Acemoglu (2012), Daron, and James Robinson, Why Nations Fail: The Origins of Power, Prosperity and Poverty, Crown Business 2012 "Some time ago a little-known Scottish philosopher wrote a book on what makes nations succeed and what makes them fail. The Wealth of Nations is still being read today. With the same perspicacity and with the same broad historical perspective, Daron Acemoglu and James Robinson have retackled this same question for our own times. Two centuries from now our great-great- . . . -great grandchildren will be, similarly, reading Why Nations Fail." —George Akerlof, Nobel laureate in economics, 2001  
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Augustine (419, 1991), and Edmond Hill (Introduction, translation and notes), and John E Rotelle (editor), The Trinity, New City Press 399-419, 1991 Written 399 - 419: De Trinitate is a radical restatement, defence and development of the Christian doctrine of the Trinity. Augustine's book has served as a foundation for most subsequent work, particularly that of Thomas Aquinas.  
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Auyang (1995), Sunny Y., How is Quantum Field Theory Possible?, Oxford University Press 1995 Jacket: 'Quantum field theory (QFT) combines quantum mechanics with Einstein's special theory of relativity and underlies elementary particle physics. This book presents a philosophical analysis of QFT. It is the first treatise in which the philosophies of space-time, quantum phenomena and particle interactions are encompassed in a unified framework.' 
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Carlson (2006), James, and Arthur Jaffe & Andrew Wiles, The Millennium Prize Problems, Clay Mathematics Institute and American Mathematical Society 2006
1: The Birch and Swinnerton-Dyer Conjecture: Andrew Wiles
2: The Hodge Conjecture: Pierre Deligne
3: The Existence and Smoothness of the Navier-Stokes Equation: Charles L Fefferman
4: The Poincare Conjecture: John Milnor
5: The P versus NP Problem: Stephen Cook
6: The Riemann Hypothesis: Enrico Bombieri
7: Quantum Yang-Mills Theory: Arthur Jaffe and Edward Whitten 
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Darwin (1871, 2004), Charles, The Descent of Man, and Selection in Relation to Sex, Penguin Classics 1871, 2004 'No book made a greater impact on the intellectual world of its first Victorian readers nor has had such an enduring influence on our thinking on science, literature, theology and philosophy. In The Descent of Man, Darwin addresses the crucial question of the origins, evolution and racial divergence of mankind, that he had deliberately left out of On the Origin of Species. And the evidence he presents forces us to question what it is that makes us uniquely human.' 
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Darwin (1875), Charles, and Harriet Ritvo (Introduction), The Variation of Animals and Plants Under Domestication (Foundations of Natural History), Johns Hopkins University Press 1875, 1998 ' "The Variation, with its thousands of hard-won observations of the facts of variation in domesticated species, is a frustrating, but worthwhile read, for it reveals the Darwin we rarely see -- the embattled Darwin, struggling to keep his project on the road. Sometimes he seems on the verge of being overwhelmed by the problems he is dealing with, but then a curious fact of natural history will engage him (the webbing between water gun-dogs' toes, the absurdly short beak of the pouter pigeon) and his determination to make sense of it rekindles. As he disarmingly declares, 'the whole subject of inheritance is wonderful.'. 
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Dauben (1990), Joseph Warren, Georg Cantor: His Mathematics and Philosophy of the Infinite, Princeton University Press 1990 Jacket: 'One of the greatest revolutions in mathematics occurred when Georg Cantor (1843-1918) promulgated his theory of transfinite sets. . . . Set theory has been widely adopted in mathematics and philosophy, but the controversy surrounding it at the turn of the century remains of great interest. Cantor's own faith in his theory was partly theological. His religious beliefs led him to expect paradox in any concept of the infinite, and he always retained his belief in the utter veracity of transfinite set theory. Later in his life, he was troubled by attacks of severe depression. Dauben shows that these played an integral part in his understanding and defense of set theory.' 
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Einstein (1916, 2005), Albert, and Robert W Lawson (translator) Roger Penrose (Introduction), Robert Geroch (Commentary), David C Cassidy (Historical Essay), Relativity: The Special and General Theory, Pi Press 1916, 2005 Preface: 'The present book is intended, as far as possible, to give an exact insight into the theory of relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics. ... The author has spared himself no pains in his endeavour to present the main ideas in the simplest and most intelligible form, and on the whole, in the sequence and connection in which they actually originated.' page 3  
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Hawking (1975), Steven W, and G F R Ellis, The Large Scale Structure of Space-Time, Cambridge UP 1975 Preface: Einstein's General Theory of Relativity . . . leads to two remarkable predictions about the universe: first that the final fate of massive stars is to collapse behind an event horizon to form a 'black hole' which will contain a singularity; and secondly that there is a singularity in our past which constitutes, in some sense, a beginning to our universe. Our discussion is principally aimed at developing these two results.' 
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Hobson (2006), M. P., and G. P. Efstathiou, A. N. Lasenby, General Relativity: An Introduction for Physicists, Cambridge University Press 2006 'After reviewing the basic concept of general relativity, this introduction discusses its mathematical background, including the necessary tools of tensor calculus and differential geometry. These tools are used to develop the topic of special relativity and to discuss electromagnetism in Minkowski spacetime. Gravitation as spacetime curvature is introduced and the field equations of general relativity derived. After applying the theory to a wide range of physical situations, the book concludes with a brief discussion of classical field theory and the derivation of general relativity from a variational principle.'  
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Hopkins (2001), Keith, A World Full of Gods: The Strange Triumph of Christianity, Penguin Random House 2001 ' In this provocative, irresistibly entertaining book, Keith Hopkins takes readers back in time to explore the roots of Christianity in ancient Rome. Combining exacting scholarship with dazzling invention, Hopkins challenges our perceptions about religion, the historical Jesus, and the way history is written. He puts us in touch with what he calls “empathetic wonder”—imagining what Romans, pagans, Jews, and Christians thought, felt, experienced, and believed-by employing a series of engaging literary devices. These include a TV drama about the Dead Sea Scrolls; the first-person testimony of a pair of time-travelers to Pompeii; a meditation on Jesus’ apocryphal twin brother; and an unusual letter on God, demons, and angels.' 
