vol VII: Notes
2018
Notes
Sunday 22 July 2018 - Saturday 28 July 2018
[Notebook: DB 82: Life and Death]
[page 195]
Sunday 22 July 2018
Auyang page 13: Fundamental category is action = act of communication (at first undefined) ( actus purus. Then the first form = frequency / time [= energy] Auyang: How is Quantum Field Theory Possible?
'This work presents a parallel analysis of the conceptual structures of quantum field theory and our everyday thinking . . .. The categorical framework enables us to match logically the formal structure of quantum theories and everyday thinking element by element. The structural fit illuminates their philosophical significance.
My difference is to replace Kant with Shannon [ie the a priori is the mathematically determined nature of error free communication].
Auyang page 19: '. . . the quantum state evolves deterministically in the same sense that the motion of a classical particle is deterministic. In fact quantum
[page 196]
states are even better behaved . . . because the Schrödinger equation is linear and its solutions periodic or quasiperiodic.'
'An operator A is a linear transformation of a Hilbert space into itself. . . .. Only self-adjoint operators represent observables' - real spectra.
William James: Goodman: "neutral monism" Russell Goodman (Stanford Encyclopedia of Philosophy): William James
Auyang page 26 sqq: Differential manifold breaks the structure of Euclidean space into many different elements.
Cartesian [euclidean] geometry:
C1: Differentiable and affine structure
C2: Metric
Differential geometry;
D1: differentiable [manifold], points labelled by [vectors of] real numbers, separate overlapping charts;
D2: [manifold has no lines so] parametrized curves mapped into manifold;
D3: [euclidean] tangent space [at each point];
D4: connection / affine structure;
D5: metric tensor - infinitesimal;
D6: length, integral over metric;
D7 : distance function, greatest lower bound of lengths
Differentiable manifold - Wikipedia
Each of these features may be considered new layers of structure added to the evolution of space from not-space.
Monday 23 July 2018
Semester 2: [Team] America Team America: World Police - Wikipedia
[page 197]
What I want to do is formulate the good news about human existence to oppose the general idea that we are inherently evilly inclined sinners. A new theology, a new vision of god, a new look at building heaven on Earth, something we need now that it looks like everything is collapsing back into the imperial past. We want to maximize entropy for maximum stability.
'The true ugliness of human nature' Hopefully what I lack in intelligence I can replace with motivation.
Creation means composing a message, that is digitizing a continuum like bringing an image out of the mist. The foundation of creation from mathematical point of view is the digitization of the geometric continuum with the real numbers and then going beyond that to bring continua into correspondence wit the transfinite numbers, made dynamic with computers.
I can't imagine I would have go to here without the life I have led, first a flirtation with monasticism, followed by fifty years of fermentation in the country and now back to the monastic life at university.
I want to break free: increase entropy. I want it all: Freddy Mercury.
It is easy to complain, not so easy to make things better.
Tuesday 24 July 2018
Ordering the layers. Quantum mechanics is linear, so we might think it comes first. Transition from quantum to classical is quadratic,
[page 198]
p = |Ψ|2. Relativity is quadratic, so ds2 = ds2 - dt2. So here is a clue to constructing space-time out of quantum mechanics, and we might be inclined to believe that all the trouble with quantum field theory nay arise from a misunderstanding of the relationship between wave functions and space-time, but what is the misunderstanding, and given that, how do we correct it? Auyang pp 30-32.
The clue to space may be the observation that energy and momentum transform the same way as time and space and there are quantum mechanical expressions for energy and momentum built around Planck's constant E = ℏω and p = ℏ / k which carry over into the quantum theory of space first revealed by de Broglie. . . .. Peter Weinberger: Revisiting Louis de Broglie's famous 1924 paper in the Philosophical Magazine
Auyang page 32: '. . . the general idea of [symmetry] principles is that certain physical quantities are invariant under certain groups of coordinate transformations [or physical transformations, like rotating a snowflake nπ/3 radian].
What is a coordinate? What is a physical quantity? Both are numbers specified by certain accounting practices, in each case defining a unit or dimension which specifies the derivation of the unit. The basic unit in the world is the quantum of action, which is the unit we use to measure the size of an event, which we can define in terms of logical, geometric or other formal operations, eg negate it, turn it upside down, count how many units of distance, etc [eg a group]. The first measure is time, ie rate of events, and since there is no absolute measure all rates (and energies) are ratios [what about the velocity of light, c?].
