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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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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Goddard (1998), Peter , and Stephen Hawking, Abraham Pais, Maurice Jacob, David Olive, and Michael Atiyah, Paul Dirac, The Man and His Work, Cambridge University Press 1998 Jacket: Paul Adrien Maurice Dirac was one of the founders of quantum theory and the aithor of many of its most important subsequent developments. He is numbered alongside Newton, Maxwell, Einstein and Rutherford as one of the greatest physicists of all time. This volume contains four lectures celebrating Dirac's life and work and the text of an address given by Stephen Hawking, which were given on 13 November 1995 on the occasion of the dedication of a plaque to him in Westminster Abbey. In the first lecture, Abraham Pais describes from personal knowledge Dirac's character and his approach to his work. In the second lecture, Maurice Jacob explains not only how and why Dirac was led to introduce the concept of antimatter, but also its central role in modern particle physics and cosmology. In the third lecture, David Olive gives an account of Dirac's work on magnetic monopoles and shows how it has had a profound influence in the development of fundamental physics down to the present day. In the fourth lecture, Sir Michael Atiyah explains the widespread significance of the Dirac equation in mathematics, its roots in algebra and its implications for geometry and topology.' 
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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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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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Kolmogorov (1956), Andrey Nikolaevich, and Nathan Morrison (Translator) (With an added bibliography by A T Bharucha-Reid), Foundations of the Theory of Probability, Chelsea 1956 Preface: 'The purpose of this monograph is to give an axiomatic foundation for the theory of probability. . . . This task would have been a rather hopeless one before the introduction of Lebesgue's theories of measure and integration. However, after Lebesgue's publication of his investigations, the analogies between measure of a set and mathematical expectation of a random variable became apparent. These analogies allowed of further extensions; thus, for example, various properties of independent random variables were seen to be in complete analogy with the corresponding properties of orthogonal functions . . .' 
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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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Sacks (2015), Jonathan, Not in God's Name: Confronting Religious Violence, Schocken Books Inc 2015 ' In his remarkable book, Sacks argues that believers must face the painful facts. He is careful to document that wars of religion are not unique to Islam. He believes that to persuade religious people of the Abrahamic faiths, arguments against religious violence must be rooted in theology, not in secular ideas alone. E. J. Dionne Jr. "The Washington Post  
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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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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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Albert Einstein (1905), On the Electrodynamics of Moving Bodies, An english translation of the paper that founded Special relativity. 'Examples of this sort, [in the contemporary application of Maxwell's electrodynamics to moving bodies] together with the unsuccessful attempts to discover any motion of the earth relatively to the ``light medium,'' suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good.' 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, 10, 2, Is God eternal?, 'I answer that, The idea of eternity follows immutability, as the idea of time follows movement, as appears from the preceding article. Hence, as God is supremely immutable, it supremely belongs to Him to be eternal. Nor is He eternal only; but He is His own eternity; whereas, no other being is its own duration, as no other is its own being. Now God is His own uniform being; and hence as He is His own essence, so He is His own eternity.' back

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

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

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

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

Catholic Catechism, §213 God alone IS, ' The revelation of the ineffable name "I AM WHO AM" contains then the truth that God alone IS. The Greek Septuagint translation of the Hebrew Scriptures, and following it the Church's Tradition, understood the divine name in this sense: God is the fullness of Being and of every perfection, without origin and without end. All creatures receive all that they are and have from him; but he alone is his very being, and he is of himself everything that he is.' back

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

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

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

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

Hermann Minkowski (1908), Hermann Minkowski, Wikiquote, ' The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.' Address to the 80th Assembly of German Natural Scientists and Physicians, (Sep 21, 1908) back

Hermitian matrix - Wikipedia, Hermitian matrix - Wikipedia, the free encyclopedia, ' In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column, for all indices i and j . . .. Hermitian matrices can be understood as the complex extension of real symmetric matrices. . .. Hermitian matrices are named after Charles Hermite, who demonstrated in 1855 that matrices of this form share a property with real symmetric matrices of always having real eigenvalues. Other, equivalent notations in common use are A = A^H = A^∗ = A^† although in quantum mechanics A^∗typically means the complex conjugate only, and not the conjugate transpose.' 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

