natural theology > notes

Related sites

Revealing Vatican attempts to propagate its religion by international treaty

You may copy this material freely provided only that you quote fairly and provide a link (or reference) to your source.

Aquinas, Thomas, Summa Theologica (translated by Fathers of the English Dominican Province), Tabor Publishing 1981 'Brother Thomas raised new problems in his teaching, invented a new method, used new systems of proof. To hear him teach a new doctrine, with new arguments, one could not doubt that God, by the irradiation of this new light and by the novelty of this inspiration, gave him the power to teach, by the spoken and written word, new opinions and new knowledge.' (William of Tocco, T's first biographer)
Amazon back

Augustine, Saint, and Edmond Hill (Introduction, translation and notes), and John E Rotelle (editor), The Trinity, New City Press 1991 Written 399 - 419: De Trinitate is a radical restatement, defence and development of the Christian doctrine of the Trinity. Augistine's book has served as a foundation for most subsequent work, particularly that of Thomas Aquinas.
Amazon back

Casti, John L, Five Golden Rules: Great Theories of 20th-Century Mathematics - and Why They Matter, John Wiley and Sons 1996 Preface: '[this book] is intended to tell the general reader about mathematics by showcasing five of the finest achievements of the mathematician's art in this [20th] century.' p ix. Treats the Minimax theorem (game theory), the Brouwer Fixed-Point theorem (topology), Morse's theorem (singularity theory), the Halting theorem (theory of computation) and the Simplex method (optimisation theory).
Amazon back

Chaitin, Gregory J, Information, Randomness & Incompleteness: Papers on Algorithmic Information Theory, World Scientific 1987 Jacket: 'Algorithmic information theory is a branch of computational complexity theory concerned with the size of computer programs rather than with their running time. ... The theory combines features of probability theory, information theory, statistical mechanics and thermodynamics, and recursive function or computability theory. ... [A] major application of algorithmic information theory has been the dramatic new light it throws on Gödel's famous incompleteness theorem and on the limitations of the axiomatic method. ...'
Amazon back

Chaitin, Gregory J, Algorithmic Information Theory, Cambridge UP 1987 Foreword: 'The crucial fact here is that there exist symbolic objects (i.e., texts) which are "algorithmically inexplicable", i.e., cannot be specified by any text shorter than themselves. Since texts of this sort have the properties associated with random sequences of classical probability theory, the theory of describability developed . . . in the present work yields a very interesting new view of the notion of randomness.' J T Schwartz
Amazon back

Chaitin, Gregory J, "Gödel's Theorem and Information" in Information, Randomness & Incompleteness: Papers on Algorithmic Information Theory, Reprinted from the International Journal of Theoretical Physics (1982) 22, 941-954., World Scientific 1987 Abstract: 'Gödel's theorem may be demonstrated using arguments having an information-theoretic flavour. In such an approach, it is possible to argue that if a theorem contains more information than any given set of acxoms, then it is impossible for the theorem to have been derived from the axioms. In contrast with the traditional proof based on the paradox of the liar, this new viewpoint suggests that the incompleteness phenomenon discovered by Godel is natural and widespread rather than pathological and unusual.'
Amazon back

Clancy, Susan A, The trauma Myth: The Truth About Sexual Abuse of Chiuldren-- and its Aftermathj, Basic Books 2010 From Booklist 'Clancy argues the controversial position that survivors of childhood sexual abuse are victimized not only by their abusers, whose acts often leave them more confused (due to incomprehension) than frightened, but also and inadvertently by well-intentioned health professionals, whose interpretations of abusive experiences are often more traumatic than actual events and effects. Well-meaning practitioners emphasize abuse’s violence, fear, and threats, which “do not characterize the experiences that most victims have.” Challenging the traumatogenic model’s assumptions and origins, Clancy questions the “repression” concept of “recovered” memories as oddly selective compared to conceptions of other major traumas. Skillfully interweaving case studies, statistics, and technical data, she disputes that abusive acts destabilize neurobiology as in other traumas. Positing that the trauma model damages victims with inaccurate predictions and ineffective treatments, she recommends tracking consequences via cognitive, behavioral, and developmental pathways because “what hurts most victims is not the experience itself but the meaning of the experience—how victims make sense of what happened . . . how these understandings make them feel about themselves and others.”' --Whitney Scott
Amazon back

Davis, Martin, Computability and Unsolvability, Dover 1982 Preface: 'This book is an introduction to the theory of computability and non-computability ususally referred to as the theory of recursive functions. The subject is concerned with the existence of purely mechanical procedures for solving problems. . . . The existence of absolutely unsolvable problems and the Gödel incompleteness theorem are among the results in the theory of computability that have philosophical significance.'
Amazon back