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Khinchin (1960, 1998), Aleksandr Yakovlevich, The Mathematical Foundations of Quantum Statistics, Dover 1998 'In the area of quantum statistics, I show that a rigorous mathematical basis of the computational formulas of statistical physics . . . may be obtained from an elementary application of the well-developed limit theorems of the theory of probability.' 
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Newton (1729, 1962), Isaac, Principia volume II: The System of the World, University of California Press 1962 ' In the preceding books I have laid down the principle of philosophy; principles not philosophical but mathematical such: namely, as we may build our reasonings upon in philosophical inquiries. These principles are the laws and conditions of certain motions, and powers or forces, which chiefly have respect to philosophy; . . . It remains that, from the same principles, I now demonstrate the frame of the System of the World.' 
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Nielsen (2016), Michael A., and Isaac L Chuang, Quantum Computation and Quantum Information, Cambridge University Press 2016 Review: A rigorous, comprehensive text on quantum information is timely. The study of quantum information and computation represents a particularly direct route to understanding quantum mechanics. Unlike the traditional route to quantum mechanics via Schroedinger's equation and the hydrogen atom, the study of quantum information requires no calculus, merely a knowledge of complex numbers and matrix multiplication. In addition, quantum information processing gives direct access to the traditionally advanced topics of measurement of quantum systems and decoherence.' Seth Lloyd, Department of Quantum Mechanical Engineering, MIT, Nature 6876: vol 416 page 19, 7 March 2002. 
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Pais (1982), Abraham, 'Subtle is the Lord...': The Science and Life of Albert Einstein, Oxford UP 1982 Jacket: In this . . . major work Abraham Pais, himself an eminent physicist who worked alongside Einstein in the post-war years, traces the development of Einstein's entire ouvre. . . . Running through the book is a completely non-scientific biography . . . including many letters which appear in English for the first time, as well as other information not published before.' [Raffiniert ist der Herr Gott, aber boshaft is er nicht] 
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Piketty (2022), Thomas, A Brief History of Equality, Harvard UP 2022 ' The world's leading economist of inequality presents a short but sweeping and surprisingly optimistic history of human progress toward equality despite crises, disasters, and backsliding. A perfect introduction to the ideas developed in his monumental earlier books.It's easy to be pessimistic about inequality. We know it has increased dramatically in many parts of the world over the past two generations.' 
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Walker (1988), Geoffrey de Q., The Rule of Law: Foundations of Constitutional Democracy, Melbourne University Press 1988 Jacket: 'The author argues that the survival of any useful rule of law model is currently threatened by distortions in the adjudication process, by perversion of law enforcement (by fabrication of evidence and other means), by the excessive production of new legislation with its degrading effect on long-term legal certainty and on long-standing safeguards, and by legal theories that are hostile to the very concept of rule of law. In practice these trends have produced a great number of legal failures from which we must learn.' 
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Weyl (1985), Hermann, and Henry L. Brose (translator), Space Time Matter, Dover 1985 Amazon customer review: ' The birth of gauge theory by its author: This book bewitched several generations of physicists and students. Hermann Weyl was one of the very great mathematicians of this century. He was also a great physicist and an artist with ideas and words. In this book you will find, at a deep level, the philosophy, mathematics and physics of space-time. It appeared soon after Einstein's famous paper on General Relativity, and is, in fact, a magnificent exposition of it, or, rather, of a tentative generalization of it. The mathematical part is of the highest class, striving to put geometry to the forefront. Actually, the book introduced a far-reaching generalization of the theory of connections, with respect to the Levi-Civita theory. It was not a generalization for itself, but motivated by the dream (Einstein's) of including gravitation and electromagnetism in the same (geometrical) theory. The result was gauge theory, which, slightly modified and applied to quantum mechanics resulted in the theory which dominates present particle physics. Weyl's unified theory was proved wrong by Einstein, and his criticism alone, accepted by Weyl and included in the book, would justify the reading. Though wrong, Weyl's theory is so beautiful that Paul Dirac stated that nature could not afford neglecting such perfection, and that the theory was probably only misplaced. Prophetic words! . . . ' Henrique Fleming 
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Wilczek (2008), Frank, The Lightness of Being: Mass, Ether, and the Unification of Forces, Basic Books 2008 ' In this excursion to the outer limits of particle physics, Wilczek explores what quarks and gluons, which compose protons and neutrons, reveal about the manifestation of mass and gravity. A corecipient of the 2004 Nobel Prize in Physics, Wilczek knows what he’s writing about; the question is, will general science readers? Happily, they know what the strong interaction is (the forces that bind the nucleus), and in Wilczek, they have a jovial guide who adheres to trade publishing’s belief that a successful physics title will not include too many equations. Despite this injunction (against which he lightly protests), Wilczek delivers an approachable verbal picture of what quarks and gluons are doing inside a proton that gives rise to mass and, hence, gravity. Casting the light-speed lives of quarks against “the Grid,” Wilczek’s term for the vacuum that theoretically seethes with quantum activity, Wilczek exudes a contagious excitement for discovery. A near-obligatory acquisition for circulating physics collections.' --Gilbert Taylor  
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Zee (2010), Anthony, Quantum Field Theory in a Nutshell, Princeton University Press 2010 ' Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. This expanded edition features several additional chapters, as well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading.' 
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Abiogenesis - Wikipedia, Abiogenesis - Wikipedia, the free encyclopedia, ' Abiogenesis is the natural process by which life arises from non-living matter, such as simple organic compounds. The prevailing scientific hypothesis is that the transition from non-living to living entities on Earth was not a single event, but a process of increasing complexity involving the formation of a habitable planet, the prebiotic synthesis of organic molecules, molecular self-replication, self-assembly, autocatalysis, and the emergence of cell membranes. The transition from non-life to life has never been observed experimentally, but many proposals have been made for different stages of the process.' back