[page 199]
e20_paradise has come to a standstill while we try to generate spacetime and atoms from the simple god. We have to do this on such a broad canvas of symmetry that it cannot be wrong because, like the god from which we are trying to devise it, it covers all consistent possibilities, the fullness of being [we expect natural selection to choose between the (possibly) transfinite possibilities]. The 'fullness of computability' is embraced by the NAND operation.
Symmetry relates to closure, a series of operations (like a group) which comes back to the starting point. If the universe is closed, like god, it is a group [the Einstein group]. Elmo Benedetto: Review Article: Lie Group of Spacetime
Auyang pag 33: 'The concept of symmetry contains a concept of difference, another of identity, and a third relating the two', So we can look at the doctrine of the Trinity through the eyes of symmetry.
An equivalence class of coordinates, a group of transformations and a system with certain invariant features form the trial of the concept of symmetry.'
Where quantum field theory goes wrong, misunderstanding space-time as a classical symmetry of quantum mechanics, whereas the basic symmetry is U(1)
Auyang page 28: We start with the message x. fa(x) encodes it, fa-1(x) decodes it. In an inertial frame there is no encoding and decoding and so no need for computation, so no need for digitization, ie quantization. As soon as we move to a differentiable manifold with more than one coordinate patch we need communication and digitization.
The dimensions of space are orthogonal coordinate patches which communicate in a pythagorean way (?). Dimensions are different, identical and communicate through a pythagorean relationship.
[page 200]
The relationships between different orthogonal spacetime axes are communicated by spin which comes in two sizes, ½ and 1. The quantum of action has dimensions of angular momentum. This might tell us something about space-time. The relationship between dimensions is digital rather than continuous, but transitions may take place in continuous time (?). The NOT function to which we attribute energy transforms between dimensions to give spin (?).
We can relate things to one another either by putting them in a coordinate frame, measuring the coordinates of each one and using these measurements to compute the relationship between the things, or we can simply allow the things to communicate with one another and work out their relationship through communication. In the first case, the observer is active, doing the measurements and calculations and the things related are essentially passive. In the second case the things are executing their own relationship and the observer is unnecessary. In an active world we would expect all relationships to work in the second way and the establishment of coordinate systems and transformations betwen coordinate systems is unnecessary. In the case of gravitation the geodesic deviation may be measured by the inertial systems themselves, but their methods of communication perform the same role as a coordinate system, providing a basis for measurement [but, there is no way for inertial systems to communicate with one another outside gravitation without exerting forces on one another, so destroying their inertiality].
Auyang page 34 'Symmetry transformations erase particularities. A world with high symmetry characterized by a large symmetry group is rather featureless [au contraire if it has a large symmetry group, one would expect it to have as many features as the cardinal of the group].
'Einstein was trying to formulate the most general and truly universal
[page 201]
concept that alone answers to the concept of space-time. Physicists are continuously seeking larger symmetry groups in their desire for unification; the larger group provides more encompassing concepts. For example the electromagnetic interaction is characterized by the unitary group of order 1, the weak interaction by the special unitary group SU(2) × U(1).' Is it really? One would think that by making the group more complex it embraces fewer cases, so U(1) is a lower layer that embraces all periodic functions, whereas SU(2) adds details that only apply to the weak interaction.
U(1) is the circle group of 1 × 1 matrices, ie complex numbers of absolute value 1.
Groups are the central organizing principle of contemporary mathematics. Group (mathematics) - Wikipedia
Wednesday 25 July 2018
The dominant idea here is that the universe starts off very simple and complexifies to its present state. The standard cosmological approach also says that it started off with exceedingly high energy, and so the development of accelerators that yield higher and higher energies per particle are considered to reproduce phenomena closer and closer to the beginning. Implicit in this is one of the many infinities that bug quantum field theory, given the idea that the universe began with zero size and infinite energy, giving it an extremely high energy density which is seen to naturally account for the big bang. I suppose I am trying to avoid this by taking the view that the universe
[page 202]
began like the classical God as pure act. In the modern picture action has the dimensions of spin, ie angular momentum, and energy is an emergent property of the universe being measured in units of quanta of action per second, following the Planck-Einstein relation E = ℏω. I have said this many times, and in effect my wheels are spinning and I am getting no traction, since I have not got far past the step action → energy, and am still at the threshold of the next step that goes from energy and time to space and momentum., giving us in the same move fermions and bosons. Here, maybe, the Dirac equation enters, first in a 2D version and then going up in complexity to give the 4D Minkowski space and then the Einstein space of the very early universe [the transition to Einstein space may involve the increase is spatial dimensions from 1 to 3]. One may achieve these steps by handwaving, but it would be nice to come up with something more substantial including the differentiation of energy into potential (field) and kinetic (particle). The layer beneath massive particles would perhaps be a layer of massless particles (like photons) which is in some way used to create massive particles like quarks and electrons. And we want to know how gravitation perhaps underlies electromagnetism and the weak and strong forces. Dream on, spin on, hoping that something will emerge by the end of the semester.
