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), Aurelius, 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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Darwin (1859, 2001), Charles, and Ernst Mayr, On the Origin of Species: A Facsimile of the First Edition, Harvard University Press 2001 Amazon review: 'It was a very happy idea to publish a facsimile of the first edition of On the Origin of Species; the price of copies of the original edition has reached the thousand dollar bracket, and in contemporary literature all page-references are to the original pagination, which was not followed in previous reprints of the first edition. Now, with this very reasonably priced and beautifully produced book, not only historians of science but also biologists will have the opportunity of following the fascinating thought-trails, still far from fully explored, of that remarkable man Darwin. Few if any persons are so well qualified as Harvard's Ernst Mayr to execute so helpfully and gracefully the delicate task of writing a worthy foreword to such a classic.' --Sir Gavin de Beer (Science ) 
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Dirac (1930, 1983), P A M, The Principles of Quantum Mechanics (4th ed), Oxford UP/Clarendon 1983 Jacket: '[this] is the standard work in the fundamental principles of quantum mechanics, indispensible both to the advanced student and the mature research worker, who will always find it a fresh source of knowledge and stimulation.' (Nature)  
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Dirac (1983), P A M, The Principles of Quantum Mechanics (4th ed), Oxford UP/Clarendon 1983 Jacket: '[this] is the standard work in the fundamental principles of quantum mechanics, indispensible both to the advanced student and the mature research worker, who will always find it a fresh source of knowledge and stimulation.' (Nature)  
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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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Everett III (1973), Hugh, and Bryce S Dewitt, Neill Graham (editors), The Many Worlds Interpretation of Quantum Mechanics, Princeton University Press 1973 Jacket: 'A novel interpretation of quantum mechanics, first proposed in brief form by Hugh Everett in 1957, forms the nucleus around which this book has developed. The volume contains Dr Everett's short paper from 1957, "'Relative State' formulation of quantum mechanics" and a far longer exposition of his interpretation entitled "The Theory of the Universal Wave Function" never before published. In addition other papers by Wheeler, DeWitt, Graham, Cooper and van Vechten provide further discussion of the same theme. Together they constitute virtually the entire world output of scholarly commentary on the Everett interpretation.' 
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Feynman (2002), Richard, Feynman Lectures on Gravitation, Westview Press 2002 ' The Feynman Lectures on Gravitation are based on notes prepared during a course on gravitational physics that Richard Feynman taught at Caltech during the 1962-63 academic year. For several years prior to these lectures, Feynman thought long and hard about the fundamental problems in gravitational physics, yet he published very little. These lectures represent a useful record of his viewpoints and some of his insights into gravity and its application to cosmology, superstars, wormholes, and gravitational waves at that particular time. The lectures also contain a number of fascinating digressions and asides on the foundations of physics and other issues.' [zero-energy universe, pp 9 - 10]  
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Galilei (1610, 1957), Galileo, and Stillman Drake (translator), Discoveries and Opinions of Galileo: Including the Starry Messenger (1610 Letter to the Grand Duchess Christina), Doubleday Anchor 1957 Amazon: 'Although the introductory sections are a bit dated, this book contains some of the best translations available of Galileo's works in English. It includes a broad range of his theories (both those we recognize as "correct" and those in which he was "in error"). Both types indicate his creativity. The reproductions of his sketches of the moons of Jupiter (in "The Starry Messenger") are accurate enough to match to modern computer programs which show the positions of the moons for any date in history. The appendix with a chronological summary of Galileo's life is very useful in placing the readings in context.' A Reader. 
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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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Hertz (1893, 1962), Heinrich, and D. E. Jones (translator), Lord Kelvin (Preface), Electric Waves, Macmillan 1893, Dover 1962 ' During the fifty-six years which have passed since Faraday first offended physical mathematicians with his curved lines of force, many workers and many thinkers have helped to build up the nineteenth-century school of plenum, one ether for light,heat, electricity, magnetism; and the Germans and English volumes containing Hertz's electrical papers, given to the world in the last decade of the century, will be a permanent monument of the splendid consummation now realised,' back