Alan Turing (1936), On Computable Numbers, with an application to the Entscheidungsproblem, 'The "computable" numbers may be described briefly as the real numbers whose expressions as a decimal are calculable by some finite means. Although the subject of this paper is ostensibly the computable numbers, it is almost equally easy to define and investigate computable functions of an integral variable of a real or computable variable, computable predicates and so forth. . . . ' back

Albert Einstein (1913), "Zero point energy is now as dead as a doornail" , ' Debije's work on the influence of temperature is still of great importance. Hopefully Debije will soon show us the inconsistency of the hypothesis of zero-point energy, the theoretical untenability. Soon after the publication of the work I had written together with Mr. Stern, it became terribly clear to me that it was untenable. It remains the case that the momentum & energy fluctuations are in the radiation.' back

Albert Einstein (1915), The Field Equations of Gravitation, ' In two recently published papers I have shown how to obtain field equations of gravitation that comply with the postulate of general relativity, i.e., which in their general formulation are covariant under arbitrary substitutions of space-time variables. . . . With this, we have finally completed the general theory of relativity as a logical structure. The postulate of relativity in its most general formulation (which makes space-time coordinates into physically meaningless parameters) leads with compelling necessity to a very specific theory of gravitation that also explains the movement of the perihelion of Mercury. However, the postulate of general relativity cannot reveal to us anything new and different about the essence of the various processes in nature than what the special theory of relativity taught us already.' back

Albert Einstein (1926), He does not throw dice, ' Die Quantenmechanik ist sehr achtung-gebietend. Aber eine innere Stimme sagt mir, daß das doch nicht der wahre Jakob ist. Die Theorie liefert viel, aber dem Geheimnis des Alten bringt sie uns kaum näher. Jedenfalls bin ich überzeugt, daß der nicht würfelt.
Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the "old one." I, at any rate, am convinced that He does not throw dice.' back

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

Aquinas, Summa, I, 22, 3, Does God have immediate providence over everything?, ' I answer that, Two things belong to providence—namely, the type of the order of things foreordained towards an end; and the execution of this order, which is called government. As regards the first of these, God has immediate providence over everything, because He has in His intellect the types of everything, even the smallest; and whatsoever causes He assigns to certain effects, He gives them the power to produce those effects. Whence it must be that He has beforehand the type of those effects in His mind. As to the second, there are certain intermediaries of God's providence; for He governs things inferior by superior, not on account of any defect in His power, but by reason of the abundance of His goodness; so that the dignity of causality is imparted even to creatures.' back

Aristotle, Metaphysics XII (1072b25-31): God's happiness, 'If, then, the happiness which God always enjoys is as great as that which we enjoy sometimes, it is marvellous; and if it is greater, this is still more marvellous. Nevertheless it is so. Moreover, life belongs to God. For the actuality of thought is life, and God is that actuality; and the essential actuality of God is life most good and eternal. We hold, then, that God is a living being, eternal, most good; and therefore life and a continuous eternal existence belong to God; for that is what God is.' (1072b25-31) back

Augustus - Wikipedia, Augustus - Wikipedia, the free encyclopedia, ' Gaius Julius Caesar Augustus (born Gaius Octavius; 23 September 63 BC – 19 August AD 14), also known as Octavian (Latin: Octavianus), was the founder of the Roman Empire. He reigned as the first Roman emperor from 27 BC until his death in AD 14. The reign of Augustus initiated an imperial cult, as well as an era associated with imperial peace (the Pax Romana or ,Pax Augusta) in which the Roman world was largely free of armed conflict (aside from expansionary wars and the Year of the Four Emperors, the latter of which occurring after Augustus' reign).' back

Australian Government (2013), Royal Commission into Institutional Responses to Child Sexual Abuse, 'WHEREAS all children deserve a safe and happy childhood. AND Australia has undertaken international obligations to take all appropriate legislative, administrative, social and educational measures to protect children from sexual abuse and other forms of abuse, including measures for the prevention, identification, reporting, referral, investigation, treatment and follow up of incidents of child abuse. . . . IN WITNESS, We have caused these Our Letters to be made Patent. WITNESS Quentin Bryce, Governor-General of the Commonwealth of Australia. Dated 11th January 2013 Governor-General By Her Excellency’s Command Prime Minister back

Balmer series - Wikipedia, Balmer series - Wikipedia, the free encyclopedia, ' The Balmer series is characterized by the electron transitioning from n ≥ 3 to n = 2, where n refers to the radial quantum number or principal quantum number of the electron. The transitions are named sequentially by Greek letter: n = 3 to n = 2 is called H-α, 4 to 2 is H-β, 5 to 2 is H-γ, and 6 to 2 is H-δ. As the first spectral lines associated with this series are located in the visible part of the electromagnetic spectrum, these lines are historically referred to as "H-alpha", "H-beta", "H-gamma", and so on, where H is the element hydrogen.' back

Bertrand Russell (1903, 1996), The Principles of Mathematics, ' Russell page 347: "In this capricious world nothing is more capricious than posthumous fame. One of the most notable victims of posterity's lack of judgement is the Eleatic Zeno. Having invented four arguments all immeasurably subtle and profound, the grossness of subsequent philosophers pronounced him to be a mere ingenious juggler, and his arguments to be one and all sophisms. After two thousand years of continual refutation, these sophisms were reinstated, and made the foundation of a mathematical renaissance. . ." ' Russell, Bertrand (1996) [1903]. The Principles of Mathematics. New York, NY: Norton. ISBN 978-0-393-31404-5. OCLC 247299160. back

Black hole thermodynamics - Wikipedia, Black hole thermodynamics - Wikipedia, the free encyclopedia, 'In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons. Much as the study of the statistical mechanics of black body radiation led to the advent of the theory of quantum mechanics, the effort to understand the statistical mechanics of black holes has had a deep impact upon the understanding of quantum gravity, leading to the formulation of the holographic principle.' back

Bolzano-Weierstrass theorem - Wikipedia, Bolzano-Weierstrass theorem - Wikipedia, the free encyclopedia, 'In mathematics, specifically in real analysis, the Bolzano–Weierstrass theorem, named after Bernard Bolzano and Karl Weierstrass, is a fundamental result about convergence in a finite-dimensional Euclidean space Rⁿ. The theorem states that each bounded sequence in Rⁿ has a convergent subsequence. An equivalent formulation is that a subset of Rⁿ is sequentially compact if and only if it is closed and bounded.' 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

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 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

Casimir effect - Wikipedia, Casimir effect - Wikipedia, the free encyclopedia, ' In physics, the Casimir effect or Casimir-Polder force is a physical force arising from a quantized field. The typical example is of two uncharged metallic plates in a vacuum, placed a few micrometers apart, without any external electromagnetic field. In a classical description, the lack of an external field also means that there is no field between the plates, and no force would be measured between them. When this field is instead studied using quantum mechanics, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force—either an attraction or a repulsion depending on the specific arrangement of the two plates. This force has been measured, and is a striking example of an effect purely due to second quantization.' back

