Notes
Sunday 9 May 2021 - Saturday 15 May 2021
[Notebook: DB 86: Hilbert / Minkowski]
[page 224]
Sunday 9 May 2021
Christianity is a weird and sick religion based on divine domestic violence, a very common feature of ancient theologies, where are large proportion of the characters are warlords striving for domination. My approach to quantum-theology may appear to be a little extreme, but I am consoled by the fact that it is far less so that the violent theologies that precede it.
The reification of action. A big problem in physics is coupling the mathematics to the physics by working out how physical phenomena couple to mathematical variables. Rovelli points out that Lorentz discovered the mathematical Lorentz transform and gave a rather fanciful explanation of it in terms of contraction of moving bodies through interaction with the ether. Einstein provided a true mapping based on the constant velocity of light and the symmetry of inertial frames. Carlo Rovelli: Relational Quantum Mechanics
There seems to be a lot of fudging in quantum field theory in efforts to make the mathematical coupling to physics. By starting from the beginning when things were very simple we set out to get a clearer relationship between the mathematics and the physics, particularly between the mathematics of quantum theory and the special theory of relativity. We start with the whole Hilbert space and introduce new super-symmetries as things differentiate. These symmetries are expressed in equations such as those named for Klein and Gordon, for Dirac, Schrodinger and Heisenberg and hundreds more. Klein-Gordon equation - Wikipedia, Dirac equation - Wikipedia, Schrödinger equation - Wikipedia, Heisenberg picture - Wikipedia
The action of action is to create action, as the action of gods is to create gods, so god is the raw material of the universe. As in the trinity, the [child] action (god) created by the [parent] action (god) is differentiated from the parent action by its relation of childhood to the parent, as Aquinas points out. Relationship is a reality created by communication, so this idea fits the ideas of the differentiation of fermions communicating through bosons. We may think of it in software terms as a child being a fork of the parent. These ideas seem rather arbitrary expressed in medieval theological terms but they [gain weight] when put in quantum mechanical terms via the commutator. Commutator - Wikipedia
Monday 10 May 2021
Music shows us how individual events merge into a single event [because each event is a finite waveform and their ends overlap, Aristotelian continuity]
Navigating through cognitive space is similar to navigating through geographic space. One makes a position fix every now and then. With global positioning, one can know one's position in real time but old sailors had to rely on a daily fix or less, depending on the weather. Here I am trying to steer a course between ancient religion which is clearly wrong and dangerous in many respects and a new theology based on modern knowledge. [This] relies heavily on the theory of evolution to reveal the sources of the safe and dangerous elements of our behaviour that have been built into us by a difficult and often violent path to survival, particularly in zero sum situations in which the resources for life must be obtained in competition with others driven by the same forces [the result being that we have a range of behaviour ranging from the tenderest love to the most murderous violence].
How do we deal with the cosmological constant problem? At the moment the mass associated with the calculated cosmological constant is something like 100 orders of magnitude greater than the known mass of the universe. As Zee writes:
. . . symmetry breaking generates vacuum energy. . . . We don;t have to put in actual numbers to see that there is a humungous discrepancy between theoretical expectation and observed reality. If you want the numbers, the current observational bound on the cosmological constant is ≲ (10-3eV)4. With the grand unification energy scale, we are off by (17 + 9 + 3) × 4 = 116 orders of magnitude. This is the mother of all discrepancies! Zee (2010): Quantum Field Theory in a Nutshell
[page 227]
The divine universe as we currently imagine it is an inverted pyramid built on one massless quantum of action [aka God]. The quantum, reproducing itself like a god, creates the energy of the universe. The rate of action, and therefore the creation of potential and kinetic energy goes up as we go up the pyramid, energy being conserved all the way and fixed at zero. A fraction of this energy is random, the bit we call the vacuum, but much of it is built into concrete structure, which may not contribute to the cosmological constant because it is contained in the potential wells that keep energy conserved at zero. Not an answer, but a thought!
Tuesday 11 May 2021
We are to understand that every particle in the universe is in effect a species of quantum of action whose behaviour can be described by its role in the universal computer network and each of the actions of each particle can be represented as a process involving countable number of fundamental quanta of action representing the involvement in the action of the number of fundamental particles in the complex particle of interest. We understand that local operations in a quantized . . . logical network cannot exceed the Turing or Gödel bounds in complexity, which together limit the entropy and determinism of any process in the universe through the operation of the cybernetic principle of requisite variety.
A sentence is a set of intersecting words (bins) defining a point. So the opera movie Aida is to be shown at the Prospect Palace on Sunday at 11 am. By following this instruction I can intersect with the movie.