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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Jaeger (1997), Werner Wilhelm, Aristotle: Fundamentals of the history of his development, Oxford University Press 1997 Jacket: '"Aristotle was the first thinker to set up along with his philosophy a conception of his own position in history; he thereby created a new kind of philosophical consciousness, more responsible and inwardly complex. He was the inventor of the notion of intellectual development in time . . . ." In this classic study, Professor Jaeger profoundly altered the general view of Aristotle among philosophers and classical scholars. He showed that Aristotle was not uncompromisingly opposed to Plato, that he developed gradually, applying step by step his particular genius to the problems of his age.' 
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Jones (1999), Steve, Almost like a Whale: The Origin of Species Updated, Doubleday 1999 An Historical Sketch: 'The Origin of Species is, without doubt, the book of the millennium. ... [This book] is, as far as is possible, an attempt to rewrite the Origin of Species. I use its plan, developing as it does from farms to fossils, from beehives to islands, as a framework, but my own Grand Facts ... are set firmly in the late twentieth century. Almost Like a Whale tries to read Charles Darwin's mind with the benefit of scientific hindsight and to show how the theory of evolution unites biology as his millenium draws to an end.' (xix)  
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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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Lonergan, Bernard J F, and Michael G Shields (translator), Robert M Doran & H Daniel Monsour (editors), The Triune God: Systematics, University of Toronto Press 2007 Translated from De Deo Trino: Pars systematica (1964) by Michael G Shields. Amazon Product Description 'Buried for more than forty years in a Latin text written for seminarian students at the Gregorian University in Rome, Bernard Lonergan's 1964 masterpiece of systematic-theological writing, De Deo trino: Pars systematica, is only now being published in an edition that includes the original Latin along with an exact and literal translation. De Deo trino, or The Triune God, is the third great installment on one particular strand in trinitarian theology, namely, the tradition that appeals to a psychological analogy for understanding trinitarian processions and relations. The analogy dates back to St Augustine but was significantly developed by St Thomas Aquinas. Lonergan advances it to a new level of sophistication by rooting it in his own highly nuanced cognitional theory and in his early position on decision and love. Suggestions for a further development of the analogy appear in Lonergan's late work, but these cannot be understood and implemented without working through this volume. This is truly one of the great masterpieces in the history of systematic theology, perhaps even the greatest of all time.' 
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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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Piketty (2020), Thomas, Capital and Ideology, Harvard University Press 2020 The politics of identity.
Once we understand this, we can begin to envision a more balanced approach to economics and politics. Piketty argues for a new "participatory" socialism, a system founded on an ideology of equality, social property, education, and the sharing of knowledge and power. Capital and Ideology is destined to be one of the indispensable books of our time, a work that will not only help us understand the world, but that will change it.'  
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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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Saul (1993), John Ralston, Voltaire's Bastards: The Dictatorship of Reason in the West, Vintage / Random House 1993 What flaw in Western democracies leaves so many of their citizens feeling frustrated and disempowered? How did the arms trade become the single largest industry in a world that is essentially at peace. Why have Washington, Wall Street and Hollywood all failed?
These are just come of unnerving questions that John Ralston Saul poses in Voltaire's Bastards, a phosphorescenty intelligent search-and destroy mission against the foundations of contemporary civilization. In an argument that takes in Chinese eunuchs and Henry Kissinger, the rationalized torture of the Inquisition and the scientifically managed debacle in Vietnam, medieval saints and modern-day newscasteres Saul shows how the West's love affair with the ideology of pure reason has made us cripplingly dependent on process-minded experts — "Voltaire's Bastards" — whose rational systems are bereft of both meaning and morality. The result is a learned and devastating critique of our political, economic and cultural establishments.' 
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Slobodian (2025), Quinn, Hayek's Bastards: The Neoliberal Roots of the Populist Right, Penguin, Allen Lane 2025 ' In this work of historical erudition and sharp political analysis, Quinn Slobodian explains how the myth of neoliberal freedom can be sustained only through a deeply illiberal world view. Through a painstaking reconstruction of how Hayek's offspring appeal to science served to naturalize hierarchy, and resist the calls for social equality, we come to see how rightwing authoritarianism emerged not as an alternative to neoliberalism but as its brainchild. An essential read to understand the times in which we live ― Lea Ypi  
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Streater (2000), Raymond F, and Arthur S Wightman, PCT, Spin, Statistics and All That, Princeton University Press 2000 Amazon product description: 'PCT, Spin and Statistics, and All That is the classic summary of and introduction to the achievements of Axiomatic Quantum Field Theory. This theory gives precise mathematical responses to questions like: What is a quantized field? What are the physically indispensable attributes of a quantized field? Furthermore, Axiomatic Field Theory shows that a number of physically important predictions of quantum field theory are mathematical consequences of the axioms. Here Raymond Streater and Arthur Wightman treat only results that can be rigorously proved, and these are presented in an elegant style that makes them available to a broad range of physics and theoretical mathematics.' 
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von Neumann (2018), John, and Nicholas A. Wheeler (editor), Robert T Beyer (translator), The Mathematical Foundations of Quantum Mechanics, Princeton University Press 2018 ' Quantum mechanics was still in its infancy in 1932 when the young John von Neumann, who would go on to become one of the greatest mathematicians of the twentieth century, published Mathematical Foundations of Quantum Mechanics--a revolutionary book that for the first time provided a rigorous mathematical framework for the new science. Robert Beyer's 1955 English translation, which von Neumann reviewed and approved, is cited more frequently today than ever before. But its many treasures and insights were too often obscured by the limitations of the way the text and equations were set on the page. In this new edition of this classic work, mathematical physicist Nicholas Wheeler has completely reset the book in TeX, making the text and equations far easier to read. He has also corrected a handful of typographic errors, revised some sentences for clarity and readability, provided an index for the first time, and added prefatory remarks drawn from the writings of Léon Van Hove and Freeman Dyson. The result brings new life to an essential work in theoretical physics and mathematics.' 
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Weinberg (1995), Steven, The Quantum Theory of Fields Volume I: Foundations , Cambridge University Press 1995 Jacket: 'After a brief historical outline, the book begins anew with the principles about which we are most certain, relativity and quantum mechanics, and then the properties of particles that follow from these principles. Quantum field theory then emerges from this as a natural consequence. The classic calculations of quantum electrodynamics are presented in a thoroughly modern way, showing the use of path integrals and dimensional regularization. The account of renormalization theory reflects the changes in our view of quantum field theory since the advent of effective field theories. The book's scope extends beyond quantum elelctrodynamics to elementary partricle physics and nuclear physics. It contains much original material, and is peppered with examples and insights drawn from the author's experience as a leader of elementary particle research. Problems are included at the end of each chapter. ' 
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Whitehead (1979), Alfred North, Process and Reality (Gifford Lectures Delivered in the University of Edinburgh 1927-28), Free Press 1979 ' Studied this in college and was totally blown away! Process & Reality is, in a nutshell, mathematics-based, process metaphysics, with quantum mechanics thrown in for good measure. Say that 3 times fast! Given that he wrote this in 1927-28, many of the concepts he proposed were way ahead of the times. The concepts he proposed were similar to Spinoza & Meister Eckhart, although more advanced than either one. I found it fascinating! I was a Philosophy major at the time & this was one of the first texts that really ignited my passion for philosophy & quantum mechanics. I would recommend this to Philosophers, Physicists, and anyone who is just naturally inquisitive about the way the world and its parts work.' Amazon customer Just ME 
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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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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, The happiest thought of my life, 'I was sitting in a chair in the patent office at Bern when all of sudden a thought occurred to me: If a person falls freely he will not feel his own weight. I was startled. This simple thought made a deep impression on me. It impelled me toward a theory of gravitation.' Einstein in his Kyoto address (14 December 1922) back