Code of Canon Law, Table of Contents, 'Introduction: . . . Therefore, in promulgating the Code today, I am fully aware that this act is an expression of pontifical authority and, therefore, it is invested with a "primatial" character. But I am also aware that this Code in its objective content reflects the collegial care of all my brothers in the episcopate for the Church. . . . A second question arises concerning the very nature of the Code of Canon Law. To reply adequately to this question, one must mentally recall the distant patrimony of law contained in the books of the Old and New Testament from which is derived, as from its first source, the whole juridical - legislative tradition of the Church. . . . Finally, the canonical laws by their very nature must be observed. The greatest care has therefore been taken to ensure that in the lengthy preparation of the Code the wording of the norms should be accurate, and that they should be based on a solid juridical, canonical and theological foundation. After all these considerations it is to be hoped that the new canonical legislation will prove to be an efficacious means in order that the Church may progress in conformity with the spirit of the Second Vatican Council, and may every day be ever more suited to carry out its office of salvation in this world.' back

Code of Hammurabi - Wikipedia, Code of Hammurabi - Wikipedia, the free encyclopedia, ' The Code of Hammurabi is a Babylonian legal text composed during 1755–1750 BC. It is the longest, best-organized, and best-preserved legal text from the ancient Near East. It is written in the Old Babylonian dialect of Akkadian, purportedly by Hammurabi, sixth king of the First Dynasty of Babylon. The primary copy of the text is inscribed on a basalt stele 2.25 m tall. The stele was rediscovered in 1901 at the site of Susa in present-day Iran, where it had been taken as plunder six hundred years after its creation. The text itself was copied and studied by Mesopotamian scribes for over a millennium. The stele now resides in the Louvre Museum. . . . Mesopotamia has the most comprehensive surviving legal corpus from before the Digest of Justinian, even compared to those from ancient Greece and Rome.' 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 the observed values of vacuum energy density (the small value of the cosmological constant) and theoretical large value of zero-point energy suggested by quantum field theory. Depending on the Planck energy cutoff and other factors, the discrepancy is as high as 120 orders of magnitude, a state of affairs described by physicists as "the largest discrepancy between theory and experiment in all of science" and "the worst theoretical prediction in the history of physics".' back

Daniel W Graham (Stanford Encyclopedia of Philosophy), Heraclitus, 'A Greek philosopher of Ephesus (near modern Kuşadası, Turkey) who was active around 500 BCE, Heraclitus propounded a distinctive theory which he expressed in oracular language. He is best known for his doctrines that things are constantly changing (universal flux), that opposites coincide (unity of opposites), and that fire is the basic material of the world. The exact interpretation of these doctrines is controversial, as is the inference often drawn from this theory that in the world as Heraclitus conceives it contradictory propositions must be true.' back

David Hilbert (1925), On the Infinite, ' We encounter a completely different and quite unique conception of the notion of infinity in the important and fruitful method of ideal elements. The method of ideal elements is used even in elementary plane geometry. The points and straight lines of the plane originally are real, actually existent objects. One of the axioms that hold for them is the axiom of connection: one and only one straight line passes through two points. It follows from this axiom that two straight lines intersect at most at one point. There is no theorem that two straight lines always intersect at some point, however, for the two straight lines might well be parallel. Still we know that by introducing ideal elements, viz., infinitely long lines and points at infinity, we can make the theorem that two straight lines always intersect at one and only one point come out universally true. These ideal "infinite" elements have the advantage of making the system of connection laws as simple and perspicuous as possible. Another example of the use of ideal elements are the familiar complex-imaginary magnitudes of algebra which serve to simplify theorems about the existence and number of the roots of an equation.' back

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

Eugene Wigner (1960), The Unreasonable Effectiveness of Mathematics in the Natural Sciences, ' The first point is that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it. Second, it is just this uncanny usefulness of mathematical concepts that raises the question of the uniqueness of our physical theories.' back

European wars of religion - Wikipedia, European war of religion - Wikipedia, the free encyclopedia, ' The conflicts began with the minor Knights' Revolt (1522), followed by the larger German Peasants' War (1524–1525) in the Holy Roman Empire. Warfare intensified after the Catholic Church began the Counter-Reformation in 1545 against the growth of Protestantism. The conflicts culminated in the Thirty Years' War, which devastated Germany and killed one-third of its population, a mortality rate twice that of World War I. The Peace of Westphalia broadly resolved the conflicts by recognising three separate Christian traditions in the Holy Roman Empire: Roman Catholicism, Lutheranism, and Calvinism.' back

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

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

Fisherian runaway - Wikipedia, Fisherian runaway - Wikipedia, the free encyclopedia, ' Fisherian runaway or runaway selection is a sexual selection mechanism proposed by the mathematical biologist Ronald Fisher in the early 20th century, to account for the evolution of ostentatious male ornamentation by persistent, directional female choice. An example is the colourful and elaborate peacock plumage compared to the relatively subdued peahen plumage; the costly ornaments, notably the bird's extremely long tail, appear to be incompatible with natural selection. Fisherian runaway can be postulated to include sexually dimorphic phenotypic traits such as behavior expressed by a particular sex.' back

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

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

Frank Wilczek (2004), Nobel Lecture: Asymptotic Freedom: from Paradox to Paradigm, ' Frank Wilczek held his Nobel Lecture December 8, 2004, at Aula Magna, Stockholm University. He was presented by Professor Sune Svanberg, Chairman of the Nobel Committee for Physics. Summary: The idea that Quarks that are born free are confined and can’t be pulled apart was once considered a paradox. The emerging theory for strong interactions, Quantum Chromo Dynamics (QCD) predicts the existence of gluons, which together with quarks can be seen indirectly as jets from hard scattering reactions between particles. Quantum Chromo Dynamics predicts that the forces between quarks are feeble for small separations but are powerful far away, which explains confinement. Many experiments have confirmed this property of the strong interaction. ' back

Galileo affair - Wikipedia, Galileo affair - Wikipedia, the free encyclopedia, ' The Galileo affair (Italian: il processo a Galileo Galilei) began around 1610 and culminated with the trial and condemnation of Galileo Galilei by the Roman Catholic Inquisition in 1633. Galileo was prosecuted for his support of heliocentrism, the astronomical model in which the Earth and planets revolve around the Sun at the centre of the Solar System. ' back

