardinality than A itself. For finite sets, Cantor's theorem can be seen to be true by a much simpler proof than that given below, since in addition to subsets of A with just one member, there are others as well, and since n < 2n for all natural numbers n. But the theorem is true of infinite sets as well. In particular, the power set of a countably infinite set is uncountably infinite. The theorem is named for German mathematician Georg Cantor, who first stated and proved it.' back

Claudia Taranto, Recovered grandchild 121, ' Maximiliano Menna Lanzillotto didn't trust the strange voice at the other end of the phone line. It told him he could be one of Argentina's 'missing grandchildren' — taken as a baby by the military regime during the so-called Dirty War. It couldn't be true, Maximiliano told himself. He was certain of it. But it was. At the age of 40, Maximiliano officially became 'recovered grandchild 121'. And so began a journey to discover the truth.' back

Commonweal: Editorial, After Benedict: Changing Expectations for the Papacy, Even Benedict’s most ardent supporters concede that his papacy has been marred by too many scandals and too many gaffes. The few glimpses the public has gotten into the opaque operations of the Holy See—from the Vatican bank controversy to the inept machinations of the pope’s own butler—reveal an institution in crisis. These intrigues are especially disconcerting as the church still struggles to come to terms with the legacy of the sexual-abuse crisis. Unfortunately, the courtly secrecy surrounding the deliberations to elect the next pope provides an all-too-obvious reminder of the lack of transparency and accountability in the operations of the entire hierarchy. back

DeNeen L. Brown, Hunting down runaway slaves: The cruel ads of Andrew Jackson and 'the master class', ' “Stop the Runaway,” Andrew Jackson urged in an ad placed in the Tennessee Gazette in October 1804. The future president gave a detailed description: A “Mulatto Man Slave, about thirty years old, six feet and an inch high, stout made and active, talks sensible, stoops in his walk, and has a remarkable large foot, broad across the root of the toes — will pass for a free man.…” ' 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

Elizabeth Dias and Jason Horowitz, Catholic Leaders at Meeting on Sex Abuse Hear Proposal for Removing Bishops, ' VATICAN CITY — The American cardinal entrusted by Pope Francis with organizing his global conference on clerical sexual abuse presented Roman Catholic leaders with a set of new proposals on Friday, including changes to the process for investigating bishops accused of misconduct or negligence. On the second day of a historic summit meeting in Rome, the cardinal, Blase Cupich, the archbishop of Chicago, proposed that top Catholic clerics in each country, assisted by lay people, should be given the power to investigate accusations of misconduct at the top of their local church hierarchies, instead of waiting for Rome to “come up with all the answers.” ' back

Eternal sin - Wikipedia, Eternal sin - Wikipedia, the free encyclopedia, 'Eternal sins or unforgivable sins or unpardonable sins are part of Christian hamartiology, which is the Christian theology of sins. These are sins which will not be forgiven by God whereby salvation becomes impossible. One eternal or unforgiveable sin is specified in several passages of the Synoptic Gospels.[1] Verse 29 in Mark 3 states that there is one sin considered "eternal" and that is "blasphemy against the Holy Spirit"; however this verse is rarely taken literally except by biblical literalists. Some other sins that are sometimes considered eternal or unforgivable include impenitence (refusing to accept the Mercy of God by repenting) as in the Catholic Catechism #1864 or ascribing the work of the Holy Spirit to the Devil.' back

Fermat's principle - Wikipedia, Fermat's principle - Wikipedia, the free encyclopedia, 'In optics, Fermat's principle or the principle of least time is the idea that the path taken between two points by a ray of light is the path that can be traversed in the least time. This principle is sometimes taken as the definition of a ray of light.[1] Fermat's Principle can be used to describe the properties of light rays reflected off mirrors, refracted through different media, or undergoing total internal reflection. It can be deduced from Huygens' principle, and can be used to derive Snell's law of refraction and the law of reflection.' back

Frank Bruni, The Catholic Church is Breaking People's Hearts, ' Pat Fitzgerald, 67, has long loved being a Catholic, and the part he loved maybe most of all, for the past quarter-century, was his role as a spiritual mentor at retreats for students at a church-affiliated high school in Indianapolis, where he lives. But he has been told that he’s not wanted anymore. His crime? He publicly supported his daughter, a guidance counselor at the school, after its administrators moved to get rid of her because she’s married to a woman.' back