Albert Einstein (1905), On the Electrodynamics of Moving Bodies, ' It is well known that Maxwell's electrodynamics-as usually understood at present—when applied to moving bodies, leads to asymmetries that do not seem to attach to the phenomena. Let us recall, for example, the electro-dynamic interaction between a magnet and a conductor. The observable phenomenon depends here only on the relative motion of conductor and magnet, while according to the customary conception the two cases, in which, respectively, either the one or the other of the two bodies is the one in motion, are to be strictly differentiated from each other. For if the magnet is in motion and the conductor is at rest, there arises in the surroundings of the magnet an electric field endowed with a certain energy value that produces a current in the places where parts of the conductor are located. But if the magnet is at rest and the conductor is in motion, no electric field arises in the surroundings of the magnet, while in the conductor an electromotive force will arise, to which in itself there does not correspond any energy, but which, provided that the relative motion in the two cases considered is the same, gives rise to electrical currents that have the same magnitude and the same course as those produced by the electric forces in the first-mentioned case.' back

Albert Einstein (1905c), On a heuristic point of view concerning the production and transformation of light, ' The wave theory of light, which operates with continuous spatial functions, has proved itself splendidly in describing purely optical phenomena and will probably never be replaced by another theory. One should keep in mind, however, that optical observations apply to time averages and not to momentary values, and it is conceivable that despite the complete confirmation of the theories of diffraction, reflection, refraction, dispersion, etc., by experiment, the theory of light, which operates with continuous spatial functions, may lead to contradictions with experience when it is applied to the phenomena of production and transformation of light. Indeed, it seems to me that the observations regarding "black-body" light, and other groups of phenomena associated with the production or conversion of light can be understood better if one assumes that the energy of light is discontinuously distributed in space.' 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. The opinions I recently voiced here in this regard have been in error. Every physical theory that complies with the special theory of relativity can, by means of the absolute differential calculus, be integrated into the system of general relativity theory — without the latter providing any criteria about the admissibility of such physical theory' back

Albert Einstein (1923), Nobel Lecture: Fundamental ideas and problems of the theory of relativity, ' The conclusion is obvious that any arbitrarily moved frame of reference is equivalent to any other for the formulation of the laws of Nature, that there are thus no physically preferred states of motion at all in respect of regions of finite extension (general relativity principle).
The implementation of this concept necessitates an even more profound modification of the geometric-kinematical principles than the special relativity theory. . . .
Consequently the Cartesian system of coordinates also loses its significance in terms of the stipulation of meaning. Analogous reasoning applies to time; . . .
Generalizing, we arrive at the conclusion that gravitational field and metric are only different manifestations of the same physical field.
Lecture delivered to the Nordic Assembly of Naturalists at Gothenburg: July 11, 1923.' back

Allegory of the cave - Wikipedia, Allegory of the cave - Wikipedia, the free encyclopedia, ' Plato's allegory of the cave is an allegory presented by the Greek philosopher Plato in his work Republic (514a–520a, Book VII) to compare "the effect of education (παιδεία) and the lack of it on our nature". It is written as a dialogue between Plato's brother Glaucon and his mentor Socrates and is narrated by the latter. The allegory is presented after the analogy of the Sun (508b–509c) and the analogy of the divided line (509d–511e).' back

ALPHA Collaboration, Description and first application of a new technique to measure gravitational mass of antihydrogen, ' Physicists have long wondered whether the gravitational interactions between matter and antimatter might be different from those between matter and itself. Although there are many indirect indications that no such differences exist and that the weak equivalence principle holds, there have been no direct, free-fall style, experimental tests of gravity on antimatter. Here we describe a novel direct test methodology; we search for a propensity for antihydrogen atoms to fall downward when released from the ALPHA antihydrogen trap. In the absence of systematic errors, we can reject ratios of the gravitational to inertial mass of antihydrogen >75 at a statistical significance level of 5%; worst-case systematic errors increase the minimum rejection ratio to 110. A similar search places somewhat tighter bounds on a negative gravitational mass, that is, on antigravity. This methodology, coupled with ongoing experimental improvements, should allow us to bound the ratio within the more interesting near equivalence regime.' back

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

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

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

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

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

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

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

Brouwer fixed point theorem - Wikipedia, Brouwer fixed point theorem - Wikipedia, the free encyclopedia, 'Among hundreds of fixed-point theorems] Brouwer's is particularly well known, due in part to its use across numerous fields of mathematics. In its original field, this result is one of the key theorems characterizing the topology of Euclidean spaces, along with the Jordan curve theorem, the hairy ball theorem, the invariance of dimension and the Borsuk–Ulam theorem. This gives it a place among the fundamental theorems of topology.' back

Christopher Shields (Stanford Encyclopedia of Philosophy), Aristotle, First published Thu Sep 25, 2008; substantive revision Tue Aug 25, 2020 'Aristotle (384–322 B.C.E.) numbers among the greatest philosophers of all time. Judged solely in terms of his philosophical influence, only Plato is his peer: . . . A prodigious researcher and writer, Aristotle left a great body of work, perhaps numbering as many as two-hundred treatises, from which approximately thirty-one survive. His extant writings span a wide range of disciplines, from logic, metaphysics and philosophy of mind, through ethics, political theory, aesthetics and rhetoric, and into such primarily non-philosophical fields as empirical biology, where he excelled at detailed plant and animal observation and taxonomy. In all these areas, Aristotle's theories have provided illumination, met with resistance, sparked debate, and generally stimulated the sustained interest of an abiding readership.' back