Galileo Galilei, Recantation of Galileo (June 22, 1633), ' Therefore, desiring to remove from the minds of your Eminences, and of all faithful Christians, this vehement suspicion, justly conceived against me, with sincere heart and unfeigned faith I abjure, curse, and detest the aforesaid errors and heresies, and generally every other error, heresy, and sect whatsoever contrary to the said Holy Church, and I swear that in the future I will never again say or assert, verbally or in writing, anything that might furnish occasion for a similar suspicion regarding me; ' back

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

Geoffrey F Miller (2000), The mating mind : how sexual choice shaped the evolution of human nature, Jacket: 'Many aspects of how and why the human mind evolved remain mysterious. While Darwinian natural selection has successfully explained the evolution of much life on earth, it has never seemed fully adequate to explain the aspects of our minds which seem most uniquely and profoundly human—art, morality, consciousness, creativity and language. . . . .. Now, in The Mating Mind a pioneering work of evolutionary science, these aspects of human nature are at last explored and explained. . . . .. In this brilliantly ambitious and provocative book, evolutionary psychologist Geoffrey Miller shows the evolutionary power of sexual choice and the reasons why our ancestors became attracted not only to pretty faces and healthy bodies, but to minds that were witty, articulate, generous and conscious.' back

Gnosticism - Wikipedia, Gnosticism - Wikipedia, the free encyclopedia, ' Gnosticism (from Ancient Greek: γνωστικός gnōstikós, "having knowledge") is a collection of ancient religious ideas and systems which originated in the first century AD among early Christian and Jewish sects. These various groups emphasised personal spiritual knowledge (gnosis) over orthodox teachings, traditions, and ecclesiastical authority. Gnostic cosmogony generally presents a distinction between a supreme, hidden God and a blind, malevolent demiurge responsible for creating the material universe. Viewing this material existence as flawed or evil, Gnostics considered the principal element of salvation to be direct knowledge of the supreme divinity in the form of mystical or esoteric insight.' back

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

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

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

Henricus Denzinger (1864 -1997), Enchiridion symbolorum definitionum et declarartionum de rebus fidei et morum, ' With its unique wealth of official church documents and sources, it is an essential resource for theological work. Since its first edition in 1854, Denzinger has become a standard work and an indispensable tool for serious theological work. It faithfully reflects the history of the Church's faith and its development over the centuries. Indeed, its reference system has become an established part of citing important theological sources.' back

Hermann Weyl - Wikipedia, Hermann Weyl - Wikipedia, the free encyclopedia, ' Hermann Klaus Hugo Weyl (9 November 1885 – 8 December 1955) was a German mathematician. Although much of his working life was spent in Zürich, Switzerland and then Princeton, he is associated with the University of Göttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski. His research has had major significance for theoretical physics as well as pure disciplines including number theory. He was one of the most influential mathematicians of the twentieth century, and an important member of the Institute for Advanced Study during its early years.' back

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

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

Isaac Newton (1736), Method of Fluxions and Infinite Series with its Application to the Geometry of Curve-Lines, 'The method of fluxions and infinite series with its application to the geometry of curve-lines by the inventor Sir Isaac Newton ... ; translated from the author's Latin original not yet made publick. To which is subjoin'd, A perpetual comment upon the whole work, consisting of annotations, illustrations, and supplements, to make this treatise a compleat institution for the use of learners. back

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

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

Katharine Richardson & Xuemei Bal, What are ‘planetary boundaries’ and why should we care?, ' If we keep our activities to a safe level, the sheer exuberance of life and the planet’s own processes can handle it. But in six out of nine vital life support systems, we have blown well past the safe zone. And we’re now in the danger zone, where we – as well as every other species – are now at risk. Planetary boundaries update 2023: Our breach of boundaries is very new In last week’s update, the research team found we had now gone beyond the safe zone into dangerous territory in six of the nine processes. We are still in the green for ozone-depleting chemicals. Ocean-acidification is still, just, in the green, and so is aerosol pollution and dust. But on climate change, deforestation, biodiversity loss, synthetic chemicals such as plastics, freshwater depletion, and nitrogen/phosphorus use, we’re well out of the safer zone. On these six, we’re deep in the red zone.' back

Kerson Huang (2013), A Critical History of Renormalization, ' The history of renormalization is reviewed with a critical eye,starting with Lorentz's theory of radiation damping, through perturbative QED with Dyson, Gell‐Mann & Low, and others, to Wilson's formulation and Polchinski's functional equation, and applications to "triviality", and dark energy in cosmology.
Dedication: Renormalization, that astounding mathematical trick that enabled one to tame divergences in Feynman diagrams, led to the triumph of quantum electrodynamics. Ken Wilson made it physics, by uncovering its deep connection with scale transformations. The idea hat scale determines the perception of world seems obvious. When one examines an oil painting, for example, what one sees depends on the resolution of the instrument one uses for the examination. At resolutions of the naked eye, one sees art, perhaps, but upon greater and greater magnifications, one sees pigments, then molecules and atoms, and so forth. What is non‐trivial is to formulate this mathematically, as a physical theory, and this is what Ken Wilson had achieved.' back

Kirchoff's law of thermal radiation - Wikipedia, Kirchoff's law of thermal radiation - Wikipedia, the free encyclopedia, 'Kirchhoff's law states that: For a body of any arbitrary material, emitting and absorbing thermal electromagnetic radiation at every wavelength in thermodynamic equilibrium, the ratio of its emissive power to its dimensionless coefficient of absorption is equal to a universal function only of radiative wavelength and temperature, the perfect black-body emissive power. back

Lamb shift - Wikipedia, Lamb shift - Wikipedia, the free encyclopedia, 'In physics, the Lamb shift, named after Willis Lamb (1913–2008), is a difference in energy between two energy levels ²S_½ and ²P_½ (in term symbol notation) of the hydrogen atom which was not predicted by the Dirac equation, according to which these states should have the same energy. Interaction between vacuum energy fluctuations and the hydrogen electron in these different orbitals is the cause of the Lamb Shift, as was shown subsequent to its discovery.' back