History of the term Catholic - Wikipedia, History of the term "Catholic" - Wikipedia, the free encyclopedia, 'The word catholic (derived via Late Latin catholicus, from the Greek adjective καθολικός (katholikos), meaning "universal") comes from the Greek phrase καθόλου (katholou), meaning "on the whole", "according to the whole" or "in general", and is a combination of the Greek words κατά meaning "about" and όλος meaning "whole". The word in English can mean either "including a wide variety of things; all-embracing" or "of the Roman Catholic faith" as "relating to the historic doctrine and practice of the Western Church."' back

Holy See, Congregation for the Doctrine of the Faith, Profile: 'CONGREGATION FOR THE DOCTRINE OF THE FAITH Founded in 1542 by Pope Paul III with the Constitution "Licet ab initio," . . . The only curial organism which is older is the Secretariat of State, whose forerunner, the Apostolic Secretariat, was created by Innocent VIII on December 31, 1487, with the Constitution "Non debet reprehensibile." . . . Today, according to Article 48 of the Apostolic Constitution on the Roman Curia, 'Pastor Bonus,' promulgated by the Holy Father John Paul II on June 28, 1988, "the duty proper to the Congregation for the Doctrine of the Faith is to promote and safeguard the doctrine on the faith and morals throughout the Catholic world: for this reason everything which in any way touches such matter falls within its competence." The congregation is now headed by Prefect Cardinal Joseph Ratzinger. It has a secretary, Archbishop Tarcisio Bertone, S.D.B., named June 13, an under-secretary, Msgr. Jozef Zlatnansky, and a staff of 32, according to the 1995 "Annuario Pontificio" or "Pontifical Yearbook." It also has 23 members - cardinals, archbishops and bishops - and 27 consultors. Given the nature of its task, congregation work is divided into four distinct sections: the doctrinal office, the disciplinary office, the matrimonial office and that for priests. back

Jesse Bering, Sometimes, You Won't Feel Better Tomorrow, ' “Suicide,” goes the popular expression, “is a permanent solution to a temporary problem.” . . . This tends to be the prevailing narrative around suicide and suicidality—a message cloaked in a constant admonishment to “just reach out for help” if you are feeling this way, and someone will try to see you through to the other side. The problem with this, though, is the obvious reality that some problems really are permanent, thank you very much. . . . It should not be irrational to acknowledge this existential fact, and yet it remains stubbornly difficult to talk about. ' back

John Paul II, Fides et Ratio: On the relationship between faith and reason , para 2: 'The Church is no stranger to this journey of discovery, nor could she ever be. From the moment when, through the Paschal Mystery, she received the gift of the ultimate truth about human life, the Church has made her pilgrim way along the paths of the world to proclaim that Jesus Christ is “the way, and the truth, and the life” (Jn 14:6).' back

John Paul II, Ex Corde Ecclesiae, '27. Every Catholic University, without ceasing to be a University, has a relationship to the Church that is essential to its institutional identity. As such, it participates most directly in the life of the local Church in which it is situated; at the same time, because it is an academic institution and therefore a part of the international community of scholarship and inquiry, each institution participates in and contributes to the life and the mission of the universal Church, assuming consequently a special bond with the Holy See by reason of the service to unity which it is called to render to the whole Church. One consequence of its essential relationship to the Church is that the institutional fidelity of the University to the Christian message includes a recognition of and adherence to the teaching authority of the Church in matters of faith and morals. Catholic members of the university community are also called to a personal fidelity to the Church with all that this implies. Non-Catholic members are required to respect the Catholic character of the University, while the University in turn respects their religious liberty. back

John Paul II, Fides et Ratio: On the relationship between faith and reason. , para 2: 'The Church is no stranger to this journey of discovery, nor could she ever be. From the moment when, through the Paschal Mystery, she received the gift of the ultimate truth about human life, the Church has made her pilgrim way along the paths of the world to proclaim that Jesus Christ is “the way, and the truth, and the life” (Jn 14:6).' 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

Mark 16:15, Mark 16:15 He said to them, "Go into all the world and preach the good news to all creation., 'Matthew 28:19 Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit,
Acts 1:2 until the day he was taken up to heaven, after giving instructions through the Holy Spirit to the apostles he had chosen.
Acts 1:8 But you will receive power when the Holy Spirit comes on you; and you will be my witnesses in Jerusalem, and in all Judea and Samaria, and to the ends of the earth."
Colossians 1:23 if you continue in your faith, established and firm, not moved from the hope held out in the gospel. This is the gospel that you heard and that has been proclaimed to every creature under heaven, and of which I, Paul, have become a servant.' back