Davis, Martin, The Undecidable : Basic Papers on Problems Propositions Unsolvable Problems and Computable Functions, Raven Press 1965 Description: '[Includes] ... the basic papers of Gödel, Church, Turing, and Post in which the class of recursive functions was singled out and seen to be just the class of functions that can be computed by terminating processes. Also presented is the work of Church, Turing, and Post in which problems from the theory of abstract computing machines, from mathematical logic, and finally from algebra are shown to be unsolvable in the sense that there is no terminating process for dealing with them. Finally, the book presents the work of Kleene and of Post initiating the classification theory of unsolvable problems. Already the standard reference work on the subject, The Undecidable is also ideally suited as a text or supplementary text for courses in logic, philosophy, and foundations of mathematics.
Amazon back

Dawkins, Richard, Climbing Mount Improbable, W. W. Norton & Company 1997 Amazon editorial review: 'How do species evolve? Richard Dawkins, one of the world's most eminent zoologists, likens the process to scaling a huge, Himalaya-size peak, the Mount Improbable of his title. An alpinist does not leap from sea level to the summit; neither does a species utterly change forms overnight, but instead follows a course of "slow, cumulative, one-step-at-a-time, non-random survival of random variants" -- a course that Charles Darwin, Dawkins's great hero, called natural selection. Illustrating his arguments with case studies from the natural world, such as the evolution of the eye and the lung, and the coevolution of certain kinds of figs and wasps, Dawkins provides a vigorous, entertaining defense of key Darwinian ideas.'
Amazon back

Feynman, Richard P, and Robert B Leighton, Matthew Sands, The Feynman Lectures on Physics (volume 3) : Quantum Mechanics, Addison Wesley 1970 Foreword: 'This set of lectures tries to elucidate from the beginning those features of quantum mechanics which are the most basic and the most general. ... In each instance the ideas are introduced together with a detailed discussion of some specific examples - to try to make the physical ideas as real as possible.' Matthew Sands
Amazon back

Feynman, Richard P, and Robert B Leighton et al, The Feynman Lectures on Physics (volume 1) : Mainly Mechanics, Radiation and Heat, Addison Wesley 1963 Foreword: 'This book is based on a course of lectures in introductory physics given by Prof. R P Feynman at the California Institute of Technology during the academic year 1961-62. ... The lectures constitute a major part of a fundamental revision of the introductory course, carried out over a four year period. ... The need for a basic revision arose both from the rapid development of physics in recent decades and from the fact that entering freshmen have shown a stewady incrase in mathematical ability as a result of improvements in high school mathematical course content.'
Amazon back

Gödel, Kurt, and Solomon Feferman et al (eds), Kurt Gödel: Collected Works Volume 1 Publications 1929-1936, Oxford UP 1986 Jacket: 'Kurt Gödel was the most outstanding logician of the twentieth century, famous for his work on the completeness of logic, the incompleteness of number theory and the consistency of the axiom of choice and the continuum hypotheses. ... The first volume of a comprehensive edition of Gödel's works, this book makes available for the first time in a single source all his publications from 1929 to 1936, including his dissertation. ...'
Amazon back

Gödel, Kurt, and B Meltzler (translator), R B Braithwaite (Introduction), On Formally Undecidable Propositions of Principia Mathematica and Related Systems, Dover 1992 A translation of Uber Formal Unentscheidbare Satze der Principia Mathematica und Verwandter Systeme I, Monatshefte fur Mathematik und Physic, 38(1931) 173-198. Jacket: 'In 1931 a young Austrian mathematician published an epoch making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Gödel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will mot give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th century mathematics.'
Amazon back

Gödel, Kurt, "On formally undecidable propositions of Principia Mathematica and related systems, I" in Solomon Fefferman et al (eds) Kurt Gödel: Collected Works Volume 1 Publications 1929-1936, Oxford UP 1986 Jacket: 'Kurt Gödel was the most outstanding logician of the twentieth century, famous for his work on the completeness of logic, the incompleteness of number theory and the consistency of the axiom of choice and the continuum hypotheses. ... The first volume of a comprehensive edition of Gödel's works, this book makes available for the first time in a single source all his publications from 1929 to 1936, including his dissertation. ...'
Amazon back

Nielsen, Michael A, and Isaac L Chuang, Quantum Computation and Quantum Information, Cambridge University Press 2000 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 Schrödinger '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.
Amazon back

von Campenhausen, Hans, and (English translation revised by L A Garrard), The Fathers of hte Greek Church, Adam and Charles Black 1963 Professor of Ecclesiastical History, Heidelberg Universityback