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

Last universal common ancestor - Wikipedia, Last universal common ancestor - Wikipedia, the free encyclopedia, ' The last universal common ancestor (LUCA) is the most recent population from which all organisms now living on Earth share common descent—the most recent common ancestor of all current life on Earth. . . . .. While no specific fossil evidence of the LUCA exists, the detailed biochemical similarity of all current life makes it plausible. Its characteristics can be inferred from shared features of modern genomes. These genes describe a complex life form with many co-adapted features, including transcription and translation mechanisms to convert information from DNA to mRNA to proteins. The LUCA probably lived in the high-temperature water of deep sea vents near ocean-floor magma flows around 4 billion years ago.' 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

Mateja Hajdinjak et al (2021_04_07), Initial Upper Palaeolithic humans in Europe had recent Neanderthal ancestry, ' Modern humans appeared in Europe by at least 45,000 years ago, but the extent of their interactions with Neanderthals, who disappeared by about 40,000 years ago, and their relationship to the broader expansion of modern humans outside Africa are poorly understood. Here we present genome-wide data from three individuals dated to between 45,930 and 42,580 years ago from Bacho Kiro Cave, Bulgaria. . . . Moreover, we find that all three individuals had Neanderthal ancestors a few generations back in their family history, confirming that the first European modern humans mixed with Neanderthals and suggesting that such mixing could have been common.' back

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

Meme - Wikipedia, Meme - Wikipedia, the free encyclopedia, 'A meme an idea, behavior, or style that spreads by means of imitation from person to person within a culture and often carries symbolic meaning representing a particular phenomenon or theme.A meme acts as a unit for carrying cultural ideas, symbols, or practices, that can be transmitted from one mind to another through writing, speech, gestures, rituals, or other imitable phenomena with a mimicked theme. Supporters of the concept regard memes as cultural analogues to genes in that they self-replicate, mutate, and respond to selective pressures.' back

Minkowski space - Wikipedia, Minkowski space - Wikipedia, the free encyclopedia, ' By 1908 Minkowski realized that the special theory of relativity, introduced by his former student Albert Einstein in 1905 and based on the previous work of Lorentz and Poincaré, could best be understood in a four-dimensional space, since known as the "Minkowski spacetime", in which time and space are not separated entities but intermingled in a four-dimensional space–time, and in which the Lorentz geometry of special relativity can be effectively represented using the invariant interval x² + y² + z² − c² t².' back

Newtons Laws of Motion - Wikipedia, Newton's Laws of Motion - Wikipedia, the free encyclopedia, 'Newton's laws of motion are three physical laws that together laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to said forces. . . . The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), first published in 1687' back

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

Nicole Winfield & Peter Smith, Pope apologizes for ‘catastrophic’ school policy in Canada, ' While the pope acknowledged blame, he also made clear that Catholic missionaries were merely cooperating with and implementing the government policy, which he termed the “colonizing mentality of the powers.” Notably he didn’t refer to 15th-century papal decrees that provided religious backing to European colonial powers in the first place. . . . Jeremy Bergen, a church apology expert and professor of religious and theological studies at Conrad Grebel University College in Waterloo, Ontario, said Francis made clear he was asking forgiveness for the actions of “members of the church” but not the institution in its entirety. “The idea is that, as the Body of Christ, the church itself is sinless,” he said via email. “So when Catholics do bad things, they are not truly acting on behalf of the church,” Bergen added, noting it’s a controversial idea on which many Catholic theologians disagree.' back

Nondeterministic algorithm - Wikipedia, Nondeterministic algorithm- Wikipedia, the free encyclopedia, ' In computational complexity theory, nondeterminism is often modeled using an explicit mechanism for making a nondeterministic choice, such as in a nondeterministic Turing machine. For these models, a nondeterministic algorithm is considered to perform correctly when, for each input, there exists a run that produces the desired result, even when other runs produce incorrect results. This existential power makes nondeterministic algorithms of this sort more efficient than known deterministic algorithms for many problems. The P versus NP problem encapsulates this conjectured greater efficiency available to nondeterministic algorithms. Algorithms of this sort are used to define complexity classes based on nondeterministic time and nondeterministic space complexity. They may be simulated using nondeterministic programming, a method for specifying nondeterministic algorithms and searching for the choices that lead to a correct run, often using a backtracking search.' back

Nyquist-Shannon sampling theorem - Wikipedia, Nyquist-Shannon sampling theorem - Wikipedia, the free encyclopedia, ' In the field of digital signal processing, the sampling theorem is a fundamental bridge between continuous-time signals (often called "analog signals") and discrete-time signals (often called "digital signals"). It establishes a sufficient condition for a sample rate that permits a discrete sequence of samples to capture all the information from a continuous-time signal of finite bandwidth.' back

Olivera Simic (2024_08_29), If something can happen once, it can happen again – Dennis Glover’s reading of history sounds an alarm about the present, ' Review: Repeat: A Warning from History – Dennis Glover (Black Inc.) In his latest book, Repeat: A Warning from History, Australian writer Dennis Glover uses the past to illuminate our dire present situation. Repeat is a short book divided into two parts: Tragedy and Farce. Each part consists of five chapters with a repeated sequence of titles. These chapters address the five stages that triggered the second world war and could trigger a global war if repeated. The key stages are:
Sowing the wind (creating difficult economic conditions)
Populism (allowing those willing to exploit hatred to gain power)
Savagery (descending into an era of murder and violence)
Preliminary war (letting populists plan and win early conflicts)
Consequences (waking up to the reality of massacres and global war).
According to Glover, we are in danger of repeating the mistakes of the 1920s and 1930s, which led to the most destructive war in history. . . .
The writing in Repeat is simple and easy to read, but fragmented. The book consists of short anecdotes and summaries of events, often disjointed, which are packed into 140 pages. What is novel in its account is not the events or characters, but the historical parallels it draws between past and present. Glover urges his readers to stop and think where the world might be heading and ask “is it all going to happen again?” He warns that “maybe the endgame has already begun”.' back

Øystein Linnebo (Stanford Encyclopedia of Philosophy), Platonism in the Philosophy of Mathematics, ' Platonism about mathematics (or mathematical platonism) is the metaphysical view that there are abstract mathematical objects whose existence is independent of us and our language, thought, and practices. Just as electrons and planets exist independently of us, so do numbers and sets. And just as statements about electrons and planets are made true or false by the objects with which they are concerned and these objects’ perfectly objective properties, so are statements about numbers and sets. Mathematical truths are therefore discovered, not invented.' back