[page 228]
Energy measures the speed with which something happens: linear with E = hf, quadratic with E = ½mv2 = mc2.
Dirac's gamma trick overcame this gap between quantum and classical. Gamma matrices - Wikipedia
So I am deeply interested in how to create space-time out of Hilbert space. On the grounds that quantum measurement, which provides its answers in spacetime, requires the intersection of two quantum systems and so two measurement operators, we need to look into Zurek's article and the role of the tensor product of two Hilbert spaces which may serve as the origin of the quadratic metric in Minkowski space. Wojciech Hubert Zurek: Quantum origin of quantum jumps: breaking of unitary symmetry induced by information transfer and the transition from quantum to classical
When we write the sentence E = hf = ½mv2 = mc2 it is made dimensionally consistent by the fact that h has the dimensions of angular momentum and we might ask has it been such from the beginning, or is this a consequence of the emergence of spacetime converting h from a logical operator and energy from a rate of computation into a measure of spin and kinetic motion?
We have the ingredients to make a universe, the quantum of action to create a vacuum of random processes, Zurek's explanation of the quantum origin of quantum jumps [to explain natural selection of particular states out of the vacuum] and the network system
[page 229]
to bring different quantum systems into contact with each other to create entropy, meaning, new structure.
Wednesday 12 May 2021
Physics abhors action at a distance and maintains that causal physical interactions require contact which means in effect that the distance between particles in an event be . . . zero . . . in the metric of Minkowski space. This seems inadequate insofar s [classical] continuity is defined by accumulations of discrete points, so actual causal interaction is moot. The logical approach seems to improve on this by creating real continuity, as defined by Aristotle, between two systems. In the computer world two systems become continuous ('overlap') by reading from and writing to a shared location in memory which serves, in a logical sense, as the 'middle term' between the systems. In ordinary networking this shared memory is called a buffer [and in quantum systems we may see this as the role of bosons, which, travelling at the velocity of light, are in effect eternal [as we see in photons] in Minkowski space, not changing unless they are changed by interaction. Kevin Brown: Reflections on Relativity
. . .
Antoinette in the Cervennes Antoinette dans les Cévennes - Wikipedia
Thursday 13 May 2021
Friday 14 May 2021
[page 230]
Yesterday was what a mystic might have called a dry day, a writer a day of writer's block. Making the universe divine puts all these ideas into a new context. The mystics, by physical discipline, fasting, self abnegation, self torture even, tried to experience a feeling of the closeness of god, a mystical experience. In the divine world, all experience, across the spectrum from pain to pleasure, is experience of god and it comes naturally, without too much special pleading. Reading Dante's Paradise I feel the power of words to elicit imaginative feelings of the wonder of a remote paradise which is in fact all around us all the time, with its companion states Inferno and Purgatory. In my efforts to write quantum-theology I experience all the rather random events of intellectual activity, ranging from apparent dead ends to the easy and exciting flow of words which appear to capture substantial aspects of my divine world. Spiritual dryness - Wikipedia, Dante Alighieri: Paradise
Writing about action seems relatively easy with its long positive history stemming from Aristotle. The next [step] potential, is more difficult because here lies a radical difference from the old view. The old axion 'no potential can actualize itself' no longer holds, but potential energy is exactly equivalent to kinetic energy in modern physics and in the world we imagine built on action potential is in effect the name for the quality of action moving it to act and we must find a place for gravitational potential in the structure of the world and potential in all actions that drives them to move if they are not inhibited by the fact that any motion involves
[page 231]
contradiction, stepping outside the bounds of divine omnipotence. How do we conceive of this and explain it? They key lies in local consistency, the selective process that decides what is to happen (live) or not happen. In market terms what god will buy, not buy, sell recycle, try again, the processes measured by quantum statistics. Gravitation is so weak, we might say, because it takes a huge number of trials to yield a success because the 'distance' between success and failure is very great. The roulette wheel has 1040 sectors.
Energy is conserved because the relationship between the quantum of action and energy is frequency, that is inverse time, and as of the beginning there remains only one quantum of action in the universe which is time division multiplexed o fulfill the initial potential, the inverse of the initial action, or something like that. Both potential and kinetic energy are part of the bifurcation of action into energy / time. How? Both are relative - what matters are frequency differences and potential differences, but they must be matched, as in the absorption of a photon by an electron moving in an electric potential.
We may look at potential as possibility, ie an opening for something to happen, that is an open path not blocked by a contradiction, an attractive option. This has a certain finalist tinge about it, as though systems can look ahead and see a way to go but this problem may not be so difficult in a quantum world that precedes space where all of the situation is immediately present to an agent.