Looking for a form of words that will reflect reality and show a way forward. Trying to find a way to make the quantum trinity, two fermions and a boson lead us out of the darkness - the self interaction of God. Just keep shuffling the words around until a credible sentence emerges. Such a
page 203]
sentence will survive if it becomes a self-fulfilling prophecy, a creature that successfully reproduces itself.
One cannot be serious about something unless you can get a grip on it, which is probably why I spent my life [after Catholic theology] dealing with planks, bricks, pipes and sheets of steel. Now I am out of this world, and forcing myself into the slippery world of philosophical ideas . I am looking for fixed points and invariants. The Catholic Church created a foundation for itself out of a fantastic card house of dogma which attracted me until my early twenties when it all fell down. Now fifty years later I am trying to build a new theological mansion out of the real world, looking for the sources of my being in the history of the divine initial singularity, beginning to see it in a neutral monism like William James neither materialist now spiritualist, but a realism born of scientific method rather than the arbitrary faith of divinely righteous kings and queens.
Hannah Arendt: 'I would never forgive myself if I didn't take this opportunity.' The Banality of Evil. Hannah und Heidegger, New Yorker. Colin Marshall: Hannah Arendt's Original Articles on "The Banality of Evil" in the New Yorker Archive
"The problem of evil became the fundametnal subject for Hannah Arendt. Se returned to it over and over gain and was still struggling with it at the time of her death." Hannah Arendt (film) - Wikipedia
The modern exemplar of the banality of evil is the Roman Catholic Church reflected in the indifference of its hierarchy to its crimes against children on the spectrum from sexual to intellectual abuse. Australian Government: Royal Commission into Institutional Responses to Child Sexual Abuse
[page 204]
Thursday 26 July 2018
The observational interface between science and the world is basically a matter of binning and counting. The bins contain sets of objects which may range from pure quanta of action, equivalent to empty sets, to entities of very high complexity like sheep or stars. For pure actions there is only one bin because they are simple and they cannot be divided into two or more classes. For electrons we may distinguish 2 bins, positively and negatively charged, each of which can be divided into spin up and spin down each of which may be further divided into spectra of energy and momentum and so on. Electron bins are a subset of of the set of fundamental (pointlike, indivisible) particles, and so on. The counting of particles in bins provides the numerical foundation for the probabilistic computations of quantum mechanics which are specified by the Born rule. The actual 'addresses' of the bins are provided by the eigenvalue equation, and we may think of a sheep or star as a rather complex vector of eigenvalues that characterizes an observable we call sheep. The complexity of the contents of a bin is a measure of its entropy.
The quantum of action serves as the interface between arithmetic and meaning in physical science.
Auyang page 43 sqq: Quantum field theory works but it is a conceptual mess, requiring many distinct continuous fields etc etc with no comprehensible mechanism for their operation.
Field is a new form of matter, invisible and detectable only by
[page 205]
the particles that it creates and annihilates.
After the success of QED field theory entered a dark age which led ultimately to local gauge (phase) theories.
'The root of the idea of local symmetries went back to general relativity, in which the orientation of inertial frames may vary' - geodesic deviation.
Auyang page 44: ' " If I were to rename [gauge invariance] today, it is obvious that we should call it phase invariance and the gauge fields should be called phase fields. " Chen Ning Yang '
'The quanta of the strong and weak interaction fields cary the corresponding charges and are self interacting.' Like gravitation, whose charge is energy. 1954 Yang Mills gauge fields. Yang-Mills theory - Wikipedia
Massive gauge fields, spontaneous symmetry breaking, asymptotic freedom all need explanation.
page 45: matter fields - fermions; interaction fields - bosons: spin/ statistics theorem. Here. I suspect, is a law layer closely related to the emergence of space-time.