P versus NP problem - Wikipedia, P versus NP problem - Wikipedia, the free encyclopedia, ' The P versus NP problem is a major unsolved problem in computer science. It asks whether every problem whose solution can be quickly verified (technically, verified in polynomial time) can also be solved quickly (again, in polynomial time). The underlying issues were first discussed in the 1950s, in letters from John Forbes Nash Jr. to the National Security Agency, and from Kurt Gödel to John von Neumann. The precise statement of the P versus NP problem was introduced in 1971 by Stephen Cook in his seminal paper " The complexity of theorem proving procedures" and is considered by many to be the most important open problem in the field.' back

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

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

Plato, Parmenides (English), Plato. Plato in Twelve Volumes, Vol. 9 translated by Harold N. Fowler. Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1925. back

Political power grows out of the barrel of a gun - Wikipedia, Political power grows out of the barrel of a gun - Wikipedia, the free encyclopedia, ' Political power grows out of the barrel of a gun (Chinese: 枪杆子里面出政权) is a phrase which was coined by Chinese communist leader . The phrase was originally used by Mao during an emergency meeting of the Chinese Communist Party (CCP) on 7 August 1927, at the beginning of the Chinese Civil War.[1] Mao employed the phrase a second time on 6 November 1938, during his concluding speech at the 6th Plenary Session of the CCP's 6th Central Committee. The speech was concerned with both the Civil War and the Second Sino-Japanese War, which had commenced the previous year.' back

Pope John Paul II (1983), Apostolic Constitution Sacrae Disciplinae Leges for the promulgation of the new Code of Canon Law , ' I order today, January 25, 1983, the promulgation of the revised Code of Canon Law. In so doing, my thoughts go back to the same day of the year 1959, when my Predecessor of happy memory, John XXIII, announced for the first time his decision to reform the existing corpus of canonical legislation which had been promulgate on the feast of Pentecost in the year 1917. Such a decision to reform the Code was taken together with two other decisions of which the Pontiff spoke on that same day, and they concerned the intention to hold a Synod of the Diocese of Rome and to convoke the Ecumenical Council. Of these two events, the first was not closely connected with the reform of the Code, but the second, that is, the Council, is of supreme importance in regard to the present matter and is closely connected with it.' back

Quantum field theory - Wikipedia, Quantum field theory - Wikipedia, the free encyclopedia, ' Quantum field theory treats particles as excited states (also called quantum levels) of their underlying quantum fields, which are more fundamental than the particles. The equation of motion of the particle is determined by minimization of the action computed for the Lagrangian, a function of fields associated with the particle. Interactions between particles are described by interaction terms in the Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by a Feynman diagram according to perturbation theory in quantum mechanics.' back

Richard P. Feynman (1965), Nobel Lecture: The Development of the Space-Time View of Quantum Electrodynamics, Nobel Lecture, December 11, 1965: I did gather from my readings, however, that two things were the source of the difficulties with the quantum electrodynamical theories. The first was an infinite energy of interaction of the electron with itself. And this difficulty existed even in the classical theory. The other difficulty came from some infinites which had to do with the infinite numbers of degrees of freedom in the field. As I understood it at the time (as nearly as I can remember) this was simply the difficulty that if you quantized the harmonic oscillators of the field (say in a box) each oscillator has a ground state energy of (½hω) and there is an infinite number of modes in a box of every increasing frequency ω, and therefore there is an infinite energy in the box. I now realize that that wasn’t a completely correct statement of the central problem; it can be removed simply by changing the zero from which energy is measured. At any rate, I believed that the difficulty arose somehow from a combination of the electron acting on itself and the infinite number of degrees of freedom of the field.' back

Rick Rojas (2024_06_19), Louisiana Requires All Public Classrooms to Display Ten Commandments, ' Gov. Jeff Landry signed legislation on Wednesday requiring the display of the Ten Commandments in every public classroom in Louisiana, making the state the only one with such a mandate and reigniting the debate over how porous the boundary between church and state should be. Critics, including the American Civil Liberties Union and the Freedom From Religion Foundation, vowed a legal fight against the law they deemed “blatantly unconstitutional.” But it is a battle that proponents are prepared, and in many ways, eager, to take on. “I can’t wait to be sued,” Mr. Landry said on Saturday at a Republican fund-raiser in Nashville, according to The Tennessean. And on Wednesday, as he signed the measure, he argued that the Ten Commandments contained valuable lessons for students. “If you want to respect the rule of law,” he said, “you’ve got to start from the original law giver, which was Moses.” back

Rule of Law - Wikipedia, Rule of Law - Wikipedia, the free encyclopedia, ' The rule of law is a political ideal that all citizens and institutions within a country, state, or community are accountable to the same laws, including lawmakers and leaders. It is sometimes stated simply as "no one is above the law". The term rule of law is closely related to constitutionalism as well as Rechtsstaat. It refers to a political situation, not to any specific legal rule. The rule of law is defined in the Encyclopædia Britannica as "the mechanism, process, institution, practice, or norm that supports the equality of all citizens before the law, secures a nonarbitrary form of government, and more generally prevents the arbitrary use of power".' back

Sacred language - Wikipedia, Sacred language - Wikipedia, the free encyclopedia, 'A sacred language, "holy language" (in religious context) or liturgical language is a language that is cultivated for religious reasons by people who speak another language in their daily life. . . . A Sacred language is often the language which was spoken (and written) in the society in which a religion's sacred texts were first set down; however, thereafter these texts, becoming fixed and holy, remain frozen and immune to later linguistic developments.' back

Sexual selection - Wikipedia, Sexual selection - Wikipedia, the free encyclopedia, ' The concept was first articulated by Charles Darwin who wrote of a "second agency" other than natural selection, in which competition between mate candidates could lead to speciation. The theory was given a mathematical basis by Ronald Fisher in the early 20th century. Sexual selection can lead males to extreme efforts to demonstrate their fitness to be chosen by females, producing sexual dimorphism in secondary sexual characteristics, such as the ornate plumage of birds-of-paradise and peafowl, or the antlers of deer. Depending on the species, these rules can be reversed. This is caused by a positive feedback mechanism known as a Fisherian runaway, where the passing-on of the desire for a trait in one sex is as important as having the trait in the other sex in producing the runaway effect.' 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