Ian Duck and E.C.G. Sudarshan (1998), Toward an understanding of the spin-statistics theorem, 'We respond to a request from Neuenschwander for an elementary proof of the Spin-Statistics Theorem. First . . . Then we discuss an argument suggested by Sudarshan, which proves the theorem with a minimal set of requirements. . . . Motivated by our particular use of Lorentz invariance, if we are permitted to elevate the conclusion of flavour symmetry (which we explain in the text) to the status of a postulate, one could recast the proof without any relativistic assumptions, and this make it applicable even in the nonrelativistic context. . . . Finally, an argument starting with ordinary number-valued (nonmmuting), and with Grassman valued (anticommuting) operators, shows in a natural way that these relativitcally embed into Klein-Gordon spin-0 and Dirac spin-½ fields, respectively. In this way the Spin Statistics theorem is understood at the expense of admitting the existence of the simplest Grassman-valued field.' back

John J. Hopfield (2024_12_08), Nobel Lecture: Physics is a point of view, ' John J. Hopfield delivered his Nobel Prize lecture "Physics is a point of view" on 8 December 2024 at the Aula Magna, Stockholm University. He was introduced by Professor Ellen Moons, Chair of the Nobel Committee for Physics. … 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

John Willinsky (U of Chicago Press, 2018), The Intellectual Properties of Learning: A Prehistory from Saint Jerome to John Locke (Chapter 7), ' Chapter 7 The Medieval Universities of Oxford and Paris A new educational entity for advanced studies, known as the studium generale, emerged in Europe during the twelfth century. It initially arose out of the congregation of masters and scholars to be found in such centers of learning as Bologna, Paris, and Oxford. These prototypes of the medieval university formed through such an unremarkable series of steps that little or no record was left behind. As if by spontaneous generation, masters and scholars began to organize themselves, outside of episcopal schools, monasteries, and private tutoring arrangements. By the early years of the thirteenth century, these masters were operating within what could be identified as faculties of arts, law, medicine, and theology. The studium generale was attracting considerable attention. One after another of these new institutions was formed in Cambridge, Salamanca, Siena, Naples, and elsewhere during the thirteenth century.' back

Joshua 10:12-13, Sun, stand still at Gibeon (USCCB), 'It was then, when the LORD delivered up the Amorites to the Israelites, that Joshua prayed to the LORD, and said in the presence of Israel: Sun, stand still at Gibeon, Moon, in the valley of Aijalon! The sun stood still, the moon stayed, while the nation took vengeance on its foes. This is recorded in the Book of Jashar. The sun halted halfway across the heavens; not for an entire day did it press on. back

Mario Baghos, The Historical Context of the Nicene-Constantinopolitan Creed, ' This paper gives a brief outline of the historical context within which the Nicene- Constantinopolitan Creed was formulated. It will begin by giving a background to the first ecumenical council held at Nicaea in 325 AD, which will include an assessment of the theological dimension to Christian councils, beginning with the Apostolic council of Jerusalem which became a paradigm for the synods held before the council of Nicaea. This latter council was marked by an important change in format, namely that it was convoked by a Roman emperor, Constantine the Great (r. 306-337), which means that part two of this paper will analyse the historical circumstances that influenced an emperor of Rome – which had up to this point in time persecuted Christians – to convoke a Church council. ' 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

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

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

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

Proton decay - Wikipedia, Proton decay - Wikipedia, the free encyclopedia, ' In particle physics, proton decay is a hypothetical form of particle decay in which the proton decays into lighter subatomic particles, such as a neutral pion and a positron. The proton decay hypothesis was first formulated by Andrei Sakharov in 1967. Despite significant experimental effort, proton decay has never been observed. If it does decay via a positron, the proton's half-life is constrained to be at least 1.67×10³⁴ years.' back

Richard Zach (Stanford Encyclopedia of Philosophy), Hilbert's Program, 'In the early 1920s, the German mathematician David Hilbert (1862–1943) put forward a new proposal for the foundation of classical mathematics which has come to be known as Hilbert's Program. It calls for a formalization of all of mathematics in axiomatic form, together with a proof that this axiomatization of mathematics is consistent. The consistency proof itself was to be carried out using only what Hilbert called “finitary” methods. The special epistemological character of finitary reasoning then yields the required justification of classical mathematics.' back

Roger Penrose (2020), Nobel lecture 2020: Black Holes, Cosmology and Space-Time Singularities, Roger Penrose delivered his Nobel Lecture on Tuesday 8 December 2020. He was introduced by Professor Ariel Gobar. 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