Saturday 15 May 2020
A long night of dreams. First installing a hot water system in an old decrepit house with no plumbing. And then a big party in another old house, much bigger than my old house, every room full of people. I woke up and wandered around naked looking for my clothes, no one took much notice of me until I met a boy whom I had known long ago. We looked out the window to see water rushing past. I went to investigate and found a 24 inch water main broken by a bulldozer. As a background to all this I spent a lot of time thinking about action, entropy and the Lagrangian function ∫(kinetic energy - potential energy) dt trying to solve the problem about potential that has been worrying me for the last few days. The persistent conclusion: if potential energy and kinetic energy are equal the action, the time integral of the Lagrangian is zero. I would have preferred it to be 1, the integral representing one quantum of action, that is 2π of phase. Now it is morning, a cup of coffee, read the news and back to work to see what else I can dredge up out of my mind. I hope my dream points to another clue in my 60 year quest for theological enlightenment.
FLP III:07: Radiation or absorption goes in the direction of increasing entropy. Feynman Lectures on Physics: III:07
Amplitude of particle at rest has nothing to do with its position in space but is a function of time ae-iωt [ℏ ω = E0 = Mc2].
'There are three different ways of specifying the energy: by the frequency of an amplitude; by the energy in the classical sense; or by inertia' (mass).
[page 233]
'The choice of an origin for our energy scale makes no difference; we can measure energy from any zero we want'' which must include potential and kinetic energy, so they are closely coupled.
' [A uniform potential] is just like a change in the zero of our energy scale. It produces an equal phase change in all amplitudes . . . but this doesn't change the probabilities.' Subtracting the potential would give the same result. So subtracting a potential equal to mc2 would leave us with zero energy, zero frequency, eternity, so we might imagine that gravitation is a consequence of the eternity of the initial singularity.
' [potential energy] is that energy whose derivatives gives a force.'
Reading Paradise gaves me some concrete insight into the Catholic religious beliefs of the early 14th century. Not much has changed among these people in the 21st century, 700 years later, which gives me confidence that no matter how ineffectual my theological efforts turn out to be they may be the precursor to a non-sectarian scientific theology. [This might] unite the human species in a common organism working to ensure [the health] of the planet that it must occupy for the next five billion years. We are yet very young and a little stupid and violent but there is hope for the future if those too weak to face reality can be prevented from exercising too much power [the Trump lunacy exemplifies the danger of departing too far from reality, but he is no further from reality than the Christian churches].
Our proposed chain of theory begins with logic (conceiving action as the operation of the logical not) to quantum physics to spacetime and so we might seek a logical explanation of energy, potential and force prior to the introduction of Hilbert space and quantum mechanics. Force, like communication, binds by continuity.
[page 234]
So, continuing the reification program, we reify continuity, communication and relationship, physically realised in bosons, the power of words.
Quantum-theology is in some ways an act of desperation devoted to breaking the monopoly of theology and religion over sectarian warmaking by unifying theology as a science, and my hope has always been to make some intellectual / model breakthrough which would catch the attention of the world, but there is little hope of instant results. Quantum theory is 120 years old and in many ways it has just begin to bite with solar panels, smart phones and many other consumer products. But how does quantum theology become a consumer product in competition with other religions when it does not offer such popular products as heaven and hell, human sacrifice, cannibalism, mega-churches and rabid opposition to human rights, science, democratic politics [together with] the companionship of like minded believers?. So what? Press on. I have a lot of good ingredients, just have to perfect the cake. But I have fear of not living up to my promise.
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Further readingBooks
Alighieri, Dante, and Mark Musa (translator), The Divine Comedy Vol. III: Paradise, Penguin Classics 1986 'In his translation of Paradise, Mark Musa exhibits the same sensitivity to language and knowledge of translation that enabled his versions of Inferno and Purgatory to capture the vibrant power and full dramatic force of Dante’s poetry. Dante relates his mystical interpretation of the heavens, and his moment of transcendent glory, as he journeys, first with Beatrice, then alone, toward the Trinity. Professor Musa’s extraordinary translation and his interpretive commentary, informative glossary, and bibliography clarify the theological themes and make Dante accessible to the English-speaking public.'
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Brandt, Siegmund, and Hans Dieter Dahmen, The Picture Book of Quantum Mechanics, Springer-Verlag 1995 Jacket: 'This book is an introduction to the basic concepts and phenomena of quantum mechanics. Computer-generated illustrations are used extensively throughout the text, helping to establish the relation between quantum mechanics on one side and classical physics . . . on the other side. Even more by studying the pictures in parallel with the text, readers develop an intuition for notoriously abstract quantum phenomena . . .'