Claude E Shannon (1948), A Mathematical Theory of Communication, ' The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point. Frequently the messages have meaning; that is they refer to or are correlated according to some system with certain physical or conceptual entities. These semantic aspects of communication are irrelevant to the engineering problem. The significant aspect is that the actual message is one selected from a set of possible messages.' back

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

Conrad Hackett (et. al.) (Pew Reearch Center 2025_06_09), How the Global Religious Landscape Changed From 2010 to 2020, ' All other religions combined (including Baha’is, Daoists, Jains, Sikhs, adherents of folk religions and numerous other groups) expanded in tandem with the rest of the world. Their share of the global population held steady at 2.2%.
Collectively, 75.8% of the world’s people identified with a religion as of 2020. The remaining 24.2% did not identify with any religion, making people with no religious affiliation the third-largest group in this study, after Christians and Muslims.
Since 2010, the share of the global population that has any religious affiliation has declined by nearly 1 percentage point (from 76.7%) while the share without an affiliation has risen by the same amount (from 23.3%).
The growth of religious “nones” is striking because they are at a “demographic disadvantage” – their population is relatively old, on average, with relatively low fertility rates. However, unaffiliated people continued to grow as a share of the global population because many affiliated people around the world – primarily Christians – are “switching” out of religion. ' back

Copenhagen interpretation - Wikipedia, Copenhagen interpretation - Wikipedia, the free encyclopedia, ' According to the Copenhagen interpretation, physical systems generally do not have definite properties prior to being measured, and quantum mechanics can only predict the probability distribution of a given measurement's possible results. The act of measurement affects the system, causing the set of probabilities to reduce to only one of the possible values immediately after the measurement. This feature is known as wave function collapse.' back

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

Dale Tuggy (Stanford Encyclopedia of Philosophy), History of Trinitarian Doctrines, ' The New Testament contains no explicit trinitarian doctrine. However, many Christian theologians, apologists, and philosophers hold that the doctrine can be inferred from what the New Testament does teach about God. But how may it be inferred? Is the inference deductive, or is it an inference to the best explanation? And is it based on what is implicitly taught there, or on what is merely assumed there? Many Christian theologians and apologists seem to hold it is a deductive inference. In contrast, other Christians admit that their preferred doctrine of the Trinity not only (1) can’t be inferred from the Bible alone, but also (2) that there’s inadequate or no evidence for it there, and even (3) that what is taught in the Bible is incompatible with the doctrine.' back

Differentiable manifold - Wikipedia, Differentiable manifold - Wikipedia, the free encyclopedia, ' In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a collection of charts (atlas). One may then apply ideas from calculus while working within the individual charts, since each chart lies within a vector 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

Elementary particle - Wikipedia, Elementary particle - Wikipedia, the free encyclopedia, ' In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include the fundamental fermions (quarks, leptons, antiquarks, and antileptons), which generally are "matter particles" and "antimatter particles", as well as the fundamental bosons (gauge bosons and the Higgs boson), which generally are "force particles" that mediate interactions among fermions. A particle containing two or more elementary particles is a composite particle.' back

Elizabeth Gibney (2025_07_30), Physicists disagree wildly on what quantum mechanics says about reality, Nature survey shows, 'Quantum mechanics is one of the most successful theories in science — and makes much of modern life possible. Technologies ranging from computer chips to medical-imaging machines rely on the application of equations, first sketched out a century ago, that describe the behaviour of objects at the microscopic scale.
But researchers still disagree widely on how best to describe the physical reality that lies behind the mathematics, as a Nature survey reveals.
Quantum mechanics 100 years on: an unfinished revolution
At an event to mark the 100th anniversary of quantum mechanics last month, lauded specialists in quantum physics argued politely — but firmly — about the issue. “There is no quantum world,” said physicist Anton Zeilinger, at the University of Vienna, outlining his view that quantum states exist only in his head and that they describe information, rather than reality. “I disagree,” replied Alain Aspect, a physicist at the University of Paris-Saclay, who shared the 2022 Nobel Prize with Zelinger.
The responses — numbering more than 1,100, mainly from physicists — showed how widely researchers vary in their understanding of the most fundamental features of quantum experiments.'
To gain a snapshot of how the wider community interprets quantum physics in its centenary year, Nature carried out the largest ever survey on the subject. We e-mailed more than 15,000 researchers whose recent papers involved quantum mechanics, and also invited attendees of the centenary meeting, held on the German island of Heligoland, to take the survey.
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Equivalence principle - Wikipedia, Equivalence principle - Wikipedia, the free encyclopedia, ' In the physics of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.' back

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

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

Feynman, Leighton and Sands FLP II_02, Chapter 2: Differential Calculus of Vector Fields, ' What it means really to understand an equation—that is, in more than a strictly mathematical sense—was described by Dirac. He said: “I understand what an equation means if I have a way of figuring out the characteristics of its solution without actually solving it.” So if we have a way of knowing what should happen in given circumstances without actually solving the equations, then we “understand” the equations, as applied to these circumstances. A physical understanding is a completely unmathematical, imprecise, and inexact thing, but absolutely necessary for a physicist. ' back