Papers

Shannon, Claude E, "Communication in the Presence of Noise", Proceedings of the IEEE, 86, 2, February 1998, page 447-457. Reprint of Shannon, Claude E. "Communication in the Presence of Noise." Proceedings of the IEEE, 37 (January 1949) : 10-21. '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 this maximum rate are discussed. The equivalent number of binary digits per second of certain information sources is calculated.' . back

Zurek, Wojciech Hubert, "Quantum origin of quantum jumps: Breaking of unitary symmetry induced by information transfer in the transition from quantum to classical", Physical Review A, 76, 5, 16 November 2007, page 052110-1--5. Abstract: 'Measurements transfer information about a system to the apparatus and then, further on, to observers and (often inadvertently) to the environment. I show that even imperfect copying essential in such situations restricts possible unperturbed outcomes to an orthogonal subset of all possible states of the system, thus breaking the unitary symmetry of its Hilbert space implied by the quantum superposition principle. Preferred outcome states emerge as a result. They provide a framework for 'wave-packet collapse', designating terminal points of quantum jumps and defining the measured observable by specifying its eigenstates. In quantum Darwinism, they are the progenitors of multiple copies spread throughout the environment — the fittest quantum states that not only survive decoherence, but subvert the environment into carrying information about them — into becoming a witness.'. back

Zurek, Wojciech Hubert, "Decoherence, einselection, and the quantum origins of the classical", Review of Modern Physics, 75, , 2003, page 715-775. The manner in which states of some quantum systems become effectively classical is of great significance for the foundations of quantum physics, as well as for problems of practical interest such as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the Universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal “Schrödinger-cat states.” The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation. Only the preferred pointer observable of the apparatus can store information that has predictive power. When the measured quantum system is microscopic and isolated, this restriction on the predictive utility of its correlations with the macroscopic apparatus results in the effective “collapse of the wave packet.” The existential interpretation implied by einselection regards observers as open quantum systems, distinguished only by their ability to acquire, store, and process information. Spreading of the correlations with the effectively classical pointer states throughout the environment allows one to understand “classical reality” as a property based on the relatively objective existence of the einselected states. Effectively classical pointer states can be “found out” without being re-prepared, e.g, by intercepting the information already present in the environment. The redundancy of the records of pointer states in the environment (which can be thought of as their “fitness” in the Darwinian sense) is a measure of their classicality. A new symmetry appears in this setting. Environment-assisted invariance or envariance sheds new light on the nature of ignorance of the state of the system due to quantum correlations with the environment and leads to Born’s rules and to reduced density matrices, ultimately justifying basic principles of the program of decoherence and einselection.. back

Links

Bubble chamber - Wikipedia Bubble chamber - Wikipedia, the free encyclopedia 'A bubble chamber is a vessel filled with a superheated transparent liquid (most often liquid hydrogen) used to detect electrically charged particles moving through it. It was invented in 1952 by Donald A. Glaser,[1] for which he was awarded the 1960 Nobel Prize in Physics.[2] Anecdotally, Glaser was inspired by the bubbles in a glass of beer; however, in a 2006 talk, he refuted this story, saying that although beer was not the inspiration for the bubble chamber, he did experiments using beer to fill early prototypes.' back

CERN LHC Homepage 'The Large Hadron Collider (LHC) sits in a circular tunnel 27 km in circumference. The tunnel is buried around 50 to 175 m. underground. It straddles the Swiss and French borders on the outskirts of Geneva. The first collisions at an energy of 3.5 TeV per beam took place on 30th March 2010. The LHC is designed to collide two counter rotating beams of protons or heavy ions. Proton-proton collisions are foreseen at an energy of 7 TeV per beam. The beams move around the LHC ring inside a continuous vacuum guided by magnets. The magnets are superconducting and are cooled by a huge cryogenics system. The cables conduct current without resistance in their superconducting state. The beams will be stored at high energy for hours. During this time collisions take place inside the four main LHC experiments.' back

Compact space - Wikipedia Compact space - Wikipedia, the free encyclopedia 'In mathematics, more specifically general topology and metric topology, a compact space is an abstract mathematical space in which, intuitively, whenever one takes an infinite number of "steps" in the space, eventually one must get arbitrarily close to some other point of the space. Thus a closed and bounded subset (such as a closed interval or rectangle) of a Euclidean space is compact because ultimately one's steps are forced to "bunch up" near a point of the set, a result known as the Bolzano–Weierstrass theorem, whereas Euclidean space itself is not compact because one can take infinitely many equal steps in any given direction without ever getting very close to any other point of the space.' back