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Churchill, Winston S, Arms and the Covenant: Speeches on Foreign Affairs and National Defence, George G. Harrap And Co. Ltd 1938 ' The precursor to Churchill's great war speeches. A collection of speeches spanning the years 1928 to 1938 criticizing British foreign policy and warning prophetically of the coming danger. Churchill bibliographer Frederick Woods called this book "probably the most crucial volume of speeches that he ever published."' Churchill Book Collector
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Cummins, Denise Dellarosa, and Colin Allen (editors), The Evolution of Mind, Oxford University Press 1998 Introduction: 'This book is an interdisciplinary endeavour, a collection of essays by ethologists, psychologists, anthropologists and philosophers united in the common goal of explaining cognition. . . . the chief challenge is to make evolutionary psychology into an experimental science. Several of the chapters in this volume describe experimental techniques and results consistent with this aim; our hope and intention is that they lead by example in the development of evolutionary psychology from the realm of speculation to that of established research program'
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Feynman, Richard P, and Robert B Leighton, Matthew Sands, The Feynman Lectures on Physics (volume 3) : Quantum Mechanics, Addison Wesley 1970 Foreword: 'This set of lectures tries to elucidate from the beginning those features of quantum mechanics which are the most basic and the most general. . . . In each instance the ideas are introduced together with a detailed discussion of some specific examples - to try to make the physical ideas as real as possible.' Matthew Sands
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Gatlin, Lila L, Information Theory and the Living System, Columbia University Press 1972 Chapter 1: 'Life may be defined operationally as an information processing system -- a structural hierarchy of functioning units -- that has acquired through evolution the ability to store and process the information necessary for its own accurate reproduction. The key word in the definition is information. This definition, like all definitions of life, is relative to the environment. My reference system is the natural environment we find on this planet. However, I do not think that life has ever been defined even operationally in terms of information. This entire book constitutes a first step towar dsuch a definition.'
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Horgan, John, The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age, Little Brown and Co 1996 Amazon Editorial Review From Publishers Weekly
'Scientific American columnist Horgan here interviews an impressive array of scientists and philosophers, who seem sharply divided over the prospects and possibilities of science. Among the pessimists, molecular biologist Gunther Stent suggests that science is reaching a point of incremental, diminishing returns as it comes up against the limits of knowledge; philosopher Thomas Kuhn sees science as a nonrational process that does not converge with truth; Vienna-born thinker Paul Feyerabend objects to science's pretensions to certainty and its potential to stamp out the diversity of human thought and culture. More optimistic are particle physicist Edward Witten, pioneer of superstring theory (which posits a universe of 10 dimensions); robotics engineer Hans Moravec, who envisions superintelligent creative robots; and physicist Roger Penrose, who theorizes that quantum effects percolating through the brain underlie consciousness. Other interviewees are Francis Crick, Noam Chomsky, David Bohm, Karl Popper, Murray Gell-Mann, Sheldon Glashow, Ilya Prigogine and Clifford Geertz. Despite the dominant doomsaying tone, this colloquium leaves much room for optimism.'
Copyright 1996 Reed Business Information, Inc.
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Knightley, Phillip, Philby: KGB Master Spy, Pan Books 1989 Back Cover: 'The name Kim Philby has become synonymous with the most amazing exploits in the history of espionage. Agent, double agent, traitor, enigma. Few knew the real man behind the impenetrable facade that for years fooled British Intelligence, the CIA and the FBI. After Philby defected to Russio in 1968 he maintained a code of silence for 25 years - until a few weeks before his death. Then, in an unprecedented move, he invited journalist Phillip Knightley to his Moscow apartment, and in six days of conversation he bared his sour as never before. He told of his childhood, the influence of his extraordinary father and the events that lead him inexorably to turn traitor. For the first time, Philby - KGB Masterspy tells the full story -- before and after defection. Through his views on everything from loyalty and patriotism to pop muic and Margaret Thatcher, revelation after revelation combine to build a unique picture of the most notorious spy of the 20th Century, a tale that rivals the best spy fiction.