12 matter fields, 4 interaction fields: gravity, EM, weak, strong.
[page 206]
Auyang page 46: 'In fully interactive field theories, the interaction fields are permanently coupled to the matter fields.'
So, 12 sources, 4 classes of messages.
Friday 27 July 2018
We have a tree of genetic trees to explain the enormous complexity of the universe. The largest is the tree of life, based on a molecular tree, based on an atomic tree (Mendeleyev) which is based on the particle tree, based on the fundamental particles. There is an embracing tree describing the generation of the stars, galaxies, planetary systems, and we are looking for a tree to describe the generation of the fundamental particles, beginning with the bifurcation into fermions and bosons. Each branching in each of these trees corresponds to a new layer of structure in the universal network, and we understand all communications in this network to be based on the lowest physical layers of the fundamental particles whose enormous communication rates are reflected in their high energies. At the bottom we find the undifferentiated quantum of action which we are inclined to identify with the initial singularity or the traditional god. [We may imagine that every particle in the universe has a place somewhere in this forest of trees, whose detailed instantiation changes as its symmetries remain fixed.]
This paper is particularly concerned with the lowest layers of this network where we find the origins of spacetime, the bifurcation into bosons and fermions, the four bosonic communication protocols
[page 207]
and the resulting network of fundamental sources. Once this is in place most of the rest of the creation of the divine universe is already quite well documented. As usual woke up depressed and then began to cheer up as the text above began to emerge from my pen. Also greatly cheered that the fake news industry based around facebook has taken a big hit with a 20% drop in facebok share price. Now feeling a bit excited - William James emotion is physical.
Long ago I wrote tiny recursive Turing machines in basic. Maybe time to revisit this idea.
Saturday 28 July 2018
Probably more than fifty years ago I thought that the universe was a computational process, but the question was what is the hardware the universe runs on. Now I know [an] answer: God [(?)]. God is both the hardware and the software of the universe, but it is still not clear how this is realized, but the layered network seems the best idea yet, and the software, like all information, is physical and I am a subset of it, a microcosm from which I can extrapolate to the whole universe as Einstein extrapolated from the inertial frame.
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Further readingBooks
Click on the "Amazon" link below each book entry to see details of a book (and possibly buy it!)
Anonymous, The Cloud of Unknowing, HarperOne 2004 Book Description
'Written by an anonymous English monk during the late fourteenth century, The Cloud of Unknowing is a sublime expression of what separates God from humanity and is widely regarded as a hallmark of Western literature and spirituality. A work of simplicity, courage, and lucidity, it is a contemplative classic on the deep mysteries of faith.
"Lift up your heart to God with a humble impulse of love and have himself as your aim, not any of his goods ... Set yourself to rest in this darkness, always crying out after him whom you love. For if you are to experience him or to see him at all, insofar as it is possible here, it must always be in this cloud and in this darkness." –– The Cloud of Unknowing'
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Auyang, Sunny Y., How is Quantum Field Theory Possible?, Oxford University Press 1995 Jacket: 'Quantum field theory (QFT) combines quantum mechanics with Einstein's special theory of relativity and underlies elementary particle physics. This book presents a philosophical analysis of QFT. It is the first treatise in which the philosophies of space-time, quantum phenomena and particle interactions are encompassed in a unified framework.'
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Christie, Agatha, Elephants Can Remember, Bantam Books 1984 'A Classic example of the ingenious three-card trick she has been playing on us for so many years.' Sunday Express
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Crombie, A C, The History of Science from Augustine to Galileo, Dover Publications 1996 Amazon customer review: 'This is a very widely encompassing account of the evolution and development of science through history. The considerations of the sociopolitical and philosophical climates pertaining to the times gives the reader a basis of understanding why science progressed as it did. The account is very well organised and lucid, although it fails in some aspects to consider the contributions of the Far Eastern civilizations. It makes a very valuable contribution to help appreciate acutely the value of those who contributed to science's development.' A Customer
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Electronic Frontier Foundation,
, Cracking DES: Secrets of Encryption Research, Wiretap Policies and Chip Design, O'Reilly and Associates 1998 Jacket: 'Sometimes you have to do good engineering to straighten out twisted politics. The Electronic Frontier Foundation has done so by exploding the government-supported myth that the Data Encryption Standard (DES) has real security. National Security Agency and FBI officials say our civil liberties must be curtailed because the government can't crack the security of DES to wiretap bad guys. Bu somehow a tiny nonprofit has designed and built a $200 000 machine that can crack DES in a week. Who's lying and why? For the first time, the book reveals full technical details on how researchers and data recovery engineers can build a working DES Cracker.