Maupertuis' principle - Wikipedia, Maupertuis' principle - Wikipedia, the free encyclopedia, 'In classical mechanics, Maupertuis' principle (named after Pierre Louis Maupertuis) is an integral equation that determines the path followed by a physical system without specifying the time parameterization of that path. It is a special case of the more generally stated principle of least action. More precisely, it is a formulation of the equations of motion for a physical system not as differential equations, but as an integral equation, using the calculus of variations.' back

Maurice Healy, Eirlys Roberts, 'The mother of the modern consumer movement and co-founder of Which? . . . She was a professional, and believed the magazine had to come out, whatever the difficulties. And she was fired by a principle - that people deserve good information to make them effective members of society. Good information meant an unbiased source, as accurate as humanly possible, and supported by the force of reason. It was no accident that one of the chapter headings in Eirlys's book Consumers (1966) was The Scientific Content of Consumer Research. . . . Above all, she had a conviction that good information, put in the hands of the people, could change the world.' back

Paul Kelly, Tribal warfare saps our energy, ' Australia is being convulsed by its contradictory identity: a fossil fuel-endowed nation enriched by its resources set against a middle-class moralism hooked on climate change action — an internal division that plagues the voting base of both Coalition and Labor. Party values and voting loyalties are being trashed. As climate change activism turns into an anti-coal mantra buttressed by a finance sector unwilling to invest, the clash over competing economic interests and cultural values will provoke large-scale political disruption. Both Scott Morrison and Bill Shorten are trapped in these dilemmas.' back

Peter Millard, Cindy Hoffman, Mrisa Gertz and Jeremy C.F. Lin, The Rise and Fall of Chavismo in Venezuela, ' Venezuela’s economic fortunes have been tethered to the price of oil for most of the country’s modern history, a dependency that only worsened after a charismatic former paratrooper named Hugo Chavez took office in 1999. Chavez, who came to power in the wake of an oil crash that decimated Venezuela’s traditional parties, ramped up political patronage to a degree the country had never seen when crude prices suddenly began to soar again. The windfall temporarily masked the economic devastation caused by his version of socialism—a toxic mix of expropriations, subsidies, and currency and price controls. By Chavez’s final years, Venezuela’s economy was starting to buckle, even with prices north of $100 a barrel, and then they crashed. His chosen successor, Nicolas Maduro, replaced patronage with repression and persecution. Maduro’s iron-fisted rule has allowed him to remain in charge of what’s become a failed state. His days may be numbered.' back

Pontifical Academy of Sciences, Home page of the Pontifical Academy of Scences, 'Founded in Rome on 17 August 1603 as the first exclusively scientific academy in the world by Federico Cesi, Giovanni Heck, Francesco Stelluti and Anastasio de Filiis with the name Linceorum Academia, to which Galileo Galilei was appointed member on 25 August 1610, it was reestablished in 1847 by Pius IX with the name Pontificia Accademia dei Nuovi Lincei. It was moved to its current headquarters in the Casina Pio IV in the Vatican Gardens in 1922, and given its current name and statutes by Pius XI in 1936.Its mission is to honour pure science wherever it may be found, ensure its freedom and encourage research for the progress of science.' back

Pontifical Academy of Sciences: Disciplines, Home Page of the Pontifical Academy of Sciences, 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

Scientific method - Wikipedia, Scientific method - Wikipedia, the free encyclopedia, 'Scientific method refers to a body of techniques for investigating phenomena, acquiring new knowledge, or correcting and integrating previous knowledge. To be termed scientific, a method of inquiry must be based on gathering empirical and measurable evidence subject to specific principles of reasoning. The Oxford English Dictionary says that scientific method is: "a method or procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses." back

Tobin Harshaw, Winning the Nuclear Game Against North Korea, ' Tobin Harshaw: Before we look at the challenges facing the U.S., can you briefly describe game theory and how it relates to nuclear deterrence? Vipin Narang: Most of the original work on deterrence was done by the Nobel-winning economist Tom Shelling in his very influential book "Arms and Influence," which came out in the mid-’60s. Back then it was rudimentary game. But it's really about a strategic logic -- how your adversary behaves based on your moves and how you react to their reaction to your moves.' 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