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Liddell, and Scott, A Lexicon: Abridged from Liddell and Scott's Greek-English Lexicon, Clarendon Press 1963 Advertisement: 'The Abridgement of Liddell and Scott's Greek-English Lexicon is intended chiefly for use in Schools. It has been reduced to its present compass by the omission I. Of passages cited as authorities .. II. Of discussions upon the Derivation of words; III. Of words used only by authors not read in Schools ... '
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Lonergan, Bernard J F, Insight: A Study of Human Understanding (Collected Works of Bernard Lonergan : Volume 3), University of Toronto Press 1992 '. . . Bernard Lonergan's masterwork. Its aim is nothing less than insight into insight itself, an understanding of understanding'
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Misner, Charles W, and Kip S Thorne, John Archibald Wheeler, Gravitation, Freeman 1973 Jacket: 'Einstein's description of gravitation as curvature of spacetime led directly to that greatest of all predictions of his theory, that the universe itself is dynamic. Physics still has far to go to come to terms with this amazing fact and what it means for man and his relation to the universe. John Archibald Wheeler. . . . this is a book on Einstein's theory of gravity. . . . '
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Orwell, George, Homage to Catalonia, Mariner Books 1980 Amazon.com Review
'"I wonder what is the appropriate first action when you come from a country at war and set foot on peaceful soil. Mine was to rush to the tobacco-kiosk and buy as many cigars and cigarettes as I could stuff into my pockets." Most war correspondents observe wars and then tell stories about the battles, the soldiers and the civilians. George Orwell--novelist, journalist, sometime socialist--actually traded his press pass for a uniform and fought against Franco's Fascists in the Spanish Civil War during 1936 and 1937. He put his politics and his formidable conscience to the toughest tests during those days in the trenches in the Catalan section of Spain. Then, after nearly getting killed, he went back to England and wrote a gripping account of his experiences, as well as a complex analysis of the political machinations that led to the defeat of the socialist Republicans and the victory of the Fascists.'
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Polya, George, and Gordon Latta, Complex Variables, John Wiley & Sons Inc 1974 Preface: 'After having lectured for several decades on complex variables to prospective engineers and physicists, I have definite and, I hope, not unrealistic ideas about their requirements and preferences. . . .
I hope that this book is useful not only to future engineers and physicists, but also to future mathematicians. Mathematical concepts and facts gain in vividness and clarity if they are well connected with the world around us and with general ideas, and if we obtain them by our own work through successive stages instead of in one lump.'
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von Neumann, John, and Robert T Beyer (translator), Mathematical Foundations of Quantum Mechanics, Princeton University Press 1983 Jacket: '. . . a revolutionary book that caused a sea change in theoretical physics. . . . JvN begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which JvN regards as the definitive form of quantum mechanics. . . . Regarded as a tour de force at the time of its publication, this book is still indispensable for those interested in the fundamental issues of quantum mechanics.'
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Wiener, Norbert, Cybernetics or Control and Communication in the Animal and the Machine, MIT Press 1996 The classic founding text of cybernetics.
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Zee, Anthony, Quantum Field Theory in a Nutshell, Princeton University Press 2003 Amazon book description: 'An esteemed researcher and acclaimed popular author takes up the challenge of providing a clear, relatively brief, and fully up-to-date introduction to one of the most vital but notoriously difficult subjects in theoretical physics. A quantum field theory text for the twenty-first century, this book makes the essential tool of modern theoretical physics available to any student who has completed a course on quantum mechanics and is eager to go on.
Quantum field theory was invented to deal simultaneously with special relativity and quantum mechanics, the two greatest discoveries of early twentieth-century physics, but it has become increasingly important to many areas of physics. These days, physicists turn to quantum field theory to describe a multitude of phenomena.
Stressing critical ideas and insights, Zee uses numerous examples to lead students to a true conceptual understanding of quantum field theory--what it means and what it can do. He covers an unusually diverse range of topics, including various contemporary developments,while guiding readers through thoughtfully designed problems. In contrast to previous texts, Zee incorporates gravity from the outset and discusses the innovative use of quantum field theory in modern condensed matter theory.
Without a solid understanding of quantum field theory, no student can claim to have mastered contemporary theoretical physics. Offering a remarkably accessible conceptual introduction, this text will be widely welcomed and used.
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Zee (2010), Anthony, Quantum Field Theory in a Nutshell, Princeton University Press 2010 ' Since it was first published, Quantum Field Theory in a Nutshell has quickly established itself as the most accessible and comprehensive introduction to this profound and deeply fascinating area of theoretical physics. Now in this fully revised and expanded edition, A. Zee covers the latest advances while providing a solid conceptual foundation for students to build on, making this the most up-to-date and modern textbook on quantum field theory available. This expanded edition features several additional chapters, as well as an entirely new section describing recent developments in quantum field theory such as gravitational waves, the helicity spinor formalism, on-shell gluon scattering, recursion relations for amplitudes with complex momenta, and the hidden connection between Yang-Mills theory and Einstein gravity. Zee also provides added exercises, explanations, and examples, as well as detailed appendices, solutions to selected exercises, and suggestions for further reading.'