First Vatican Council, Session 3, Chaper 1, On God, the creator of all things, ' The holy, catholic, apostolic and Roman church believes and acknowledges that there is one true and living God, creator and lord of heaven and earth, almighty, eternal, immeasurable, incomprehensible, infinite in will, understanding and every perfection. Since he is one, singular, completely simple and unchangeable spiritual substance, he must be declared to be in reality and in essence, distinct from the world, supremely happy in himself and from himself, and inexpressibly loftier than anything besides himself which either exists or can be imagined. This one true God, by his goodness and almighty power, not with the intention of increasing his happiness, nor indeed of obtaining happiness, but in order to manifest his perfection by the good things which he bestows on what he creates, by an absolutely free plan, together from the beginning of time brought into being from nothing the twofold created order, that is the spiritual and the bodily, the angelic and the earthly, and thereafter the human which is, in a way, common to both since it is composed of spirit and body. Everything that God has brought into being he protects and governs by his providence, which reaches from one end of the earth to the other and orders all things well . All things are open and laid bare to his eyes, even those which will be brought about by the free activity of creatures.' back

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

Hellenistic Judaism - Wikipedia, Hellenistic Judaism - Wikipedia, the free encyclopedia, Hellenistic Judaism was a form of Judaism in classical antiquity that combined Jewish religious tradition with elements of Hellenistic culture and religion. Until the early Muslim conquests of the eastern Mediterranean, the main centers of Hellenistic Judaism were Alexandria in Egypt and Antioch in Syria (modern-day Turkey), the two main Greek urban settlements of the Middle East and North Africa, both founded in the end of the 4th century BCE in the wake of the conquests of Alexander the Great. Hellenistic Judaism also existed in Jerusalem during the Second Temple Period, where there was a conflict between Hellenizers and traditionalists.' back

Hilbert space - Wikipedia, Hilbert space - Wikipedia, the free encyclopedia, ' In mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces. Formally, a Hilbert space is a vector space equipped with an inner product that induces a distance function for which the space is a complete metric space. A Hilbert space is a special case of a Banach space. ' 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

International System of Units - Wikipedia, International System of Units - Wikipedia, the free encyclopedia, ' The International System of Units (SI, abbreviated from the French Système international (d'unités)) is the modern form of the metric system. It is the only system of measurement with an official status in nearly every country in the world. It comprises a coherent system of units of measurement starting with seven base units, which are the second (the unit of time with the symbol s), metre (length, m), kilogram (mass, kg), ampere (electric current, A), kelvin (thermodynamic temperature, K), mole (amount of substance, mol), and candela (luminous intensity, cd).' back

J. Clerk Maxwell (1865), A Dynamical Theory of the Electromagnetic Field, '(3) The theory I propose may therefore be called a theory of the Elecromagnetic Field, because it has to do with the space in the neighbourhood of electric or magnetic bodies, and it may be called a Dynamical Theory because it assumes that in that space there is matter in motion, by which the observed electromagnetic phenomena are produced.' back

Jan Faye (Stanford Encyclopedia of Philosophy), Copenhagen Interpretation of Quantum Mechanics, ' Some physicists and philosophers of science see the measurement problem as a real puzzle with respect to the Copenhagen interpretation. On the one hand, we have that the wave function evolved deterministically according to Schrödinger’s equation as a linear superposition of different states; and the other hand an actual measurement always detect (sic) one definite state. To be or not to be in a superposition; that’s the question.' back

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

John Paul II (1983), Code of Canon Law: §331: Papal Power, ' Can. 331 The bishop of the Roman Church, in whom continues the office given by the Lord uniquely to Peter, the first of the Apostles, and to be transmitted to his successors, is the head of the college of bishops, the Vicar of Christ, and the pastor of the universal Church on earth. By virtue of his office he possesses supreme, full, immediate, and universal ordinary power in the Church, which he is always able to exercise freely. . . . §3 No appeal or recourse is permitted against a sentence or decree of the Roman Pontiff. ' back

John Preskill (1999), Battling Decoherence: The Fault-Tolerant Quantum Computer, ' Information carried by a quantum system has notoriously weird properties. Physicists and engineers are now learning how to put that weirdness to work. Quantum computers, which manipulate quantum states rather than classical bits, may someday be able to perform tasks that would be inconceivable with conventional digital technology. (See the article by Charles H. Bennett, Physics Today, October 1995, page 24, and the “Search and Discovery” report in Physics Today, March 1996, page 21.)' back

John Preskill (2025_07_01), Battling Decoherence: The Fault-Tolerant Quantum Computer, ' Information carried by a quantum system has notoriously weird properties. Physicists and engineers are now learning how to put that weirdness to work. Quantum computers, which manipulate quantum states rather than classical bits, may someday be able to perform tasks that would be inconceivable with conventional digital technology. back

John Warhurst (Papers on Parliament No 46), Religion in 21st Century Australian National Politics, ' The religious factor generally means a number of things in politics. One is the political activity of the organised face of religion, the churches and their agencies and lobby groups, and the attitude of governments towards those churches. Another is the relationship between religious affiliation and parliamentary representation. A third is the relationship between individual religious belief and the actions and voting behaviour of citizens. This lecture, largely about Christianity, discusses all these things and more, and tries to convey the overall flavour of religion and politics early in the twenty-first century. It reveals the wide range of intersections between religion and politics. Before going any further I should make clear that religion is often a slippery variable to deal with. The religious affiliations of individual MPs, much less private citizens, are often not at all clear. One certainly needs to distinguish between religious background, such as family and schooling, religious and denominational affiliation, and religious practice and values. Religion and politics has a long and often controversial history in Australia, most of it associated with Christianity. One resolution of the relationship came with the incorporation into the Constitution of s. 116. That section reads: s. 116: The Commonwealth shall not make any law for establishing any religion, or for imposing any religious observance, or for prohibiting the free exercise of any religion, and no religious test shall be required as a qualification for any office or public trust under the Commonwealth. back