Convex set - Wikipedia Convex set - Wikipedia, the free encyclopedia 'In Euclidean space, an object is convex if for every pair of points within the object, every point on the straight line segment that joins them is also within the object. For example, a solid cube is convex, but anything that is hollow or has a dent in it, for example, a crescent shape, is not convex.' back

Erlangen program - Wikipedia Erlangen program - Wikipedia, the free encyclopedia 'An influential research program and manifesto was published in 1872 by Felix Klein, under the title Vergleichende Betrachtungen über neuere geometrische Forschungen. This Erlangen Program (Erlanger Programm) — Klein was then at Erlangen — proposed a new solution to the problem how to classify and characterize geometries on the basis of projective geometry and group theory.' back

Hexapla - Wikipedia Hexapla - Wikipedia, the free encyclopedia 'Hexapla (Ἑξαπλά: Gr. for "sixfold") is the term for an edition of the Bible in six versions. Especially it applies to the edition of the Old Testament compiled by Origen of Alexandria, which placed side by side: Hebrew Hebrew transliterated into Greek characters Aquila of Sinope Symmachus the Ebionite A recension of the Septuagint, with (1) interpolations to indicate where the Hebrew is not represented in the Septuagint -- these are taken mainly from Theodotion's text and marked with asterisks, and (2) indications, using signs called obeloi (singular: obelus), of where words, phrases, or occasionally larger sections in the Septuagint do not reflect any underlying Hebrew. Theodotion.' back

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

Homeomorphism - Wikipedia Homeomorphism - Wikipedia, the free encyclopedia 'In the mathematical field of topology, a homeomorphism or topological isomorphism (from the Greek words (homoios) = similar and (morph) = shape = form (. . . ) is a bicontinuous function between two topological spaces. Homeomorphisms are the isomorphisms in the category of topological spaces — that is, they are the mappings which preserve all the topological properties of a given space. Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same.' back

Hypatia - Wikipedia Hypatia - Wikipedia, the free encyclopedia 'Hypatia (Greek: Ὑπατία, Hypatía, . . . born between AD 350 and 370; died March 415) was a Greek scholar from Alexandria, Egypt, considered the first notable woman in mathematics, who also taught philosophy and astronomy. She lived in Roman Egypt, and was killed by a Christian mob who falsely blamed her for religious turmoil.[ Some suggest that her murder marked the end of what is traditionally known as Classical antiquity, although others such as Christian Wildberg observe that Hellenistic philosophy continued to flourish until the age of Justinian in the sixth century.' back

IUPAC nomenclature - Wikipedia IUPAC nomenclature - Wikipedia, the free encyclopedia 'IUPAC nomenclature is a system of naming chemical compounds and of describing the science of chemistry in general. It is developed and kept up to date under the auspices of the International Union of Pure and Applied Chemistry (IUPAC). ...

This article treats the system of nomenclature in general, notably its aims and historical development. Separate articles treat the naming of organic compounds and inorganic compounds in more detail.' . . .

The primary function of chemical nomenclature is to ensure that the person who hears or reads a chemical name is under no ambiguity as to which chemical compound it refers to: each name should refer to a single substance. It is considered less important to ensure that each substance should have a single name, although the number of acceptable names is limited.' back

John Chrysostom - Wikipedia John Chrysostom - Wikipedia, the free encyclopedia 'John Chrysostom (c. 347–407, Greek: Ἰωάννης ὁ Χρυσόστομος), Archbishop of Constantinople, was an important Early Church Father. He is known for his eloquence in preaching and public speaking, his denunciation of abuse of authority by both ecclesiastical and political leaders, the Divine Liturgy of St. John Chrysostom, and his ascetic sensibilities. After his death (or, according to some sources, during his life) he was given the Greek surname chrysostomos, meaning "golden mouthed", rendered in English as Chrysostom.' back

Synesius - Wikipedia Synesius - Wikipedia, the free encyclopedia 'Synesius (Greek: Συνέσιος; c. 373 - c. 414), a Greek bishop of Ptolemais in the Libyan Pentapolis after 410, was born of wealthy parents, who claimed descent from Spartan kings, at Cyrene between 370 and 375.' back

Notes

Sunday 2 May 2004

Monday 3 May 2004

Tuesday 4 May 2004

Wednesday 5 May 2004

Thursday 6 May 2004

Friday 7 May 2004

Saturday 8 May 2004

Further reading

Books

Papers

Links