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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 |
Links
Alfred Tarski - Wikipedia, Alfred Tarski - Wikipedia, the free encyclopedia, 'Alfred Tarski (January 14, 1901, Warsaw, Russian-ruled Poland – October 26, 1983, Berkeley, California) was a Polish logician and mathematician. . . . His biographers Anita and Solomon Feferman state that, "Along with his contemporary, Kurt Gödel, he changed the face of logic in the twentieth century, especially through his work on the concept of truth and the theory of models."' back |
Antoinette dans les Cévennes - Wikipedia, Antoinette dans les Cévennes - Wikipedia, the free encyclopedia, ' The #1 comedy hit of the 2021 AF French Film Festival, writer/director Caroline Vignal’s hilarious and life-affirming ANTOINETTE IN THE CÉVENNES stars the wonderful Laure Calamy (Call My Agent!, Aurore) as a woman who finds herself on a journey of self-discovery in somewhat unexpected circumstances. [official site] back |
Associated Press, Gov. Hogan pardoning 34 victims of racial lynching in Maryland, 'ANNAPOLIS, Md. — Maryland Gov. Larry Hogan will posthumously pardon 34 victims of racial lynching in the state who were denied legal due process in the allegations against them between 1854 and 1933, a spokesman for Hogan said Saturday.
Michael Ricci, Hogan’s spokesman, said the sweeping pardon is the first of its kind by a governor.
Hogan will sign the order at an event honoring Howard Cooper, a 15-year-old who was dragged from a jailhouse and hanged from a sycamore tree by a mob of white men in 1885 before his attorneys could file an appeal of a rape conviction reached by an all-white jury in minutes. back |
Bernie Sanders, The U.S. Must Stop Being an Apologist for the Netanyahu Government, ' In the Middle East, where we provide nearly $4 billion a year in aid to Israel, we can no longer be apologists for the right-wing Netanyahu government and its undemocratic and racist behavior. We must change course and adopt an evenhanded approach, one that upholds and strengthens international law regarding the protection of civilians, as well as existing U.S. law holding that the provision of U.S. military aid must not enable human rights abuses. . . . We must recognize that Palestinian rights matter. Palestinian lives matter.' back |
Brouwer fixed point theorem - Wikipedia, Brouwer fixed point theorem - Wikipedia, the free encyclopedia, ' Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after Luitzen Brouwer. It states that for any continuous function f with certain properties there is a point x0 such that f(x0) = x0. The simplest form of Brouwer's theorem is for continuous functions f from a disk D to itself. A more general form is for continuous functions from a convex compact subset K of Euclidean space to itself.' back |
Carlo Rovelli, Relational Quantum Mechanics, ' I suggest that the common unease with taking quantum mechanics as a fundamental description ofnature (the measurement problem) could derive from the use of an incorrect notion, as the uneasewith the Lorentz transformations before Einstein derived from the notion of observer-independenttime. I suggest that this incorrect notion that generates the unease with quantum mechanics isthe notion of observer-independent state of a system, or observer-independent values of physicalquantities. I reformulate the problem of the interpretation of quantum mechanics as the problemof deriving the formalism from a set of simple physical postulates. I consider a reformulation ofquantum mechanics in terms of information theory. All systems are assumed to be equivalent, thereis no observer-observed distinction, and the theory describes only the information that systems haveabout each other; nevertheless, the theory is complete.' back |
Catholic Church - Wikipedia, Dominican Order - Wikipedia, the free encyclopedia, 'The Order of Preachers (Latin: Ordo Praedicatorum), after the 15th century more commonly known as the Dominican Order or Dominicans, is a Catholic religious order founded by Saint Dominic and approved by Pope Honorius III (1216-27) on 22 December 1216 in France. Membership in the Order includes friars, congregations of active sisters, and lay persons affiliated with the order (formerly known as tertiaries, now Lay or Secular Dominicans).' back |
Cauchy-Riemann equations - Wikipedia, Cauchy-Riemann equations - Wikipedia, the free encyclopedia, 'In mathematics, the Cauchy–Riemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations that provides a necessary and sufficient condition for a differentiable function to be holomorphic in an open set. This system of equations first appeared in the work of Jean le Rond d'Alembert (d'Alembert 1752). Later, Leonhard Euler connected this system to the analytic functions (Euler 1777). Cauchy (1814) then used these equations to construct his theory of functions. Riemann's dissertation (Riemann 1851) on the theory of functions appeared in 1851.' back |
Christina Rocha, Yes, religion plays a more prominent role in politics. But ‘secular Australia’ has always been a myth, back |
Commutator - Wikipedia, Commutator - Wikipedia, the free encyclopedia, ' In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative. There are different definitions used in group theory and ring theory. . . . The commutator of two operators acting on a Hilbert space is a central concept in quantum mechanics, since it quantifies how well the two observables described by these operators can be measured simultaneously.' back |
Complex number - Wikipedia, Complex number - Wikipedia, the free encyclopedia, 'IA complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, which satisfies the equation i2 = −1. In this expression, a is the real part and b is the imaginary part of the complex number. Complex numbers extend the concept of the one-dimensional number line to the two-dimensional complex plane (also called Argand plane) by using the horizontal axis for the real part and the vertical axis for the imaginary part.' back |
Dirac equation - Wikipedia, Dirac equation - Wikipedia, the free encyclopedia, 'In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1⁄2 massive particles such as electrons and quarks, for which parity is a symmetry, and is consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to account fully for special relativity in the context of quantum mechanics. It accounted for the fine details of the hydrogen spectrum in a completely rigorous way.' back |
DPA, German churches plan services to bless same-sex couples in defiance of Vatican, ' Churches across Germany are planning services to bless homosexual couples this week, in defiance of a Vatican decree clarifying that such blessings are banned in the Catholic Church.