Kenneth G Wilson (1982), Nobel Lecture: The Renormalisation Group and Critical Phenomena, Nobel Prize Lecture, 8 December 1982: This paper has three parts. The first part is a simplified presentation of the basic ideas of the renormalization group and the e expansion applied to critical phenomena, following roughly a summary exposition given in 1972. The second part is an account of the history (as I remember it) of work leading up to the papers in I971-1972 on the renormalization group. Finally, some of the developments since 1971 will be summarized, and an assessment for the future given.' 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 that 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

Large Hadron Collider - Wikipedia, Large Hadron Collider - Wikipedia, the free encyclopedia, ' The Large Hadron Collider (LHC) is the world's largest and highest-energy particle collider. It was built by the European Organization for Nuclear Research (CERN) between 1998 and 2008 in collaboration with over 10,000 scientists and hundreds of universities and laboratories, as well as more than 100 countries. It lies in a tunnel 27 kilometres (17 mi) in circumference and as deep as 175 metres (574 ft) beneath the France–Switzerland border near Geneva. The first collisions were achieved in 2010 at an energy of 3.5 teraelectronvolts (TeV) per beam, about four times the previous world record. After upgrades it reached 6.5 TeV per beam (13 TeV total collision energy, the present world record). At the end of 2018, it was shut down for three years for further upgrades.' back

Louis de Broglie (1929), Nobel Lecture: The Wave Nature of the Electron, ' The necessity of assuming for light two contradictory theories-that of waves and that of corpuscles - and the inability to understand why, among the infinity of motions which an electron ought to be able to have in the atom according to classical concepts, only certain ones were possible: such were the enigmas confronting physicists at the time I resumed my studies of theoretical physics. Now a purely corpuscular theory does not contain any element permitting the definition of frequency. This also renders it necessary in the case of light to introduce simultaneously the corpuscle concept and the concept of periodicity. On the other hand the determination of the stable motions of the electrons in the atom involves whole numbers, and so far the only phenomena in which whole numbers were involved in physics were those of interference and of eigenvibrations. That suggested the idea to me that electrons themselves could not be represented as simple corpuscles either, but that a periodicity had also to be assigned to them too. . . . Thus to describe the properties of matter as well as those of light, waves and corpuscles have to be referred to at one and the same time. The electron can no longer be conceived as a single, small granule of electricity; it must be associated with a wave and this wave is no myth; its wavelength can be measured and its interferences predicted. It has thus been possible to predicta whole group of phenomena without their actually having been discovered. And it is on this concept of the duality of waves and corpuscles in Nature, expressed in a more or less abstract form, that the whole recent development of theoretical physics has been founded and that all future development of this science will apparently have to be founded.' back

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

Mary Sirridge (1999), Quam videndo intus dicimus: Seeing and Saying in De Trinitate XV, ' What is being asserted is that thought has the same form as seeing or speaking respectively, i.e., that it works essentially like seeing or speaking, that thought is a formal and functional isomorph of seeing or speaking.' back

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

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

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

Max Planck (1901), On the Law of the Energy Distribution in the Normal Spectrum (Wikimedia Commons, English translation) , ' The most recent spectral measurements by O. Lummer and E. Pringsheim and, even more strikingly, those of H. Rubens and F. Kurlbaum, confirming at the same time a result previously obtained by H. Beckmann, show that the considerations of molecular kinetics first stated by W. Wien and the law of energy distribution in the normal spectrum, subsequently derived from the theory of electromagnetic radiation, have no general validity. One must improve the theory in any case, trying to achieve this based on the theory of electromagnetic radiation developed previously. For this purpose, it is necessary to draw a series of conclusions: Wien's energy distribution law led to finding the link capable of modification; it is, therefore, a matter of creating a suitable replacement for it. 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

Michael Bordt (2011), Why Aristotle's God is not the Unmoved Mover, ' The aim of this essay is to show that the view—popular among certain philosophers and theologians—that Aristotle’s God is the unmoved mover is incorrect, or at least leads to serious misunderstanding. In a nutshell: among other things, the project of the twelfth book of the Metaphysics is to determine what the first ousia is. This first ousia is not identified with God in so far as it is an unmoved mover, but in so far as it is the actual activity (energeia) of thinking. To put matters differently, the actual activity of the first ousia does not consist in moving anything. Its activity rather consists in the exercise of reason, in thinking. Since, however, thinking is without qualification the best activity, and since God is that being who just does engage in the best activity, the first ousia, in so far as it is the same as the activity of thinking, must be God. Thus we perhaps expect that, at the summit of ontology, God himself will be the object of this first philosophy. Metaphysics Λ meets such an expectation only in a very limited way. The limitation is the following: that which, so to speak, stands at the summit of metaphysics is not God, but the activity of reason. While this activity is identified with God, it is not so identified directly or immediately, but only as mediated by way of the conception of the best possible life. The twelfth book of the Metaphysics thus provides to an even lesser extent than is usually assumed the outlines of a theology. By way of recompense, however, Aristotle offers us a truly breathtaking metaphysics.' back

Minkowski space - Wikipedia, Minkowski space - Wikipedia, the free encyclopedia, ' By1908 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