Amazon
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Electronic Frontier Foundation,
, Cracking DES: Secrets of Encryption Research, Wiretap Policies and Chip Design, O'Reilly and Associates 1998 Jacket: 'Sometimes you have to do good engineering to straighten out twisted politics. The Electronic Frontier Foundaiton has done so by exploding the government-supported myth that the Data Encryption Stanbdard (DES) has real security. National Security Agency and FBI officials say our civil liberties must be curtailed because the government can't crack the security of DES to wiretap bad guys. Bu somehow a tiny nonprofit has designed and built a $200 000 machine that can crack DES in a week. Who's lying and why? For the first time, the book reveals full technical details on how researchers and data recovery engineers can build a working DES Cracker.
Amazon
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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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Hallett, Michael, Cantorian Set Theory and Limitation of Size, Oxford UP 1984 Jacket: 'This book will be of use to a wide audience, from beginning students of set theory (who can gain from it a sense of how the subject reached its present form), to mathematical set theorists (who will find an expert guide to the early literature), and for anyone concerned with the philosophy of mathematics (who will be interested by the extensive and perceptive discussion of the set concept).' Daniel Isaacson.
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Landecker, Hannah, Culturing Life: How Cells Became Technologies, Harvard University Press 2007 Amazon New Scientist : 'The discovery that it was possible to grow cells in a lab dish transformed them from being the immutable building blocks of individual bodies into plastic, malleable resources with a life of their own. In Culturing Life, anthropologist Hannah Landecker skillfully interweaves the scientific, historical, and cultural aspects of this transformation, and examines how cell culture challenges humanity's notions of individuality and immortality...An insightful and thought-provoking perspective on how technology has changed scientists' and society's understanding of life.'
--Claire Ainsworth
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Lo, Hoi-Kwong, and Tim Spiller, Sandra Popescu, Introduction to Quantum Computation and Information, World Scientific 1998 Jacket: 'This book provides a pedagogical introduction to the subjects of quantum information and computation. Topics include non-locality of quantum mechanics, quantum computation, quantum cryptography, quantum error correction, fault tolerant quantum computation, as well as some experimental aspects of quantum computation and quantum cryptography. A knowledge of basic quantum mechanics is assumed.'
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Lonergan, Bernard J F, and Robert M. Doran, Frederick E. Crowe (eds), Verbum : Word and Idea in Aquinas (Collected Works of Bernard Lonergan volume 2), University of Toronto Press 1997 Jacket: 'Verbum is a product of Lonergan's eleven years of study of the thought of Thomas Aquinas. The work is considered by many to be a breakthrough in the history of Lonergan's theology ... . Here he interprets aspects in the writing of Aquinas relevant to trinitarian theory and, as in most of Lonergan's work, one of the principal aims is to assist the reader in the search to understand the workings of the human mind.'
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Martin, Malachi, Vatican, Jove 1988 Editorial Reviews
'From Publishers Weekly
The subject of this long and intriguing novel is the Vatican's elaborate bureaucracy, in particular its powerful financial network, headed by a mysterious figure known as the Keeper. Another central character, who gives the story its slant, is American Richard Lansing, who joins the Vatican as a young monsignore in 1945, and becomes the confidant of five successive popes. When he reaches the apex of his career, he staunchly opposes any Church bargain with Mammon. Martin (author of bestsellers The Final Conclave and Hostage to the Devil), was a professor in the Vatican's Pontifical Biblical Institute: he has an insider's knowledge of the intrigues and power plays that go on behind the papacy's smooth facade. His tale encompasses the fall of Mussolini, the penetration of the Vatican by a Soviet mole, the murder of a pope in the Soviet interest (with help from Vatican officials), and other major events real or imagined. Vatican is not unlike a bureaucracy itself: intricate, far from iconoclastic, and impeded in its forward progress by obsessive attention to detail.'