Saint John Paul II (1992_10_31), x, ' However, the underlying problems of [the Galileo] case concern both the nature of science and the message of faith. It is therefore not to be excluded that one day we shall find ourselves in a similar situation, one which will require both sides to have an informed awareness of the field and of the limits of their own competencies. The approach provided by the theme of complexity could provide an illustration of this. 5. A twofold question is at the heart of the debate of which Galileo was the centre. The first is of the epistemological order and concerns biblical hermeneu­tics. In this regard, two points must again be raised. In the first place, like most of his adversaries, Galileo made no distinction between the scientific approach to natural phenomena and a reflection on nature, of the philosophical order, which that approach generally calls for. . . . Secondly, the geocentric representation of the world was commonly admit­ted in the culture of the time as fully agreeing with the teaching of the Bible, of which certain expressions, taken literally, seemed to affirm geocentrism. The problem posed by theologians of that age was, therefore, that of the compatibility between heliocentrism and Scripture. 6. From this we can now draw our first conclusion. The birth of a new way of approaching the study of natural phenomena demands a clarification on the part of all disciplines of knowledge. . . . 9. . . . The majority of theologians did not recognise the formal distinction between Sacred Scripture and its interpretation, and this led them unduly to transpose into the realm of the doctrine of the faith a question which in fact pertained to scientific investigation. . . . 12. . . .There exist two realms of knowledge, one which has its source in Revelation and one which reason can discover by its own power. To the latter belong especially the experimental sciences and philosophy. The distinction between the two realms of knowledge ought not to be understood as opposition. The two realms are not altogether foreign to each other; they have points of contact. The methodologies proper to each make it possible to bring out different aspects of reality. . . 14.  Humanity has before it two modes of development. The first involves culture, scientific research and technology, that is to say whatever falls within the horizontal aspect of man and creation, which is growing at an impressive rate. In order that this progress should not remain completely external to man, it presupposes a simultaneous raising of conscience, as well as its actuation. The second mode of development involves what is deepest in the human being, when, transcending the world and transcending himself, man turns to the One who is the Creator of all. It is only this vertical direction which can give full meaning to man’s being and action, because it situates him in relation to his origin and his end. In this twofold direction, horizontal and vertical, man realises himself fully as a spiritual being and as homo sapiens. But we see that development is not uniform and linear, and that progress is not always well ordered. This reveals the disorder which affects the human condition. The scientist who is conscious of this twofold development and takes it into account contributes to the restoration of harmony. Those who engage in scientific and technological research admit, as the premise of its progress, that the world is not a chaos but a ‘cosmos’; that is to say, that there exist order and natural laws which can be grasped and examined, and which, for this reason, have a certain affinity with the spirit. Einstein used to say: ‘What is eternally incomprehensible in the world is that it is comprehensible’.9 This intelligibility, attested to by the marvellous discoveries of science and technology, leads us, in the last analysis, to that transcendent and primordial Thought imprinted on all things.' back

Septuagint - Wikipedia, Septuagint - Wikipedia, the free encyclopedia, ' The Greek Old Testament, or Septuagint is the earliest extant Greek translation of books from the Hebrew Bible. It includes several books beyond those contained in the Masoretic text of the Hebrew Bible as canonically used in the tradition of mainstream Rabbinical Judaism. The additional books were composed in Greek, Hebrew, or Aramaic, but in most cases, only the Greek version has survived to the present. It is the oldest and most important complete translation of the Hebrew Bible made by the Jews.' back

Stephen Cook (2006), The P Versus NP Problem, ' The P versus NP problem is to determine whether every language accepted by some nondeterministic algorithm in polynomial time is also accepted by some (deterministic) algorithm in polynomial time. To define the problem precisely it is necessary to give a formal model of a computer. The standard computer model in computability theory is the Turing machine, introduced by Alan Turing in 1936 . Although the model was introduced before physical computers were built, it nevertheless continues to be accepted as the proper computer model for the purpose of defining the notion of computable function. 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

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

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

William Bialek & Allan Schweitzer (1985), Quantum Noise and the Threshold of Hearing, ' We argue that the sensitivity of the ear reaches a limit imposed by the uncertainty principle. This is possible only if the receptor holds the detector elements in a special nonequilibirium state which has the same noise characteristics as a ground (T = 0 K) state. To accomplish this "active cooling" the molecular dynamics of the system must maintain quantum mechanical coherence over the time scale of the measurement.' 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