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

Nuclear Fission - Wikipedia, Nuclear Fission - Wikipedia, the free encyclopedia, ' Nuclear fission is a reaction in which the nucleus of an atom splits into two or more smaller nuclei. The fission process often produces gamma photons, and releases a very large amount of energy even by the energetic standards of radioactive decay.
Nuclear fission was discovered on 19 December 1938 in Berlin by German chemists Otto Hahn and Fritz Strassmann. Physicists Lise Meitner and her nephew Otto Robert Frisch explained it theoretically in January 1939. Frisch named the process "fission" by analogy with biological fission of living cells. In their second publication on nuclear fission in February of 1939, Hahn and Strassmann predicted the existence and liberation of additional neutrons during the fission process, opening up the possibility of a nuclear chain reaction.' back

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

P. A. M Dirac (1928), The Quantum Theory of the Electron , The question remains as to why Nature should have chosen this particular model for the electron instead of being satisfied with the point charge. One would like to find some incompleteness in the previous methods of applying quantum mechanics to the point charge such that, when removed, the whole of the duplexity phenomena follow without arbitrary assumptions. In the present paper it is shown that this is the case, the incompleteness of previous theory lying in their disagreement with relativity, or, alternatively, with the general transformation theory of quantum mechanics. It appears that the simplest hamiltonian for a point charge electron satisfying the requirements of both relativity and the general transformation theory leads to an explanation of the duplexity phenomenon without further assumption. back

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

Pauli exclusion principle - Wikipedia, Pauli exclusion principle - Wikipedia, the free encyclopedia, 'The Pauli exclusion principle is the quantum mechanical principle that no two identical fermions (particles with half-integer spin) may occupy the same quantum state simultaneously. A more rigorous statement is that the total wave function for two identical fermions is anti-symmetric with respect to exchange of the particles. The principle was formulated by Austrian physicist Wolfgang Pauli in 1925.' back

Peter Osper (1957), Review: Albert Szent-Györgyi (1957): Bioenergetics, ' Everyone who is interested in biological chemistry will want to read and reread this book, and then design some experiments to prove Szent-Györgyi: right or wrong. One gets the impression that Szent-Györgyi will not be too unhappy to be proved wrong. . . .' In 1957 the scientist Albert Szent-Györgyi released this book which contained a part titled “Biological Structures and Functions”. The following statement without attribution was employed as an epigraph for this part (page 56): https://archive.org/details/bioenergetics00szen/page/57/mode/1up “Research is to see what everybody has seen and think what nobody has thought.” back

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

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

Richard Behiel, Electromagnetism as a Gauge Theory, ' "Why is electromagnetism a thing?" That's the question. In this video, we explore the answer given by gauge theory. In a nutshell, electromagnetism arises from local phase symmetry. But what does that mean, and how exactly does that work? That's what this video is all about!
This video is quite long and technical. Think of it as a video textbook, so you can skip around to different parts if you’d like. But I wanted to err on the side of rigor and thoroughness, to show comprehensively how local U(1) symmetry blossoms into electromagnetism. So the ideas are all there for you, but you don’t have to watch this in one sitting! ' back

Richard Feynman & Steven Weinberg (1986), Elementary Particles and the Laws of Physics The1986 Dirac Memorial Lectures, Foreword: John C Taylor: 'Dirac Died in 1984, and St John's College, Cambridge (Dirac's College), very generously endowed an annual lecture to be held at Cambridge University in Dirac's memory. The First two lectures, printed here, are contrasting variations of Dirac's theme of the union of quantum theory and relativity.' back

Richard Kraut - Plato, Plato (Stanford Encyclopedia of Philosophy), First published Sat Mar 20, 2004; substantive revision Thu Sep 17, 2009 'Plato (429–347 B.C.E.) is, by any reckoning, one of the most dazzling writers in the Western literary tradition and one of the most penetrating, wide-ranging, and influential authors in the history of philosophy. . . . Few other authors in the history of philosophy approximate him in depth and range: perhaps only Aristotle (who studied with him), Aquinas, and Kant would be generally agreed to be of the same rank.' back

Richard Kraut (Stanford Encyclopedia of Philosophy), Plato, ' Plato (429–347 B.C.E.) is, by any reckoning, one of the most dazzling writers in the Western literary tradition and one of the most penetrating, wide-ranging, and influential authors in the history of philosophy. . . . Few other authors in the history of philosophy approximate him in depth and range: perhaps only Aristotle (who studied with him), Aquinas, and Kant would be generally agreed to be of the same rank.' back

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

Richard P. Feynman (1982), Simulating Physics with Computers, ' You probably have all heard this example of the Einstein-Podolsky-Rosen paradox, but I will explain this little example of a physical experiment which can be done, and which has been done, which does give the answers quantum theory predicts, and the answers are really right, there's no mistake, if you do the experiment, it actually comes out. And I'm going to use the example of polarizations of photons, which is an example of a two-state system. When a photon comes, you can say it's either x polarized or y polarized. You can find that out by putting in a piece of calcite, and the photon goes through the calcite either out in one direction, or out in another--actually slightly separated, and then you put in some mirrors, that's not important. You get two beams, two places out, where the photon can go. If you put a polarized photon in, then it will go to one beam called the ordinary ray, or another, the extraordinary one.' back

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

Royal Commission into the Robodebt Scheme, Royal Commission Report (2023_07_07), ' On 18 August 2022, the Governor-General, His Excellency General the Honourable David Hurley AC DSC (Retd), issued Letters Patent, which established the Royal Commission into the Robodebt Scheme. Ms Catherine Holmes AC SC has been appointed as the Royal Commissioner.
The Letters Patent set out the Royal Commissioner’s terms of reference.
On 7 July 2023 Commissioner Holmes delivered her report and recommendations to His Excellency the Governor-General.
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Schrödinger equation - Wikipedia, Schrödinger equation - Wikipedia, the free encyclopedia, ' In quantum mechanics, the Schrödinger equation is a partial differential equation that describes how the quantum state of a quantum system changes with time. It was formulated in late 1925, and published in 1926, by the Austrian physicist Erwin Schrödinger. . . . In classical mechanics Newton's second law, (F = ma), is used to mathematically predict what a given system will do at any time after a known initial condition. In quantum mechanics, the analogue of Newton's law is Schrödinger's equation for a quantum system (usually atoms, molecules, and subatomic particles whether free, bound, or localized). It is not a simple algebraic equation, but in general a linear partial differential equation, describing the time-evolution of the system's wave function (also called a "state function").' back