Copyright 1985 Reed Business Information, Inc.
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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 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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Peskin, Michael E, and Dan V Schroeder, An Introduction to Quantum Field Theory, Westview Press 1995 Amazon Product Description
'This book is a clear and comprehensive introduction to quantum field theory, one that develops the subject systematically from its beginnings. The book builds on calculation techniques toward an explanation of the physics of renormalization.'
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Schrödinger, Erwin, and Roger Penrose (Foreword), What is Life?; With "Mind and Matter" and "Autobiographical Sketches", Cambridge University Press 2012 Book Description: 'Nobel laureate Erwin Schrödinger's What is Life? is one of the great science classics of the twentieth century. A distinguished physicist's exploration of the question which lies at the heart of biology, it was written for the layman, but proved one of the spurs to the birth of molecular biology and the subsequent discovery of the structure of DNA. The philosopher Karl Popper hailed it as a 'beautiful and important book' by 'a great man to whom I owe a personal debt for many exciting discussions'. It appears here together with Mind and Matter, his essay investigating a relationship which has eluded and puzzled philosophers since the earliest times. Schrodinger asks what place consciousness occupies in the evolution of life, and what part the state of development of the human mind plays in moral questions. Brought together with these two classics are Schrödinger's autobiographical sketches, published and translated here for the first time. They offer a fascinating fragmentary account of his life as a background to his scientific writings, making this volume a valuable additon to the shelves of scientist and layman alike.'
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Tomonaga, Sin-itiro, The Story of Spin, University of Chicago Press 1997 Jacket: 'The Story of Spin, as told by Sin-itiro Tomonaga and lovingly translated by Takeshi Oka, is a brilliant and witty account of the development of modern quantum theory, which takes electron spin as a pivotal concept. Reading these twelve lectures on the fundamental aspects of physics is a joyful experience that is rare indeed.' Laurie Brown, Northwestern University.
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Wigner, Eugene, Symmetries and Reflections: Scientific Essays , MIT Press 1970 Jacket: 'This volume contains some of Professor Wigner's more popular papers which, in their diversity of subject and clarity of style, reflect the author's deep analytical powers and the remarkable scope of his interests. Included are articles on the nature of physical symmetry, invariance and conservation principles, the structure of solid bodies and of the compound nucleus, the theory of nuclear fission, the effects of radiation on solids, and the epistemological problems of quantum mechanics. Other articles deal with the story of the first man-made nuclear chain reaction, the long term prospects of nuclear energy, the problems of Big Science, and the role of mathematics in the natural sciences. In addition, the book contains statements of Wigner's convictions and beliefs as well as memoirs of his friends Enrico Fermi and John von Neumann.
Eugene P. Wigner is one of the architects of the atomic age. He worked with Enrco Fermi at the Metallurgical Laboratory of the University of Chicago at the beginning of the Manhattan Project, and he has gone on to receive the highest honours that science and his country can bestow, including the Nobel Prize for physics, the Max Planck Medal, the Enrico Fermi Award and the Atoms for Peace Award. '.
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Papers
Chaitin, Gregory J, "Randomness and Mathematical Proof", Scientific American, 232, 5, May 1975, page 47-52. 'Although randomness can be precisely defined and can even be measured, a given number cannot be proved random. This enigma establishes a limit in what is possible in mathematics'. back |
Links
A priori and a posteriori - Wikipedia, A priori and a posteriori - Wikipedia, the free encyclopedia, 'The Latin phrases a priori (lit. "from the earlier") and a posteriori (lit. "from the latter") are philosophical terms of art popularized by Immanuel Kant's Critique of Pure Reason (first published in 1781, second edition in 1787), one of the most influential works in the history of philosophy. . . . The intuitive distinction between a priori and a posteriori knowledge (or justification) is best seen via examples, as below:
A priori
Consider the proposition, "If George V reigned at least four days, then he reigned more than three days." This is something that one knows a priori, because it expresses a statement that one can derive by reason alone.