The Church of St Benedict in the southern German city of Munich is holding one of just four planned blessing Masses in the majority-Catholic state of Bavaria on Sunday.' back |
Felix Klein - Wikipedia, Felix Klein - Wikipedia, the free encyclopedia, 'Felix Christian Klein (25 April 1849 – 22 June 1925) was a German mathematician, known for his work in group theory, function theory, non-Euclidean geometry, and on the connections between geometry and group theory. His 1872 Erlangen Program, classifying geometries by their underlying symmetry groups, was a hugely influential synthesis of much of the mathematics of the day.' back |
Feynman, Leighton & Sands FLP III:07, Chapter 7: The Dependence of Amplitudes on Time, 'We want now to talk a little bit about the behavior of probability amplitudes in time. We say a “little bit,” because the actual behavior in time necessarily involves the behavior in space as well. Thus, we get immediately into the most complicated possible situation if we are to do it correctly and in detail. We are always in the difficulty that we can either treat something in a logically rigorous but quite abstract way, or we can do something which is not at all rigorous but which gives us some idea of a real situation—postponing until later a more careful treatment. With regard to energy dependence, we are going to take the second course. We will make a number of statements. We will not try to be rigorous—but will just be telling you things that have been found out, to give you some feeling for the behavior of amplitudes as a function of time.' back |
Gamma matrices - Wikipedia, Gamma matrices - Wikipedia,the free encyclopedia, ' In mathematical physics, the gamma matrices, γ0, γ1, γ2, γ3, also known as the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra Cl1,3(R). It is also possible to define higher-dimensional gamma matrices. When interpreted as the matrices of the action of a set of orthogonal basis vectors for contravariant vectors in Minkowski space, the column vectors on which the matrices act become a space of spinors, on which the Clifford algebra of spacetime acts. This in turn makes it possible to represent infinitesimal spatial rotations and Lorentz boosts. Spinors facilitate spacetime computations in general, and in particular are fundamental to the Dirac equation for relativistic spin-½ particles.' back |
Heisenberg picture - Wikipedia, Heisenberg picture - Wikipedia, the free encyclopedia, 'In physics, the Heisenberg picture (also called the Heisenberg representation) is a formulation (largely due to Werner Heisenberg in 1925) of quantum mechanics in which the operators (observables and others) incorporate a dependency on time, but the state vectors are time-independent, an arbitrary fixed basis rigidly underlying the theory.' back |
Helen Clark & Ellen Johnson Sirleaf, Why is the world still being hit by wave after wave of Covid when we know how to stop it?, ' Death and illness from Covid-19 is steadily rising once again. In the last week of April, more than 93,000 people died – approaching the worst of the global second wave. How can this still be happening? How can some countries still be experiencing wave after wave of infection when we know how to prevent them?
For the past eight months, the Independent Panel for Pandemic Preparedness and Response has been rigorously reviewing the evidence of what happened to allow Covid-19 to take a firm grip – and why. The panel spoke to hundreds of experts and people on the frontline of the response, and conducted extensive original research and numerous literature reviews.
Our report, issued today, is firm but fair in its examination of how a series of failures led to the biggest health, social, and economic disaster in living memory. back |
Holy See, Congregation for the Evangelization of Peoples - Index, '1. Con la Bolla Inscrutabili Divinae, (22 giugno 1622) emanata da Papa Gregorio XV, ebbe inizio il periodo costitutivo della Congregazione, con il nome de Propaganda Fide, cui fecero seguito altri documenti pontifici fondamentali: Romanum decet (con la medesima data), Cum inter multiplices (14 dicembre 1622), Cum nuper (13 giugno 1623), ed infine Immortalis Dei (1° agosto 1627).' back |
Independent Panel for Pandemic Preparedness and Response, Main Report, ' Since September 2020, the Independent Panel has systematically, rigorously and comprehensively examined why COVID-19 became a global health and socio-economic crisis.