Square root of 2 - Wikipedia, Square root of 2 - Wikipedia, the free encyclopedia, 'Geometrically the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem. It was probably the first number known to be irrational.' back

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

Steven Weinberg (2000), The Cosmological Constant Problems, 'Abstract. The old cosmological constant problem is to understand why the vacuum energy is so small; the new problem is to understand why it is comparable to the present mass density. Several approaches to these problems are reviewed. Quintessence does not help with either; anthropic considerations offer a possibility of solving both. In theories with a scalar field that takes random initial values, the anthropic principle may apply to the cosmological constant, but probably to nothing else.' back

Supernova - Wikipedia, Supernova - Wikipediam the free encyclopedia, 'A supernova (pl.: supernovae or supernovas) is a powerful and luminous explosion of a star. A supernova occurs during the last evolutionary stages of a massive star, or when a white dwarf is triggered into runaway nuclear fusion. The original object, called the progenitor, either collapses to a neutron star or black hole, or is completely destroyed to form a diffuse nebula. The peak optical luminosity of a supernova can be comparable to that of an entire galaxy before fading over several weeks or months. ' back

Ten Commandments - Wikipedia, Ten Commandments - Wikipedia, the free encyclopedia, 'The Ten Commandments, also known as the Decalogue (Greek: δεκάλογος), are a set of biblical principles relating to ethics and worship, which play a fundamental role in Judaism and most forms of Christianity. They include instructions to worship only God and to keep the Sabbath, and prohibitions against idolatry, blasphemy, murder, theft, and adultery. Different groups follow slightly different traditions for interpreting and numbering them.' back

Theodicy - Wikipedia, Theodicy - Wikipedia, the free encyclopedia, ' In the philosophy of religion, a theodicy (meaning 'vindication of God', from Ancient Greek θεός theos, "god" and δίκη dikē, "justice") is an argument that attempts to resolve the problem of evil that arises when omnipotence, omnibenevolence, and omniscience are all simultaneously ascribed to God. Unlike a defence, which merely tries to demonstrate that the coexistence of God and evil is logically possible, a theodicy additionally provides a framework wherein God's existence is considered plausible. The German philosopher and mathematician Gottfried Leibniz coined the term "theodicy" in 1710 in his work Théodicée, though numerous attempts to resolve the problem of evil had previously been proposed.' back

Theory of Forms - Wikipedia, Theory of Forms - Wikipedia, the free encyclopedia, 'Plato's theory of Forms or theory of Ideas asserts that non-material abstract (but substantial) forms (or ideas), and not the material world of change known to us through sensation, possess the highest and most fundamental kind of reality. When used in this sense, the word form or idea is often capitalized. Plato speaks of these entities only through the characters (primarily Socrates) of his dialogues who sometimes suggest that these Forms are the only true objects of study that can provide us with genuine knowledge; thus even apart from the very controversial status of the theory, Plato's own views are much in doubt. Plato spoke of Forms in formulating a possible solution to the problem of universals.' back

Thermodynamic limit - Wikipedia, Thermodynamic limit - Wikipedia, the free encyclopedia, ' In statistical mechanics, the thermodynamic limit or macroscopic limit, of a system is the limit for a large number N of particles (e.g., atoms or molecules) where the volume is taken to grow in proportion with the number of particles. The thermodynamic limit is defined as the limit of a system with a large volume, with the particle density held fixed. In this limit, macroscopic thermodynamics is valid. There, thermal fluctuations in global quantities are negligible, and all thermodynamic quantities, such as pressure and energy, are simply functions of the thermodynamic variables, such as temperature and density. For example, for a large volume of gas, the fluctuations of the total internal energy are negligible and can be ignored, and the average internal energy can be predicted from knowledge of the pressure and temperature of the gas.' 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

Ultraviolet catastrophe - Wikipedia, Ultraviolet catastrophe - Wikipedia, the free encyclopedia, ' The term "ultraviolet catastrophe" was first used in 1911 by Paul Ehrenfest, but the concept originated with the 1900 statistical derivation of the Rayleigh–Jeans law. The phrase refers to the fact that the Rayleigh–Jeans law accurately predicts experimental results at radiative frequencies below 10⁵5 GHz, but begins to diverge with empirical observations as these frequencies reach the ultraviolet region of the electromagnetic spectrum. Since the first appearance of the term, it has also been used for other predictions of a similar nature, as in quantum electrodynamics and such cases as ultraviolet divergence.' back

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

Vacuum energy - Wikipedia, Vacuum energy - Wikipedia, the free encyclopedia, 'The effects of vacuum energy can be experimentally observed in various phenomena such as spontaneous emission, the Casimir effect and the Lamb shift, and are thought to influence the behavior of the Universe on cosmological scales. Using the upper limit of the cosmological constant, the vacuum energy of free space has been estimated to be 10⁻⁹ joules . . . per cubic meter. However, in both quantum electrodynamics (QED) and stochastic electrodynamics (SED), consistency with the principle of Lorentz covariance and with the magnitude of the Planck constant requires it to have a much larger value of 10¹¹³ joules per cubic meter. This huge discrepancy is known as the vacuum catastrophe.' back

Whitehead and Russell (1910), Principia Mathematica, Jacket: 'Principia Mathematica was first published in 1910-1913; this is the fifth impression of the second edition of 1925-7. The Principia has long been recognized as one of the intellectual landmarks of the century. It was the first book to show clearly the close relationship between mathematics and formal logic. Starting with a minimal number of axioms, Whitehead and Russell display the structure of both kinds of thought. No other book has had such an influence on the subsequent history of mathematical philosophy .' back

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

Zero-point energy - Wikipedia, Zero-point energy - Wikipedia, the free encyclopedia, ' Zero-point energy is fundamentally related to the Heisenberg uncertainty principle. Roughly speaking, the uncertainty principle states that complementary variables (such as a particle's position and momentum, or a field's value and derivative at a point in space) cannot simultaneously be specified precisely by any given quantum state. In particular, there cannot exist a state in which the system simply sits motionless at the bottom of its potential well, for then its position and momentum would both be completely determined to arbitrarily great precision. Therefore, the lowest-energy state (the ground state) of the system must have a distribution in position and momentum that satisfies the uncertainty principle, which implies its energy must be greater than the minimum of the potential well.' back