Theogony - Wikipedia, Theogony - Wikipedia, the free encyclopedia, ' The Theogony (Ancient Greek: Θεογονία, romanized: Theogonía, lit. 'the genealogy or birth of the gods') is a poem by Hesiod (8th–7th century BC) describing the origins and genealogies of the Greek gods, composed c. 730–700 BC. It is written in the epic dialect of Ancient Greek and contains 1,022 lines. It is one of the most important sources for the understanding of early Greek cosmology.
Hesiod's Theogony is a large-scale synthesis of a vast variety of local Greek traditions concerning the gods, organized as a narrative that tells how they came to be and how they established permanent control over the cosmos. It is the first known Greek mythical cosmogony. The initial state of the universe is chaos, a dark indefinite void considered a divine primordial condition from which everything else appeared. Theogonies are a part of Greek mythology which embodies the desire to articulate reality as a whole; this universalizing impulse was fundamental for the first later projects of speculative theorizing.' back

Thomas Aquinas Summa Theologiae; Part I, Q. 1, The Nature and Extent of Sacred Doctrine, PROLOGUE TO PART 1 Since, according to the Apostle in 1 Corinthians 3:1-2 (“As unto little ones in Christ, I gave you milk to drink, not meat”), a teacher of Catholic truth not only ought to instruct those who are advanced, but is also charged with teaching beginners, our intention in the present work is to propound the things belonging to the Christian religion in a way consonant with the education of beginners. For we have noticed that newcomers to this study are commonly hampered by the writings of different authors—partly because of the proliferation of superfluous questions, articles, and arguments; partly because the things they need to know are taught not according to the order of learning, but instead as is required for the exposition of texts or as opportunities for disputing certain questions present themselves; and partly because frequent repetition in these same writings generates both antipathy and confusion in the minds of the listeners. In an effort to avoid these and other such problems, we will try, with trust in God’s help, to set forth what belongs to sacred doctrine as briefly and clearly as the subject matter allows. back

Unitarity (physics) - Wikipedia, Unitarity (physics) - Wikipedia, the free encyclopedia, ' In quantum physics, unitarity means that the sum of probabilities of all possible outcome of any event is always 1. This is necessary for the theory to be consistent. This implies that the operator which describes the progress of a physical system in time must be a unitary operator. This operator is e ^iHt where H is the Hamiltonian of the system and t is [an increasing number, not necessarily time since we are in Hilbert space where there is no space-time].' back

Wave function collapse - Wikipedia, Wave function collapse - Wikipedia, the free encyclopedia, 'In quantum mechanics, wave function collapse is said to occur when a wave function—initially in a superposition of several eigenstates—appears to reduce to a single eigenstate (by "observation"). It is the essence of measurement in quantum mechanics and connects the wave function with classical observables like position and momentum. Collapse is one of two processes by which quantum systems evolve in time; the other is continuous evolution via the Schrödinger equation.' back

William Bristow (Stanford Encyclopedia of Philosophy), Enlightenment, ' The Enlightenment is often associated with its political revolutions and ideals, especially the French Revolution of 1789. The energy created and expressed by the intellectual foment of Enlightenment thinkers contributes to the growing wave of social unrest in France in the eighteenth century. The social unrest comes to a head in the violent political upheaval which sweeps away the traditionally and hierarchically structured ancien régime (the monarchy, the privileges of the nobility, the political power of the Catholic Church). The French revolutionaries meant to establish in place of the ancien régime a new reason-based order instituting the Enlightenment ideals of liberty and equality.' back

William K. Wootters & Wojciech H. Zurek (2025_04_01), The no-cloning theorem, ' The principle of superposition is a cornerstone of quantum mechanics. It says that when two evolving states solve the Schrödinger equation, any linear combination of the two is also a solution. For that reason, waves from the two slits in the double-slit experiment simply add together to create the familiar interference pattern. As it happens, the superposition principle also prohibits the arbitrary copying of quantum states. [. . .]
The difficulty stems from the inherent nonlinearity of copying: When one asks for “two of the same,” a square |⁠s⟩|⁠s⟩ of the original |⁠s⟩ is requested. The desire for a squared state is in conflict with the strict linearity of quantum theory. As a result, a single cloner cannot make a perfect copy of every quantum state. So what states can it clone? [. . .]
In sum, one cannot make a perfect copy of an unknown quantum state, since, without prior knowledge, it is impossible to select the right copier for the job. That formulation is one common way of stating the no-cloning theorem.' back

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

Xavier Waintal (2023), The quantum house of cards, 'Abstract: Quantum computers have been proposed to solve a number of important problems such as discovering new drugs, new catalysts for fertilizer production, breaking encryption protocols, optimizing financial portfolios, or implementing new artificial intelligence applications. Yet, to date, a simple task such as multiplying 3 by 5 is beyond existing quantum hardware. This article examines the difficulties that would need to be solved for quantum computers to live up to their promises. I discuss the whole stack of technologies that has been envisioned to build a quantum computer from the top layers (the actual algorithms and associated applications) down to the very bottom ones (the quantum hardware, its control electronics, cryogeny, etc.) while not forgetting the crucial intermediate layer of quantum error correction.' 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