In May 2021, the Independent Panel presented its findings and recommendations for action to curb the COVID-19 pandemic and to ensure that any future infectious disease outbreak does not become another catastrophic pandemic.
1. The main report presents the Panel’s findings and recommendations.
2. Summary of the main report
3. 3. The companion evidence-based narrative describes 13 defining moments which have shaped the course of the pandemic.
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John Palmer - Parmenides, Parmenides (Stanford Encyclopedia of Philosophy), First published Fri Feb 8, 2008
'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 |
Kevin Brown, Reflections on Relativity, page 693: 'A completely free massless particle — if such existed — might be represented by a monochromatic plane wave, but a real photon is necessarily emitted and absorbed as a directed quantum of action, so it corresponds to a bounded null interval in spacetime (note that the quantum phase of a photon does not advance while in transit between its emission and absorption, unlike massive particles. The oscillatory nature of electromagnetic waves arises from the advancing phase of the source rather than any phase activity of photon "in flight".) Thus the field excitation corresponding to a massless particle In contrast a massive particle has a rest frame propagates at the speed of light and has no rest frame. In contrast, a massive particle has a rest frame following a time-like path through spacetime. Nevertheless we recall Dirac's general argument (from the uncertainty principle) that all energy must propagate at essentially the speed of light if examined on the smallest scale.' back |
Klein-Gordon equation - Wikipedia, Klein-Gordon equation - Wikipedia, the free encyclopedia, 'It is the equation of motion of a quantum scalar or pseudoscalar field, a field whose quanta are spinless particles. It cannot be straightforwardly interpreted as a Schrödinger equation for a quantum state, because it is second order in time and because it does not admit a positive definite conserved probability density. Still, with the appropriate interpretation, it does describe the quantum amplitude for finding a point particle in various places, the relativistic wavefunction, but the particle propagates both forwards and backwards in time. Any solution to the Dirac equation is automatically a solution to the Klein–Gordon equation, but the converse is not true.' back |
Massimo Fagioli, From Princes to Managers
Understanding the history of the Catholic episcopate, ' The system is in serious crisis, but it’s a crisis to which centuries’ worth of shifting and complicated networking dynamics have led. We need bishops, and we need reform. It can be dispiriting to think how long it might be before the work of dismantling, reimagining, and building anew is complete.' back |
MS-DOS - Wikipedia, MS-DOS - Wikipedia, the free encyclopedia, 'MS-DOS (pronounced . . . em-es-dos; short for MicroSoft Disk Operating System) is an operating system for x86-based personal computers, which was purchased by Microsoft. It was the most commonly used member of the DOS family of operating systems, and was the main operating system for personal computers during the 1980s up to mid 1990s.' back |
News Agencies, 'World could have prevented COVID-19 catastrophe: Expert panel, 'An independent panel has concluded that the catastrophic scale of the coronavirus pandemic could have been prevented but a “toxic cocktail” of dithering and poor coordination meant the warning signs went unheeded.
In its long-awaited final report on Wednesday, the Independent Panel for Pandemic Preparedness and Response (IPPPR) said a series of bad decisions meant COVID-19 went on to kill at least 3.3 million people so far and ravage the global economy.
Institutions “failed to protect people” and science-denying leaders eroded public trust in health interventions, the IPPPR said.' back |
Schrödinger equation - Wikipedia, Schrödinger equation - Wikipedia, the free encyclopedia, 'IIn 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 |
Spiritual dryness - Wikipedia, Spiritual dryness - Wikipedia, the free encyclopedia, ' The Catechism of the Catholic Church (CCC) describes spiritual dryness as a difficulty sometimes experienced in one's prayer life, which may lead to discouragement. Dryness can expose a lack of "rootedness" in the faith, but also provides an opportunity to cling more strongly to God. The CCC makes reference to the seed that fell on the rocks in Parable of the Sower, as well as to the Grain of Wheat allegory found in the Gospel of John (§ 2731). The Catholic Encyclopedia calls it a form of "passive purification," the fruit of which is "the purification of love, until the soul is so inflamed with love of God that it feels as if wounded and languishes with the desire to love Him still more intensely." . . .
A number of Catholic saints have written about their experiences of spiritual dryness. In the 16th century, Saint John of the Cross famously described it as "the Dark Night of the Soul".' back |
Wojciech Hubert Zurek, 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 |
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