A posteriori
Compare this with the proposition expressed by the sentence, "George V reigned from 1910 to 1936." This is something that (if true) one must come to know a posteriori, because it expresses an empirical fact unknowable by reason alone.' back |
Absolute infinite - Wikipedia, Absolute infinite - Wikipedia, the free encyclopedia, 'The Absolute Infinite is mathematician Georg Cantor's concept of an "infinity" that transcended the transfinite numbers. Cantor equated the Absolute Infinite with God. He held that the Absolute Infinite had various mathematical properties, including that every property of the Absolute Infinite is also held by some smaller objec' back |
Alexis Carrel - Wikipedia, Alexis Carrel - Wikipedia the free encyclopedia, 'Alexis Carrel (June 28, 1873 - November 5, 1944) was a French surgeon, biologist and eugenicist, who was awarded the Nobel Prize in Physiology or Medicine in 1912. He was also a member of Jacques Doriot's Parti Populaire Francais (PPF), the most collaborationist party during Vichy France.' back |
Aquinas 13, 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. . . . The second way is from the nature of the efficient cause. . . . The third way is taken from possibility and necessity . . . The fourth way is taken from the gradation to be found in things. . . . The fifth way is taken from the governance of the world. back |
Aquinas 13 (Latin), Summa: I 2 3: Whether God exists?, 'Respondeo dicendum quod Deum esse quinque viis probari potest. Prima autem et manifestior via est, quae sumitur ex parte motus. Certum est enim, et sensu constat, aliqua moveri in hoc mundo. Omne autem quod movetur, ab alio movetur. Nihil enim movetur, nisi secundum quod est in potentia ad illud ad quod movetur, movet autem aliquid secundum quod est actu. Movere enim nihil aliud est quam educere aliquid de potentia in actum, de potentia autem non potest aliquid reduci in actum, nisi per aliquod ens in actu, sicut calidum in actu, ut ignis, facit lignum, quod est calidum in potentia, esse actu calidum, et per hoc movet et alterat ipsum. Non autem est possibile ut idem sit simul in actu et potentia secundum idem, sed solum secundum diversa, quod enim est calidum in actu, non potest simul esse calidum in potentia, sed est simul frigidum in potentia. Impossibile est ergo quod, secundum idem et eodem modo, aliquid sit movens et motum, vel quod moveat seipsum. Omne ergo quod movetur, oportet ab alio moveri. Si ergo id a quo movetur, moveatur, oportet et ipsum ab alio moveri et illud ab alio. Hic autem non est procedere in infinitum, quia sic non esset aliquod primum movens; et per consequens nec aliquod aliud movens, quia moventia secunda non movent nisi per hoc quod sunt mota a primo movente, sicut baculus non movet nisi per hoc quod est motus a manu. Ergo necesse est devenire ad aliquod primum movens, quod a nullo movetur, et hoc omnes intelligunt Deum.' back |
Aquinas 39, Whether God is in all things, 'I answer that, God is in all things; not, indeed, as part of their essence, nor as an accident, but as an agent is present to that upon which it works. For an agent must be joined to that wherein it acts immediately and touch it by its power; hence it is proved in Phys. vii that the thing moved and the mover must be joined together. Now since God is very being by His own essence, created being must be His proper effect; as to ignite is the proper effect of fire. Now God causes this effect in things not only when they first begin to be, but as long as they are preserved in being; as light is caused in the air by the sun as long as the air remains illuminated. Therefore as long as a thing has being, God must be present to it, according to its mode of being. But being is innermost in each thing and most fundamentally inherent in all things since it is formal in respect of everything found in a thing, as was shown above (7, 1). Hence it must be that God is in all things, and innermostly.' back |
Aquinas 608, Does man's happiness consists in the vision of the divine essence?, 'Final and perfect happiness can consist in nothing else than the vision of the Divine Essence. To make this clear, two points must be observed. First, that man is not perfectly happy, so long as something remains for him to desire and seek: secondly, that the perfection of any power is determined by the nature of its object.' back |
Australian Government, Royal Commission into Institutional Responses to Child Sexual Abuse, 'WHEREAS all children deserve a safe and happy childhood.
AND Australia has undertaken international obligations to take all appropriate legislative, administrative, social and educational measures to protect children from sexual abuse and other forms of abuse, including measures for the prevention, identification, reporting, referral, investigation, treatment and follow up of incidents of child abuse. . . . IN WITNESS, We have caused these Our Letters to be made Patent.
WITNESS Quentin Bryce, Governor-General of the Commonwealth of Australia.
Dated 11th January 2013
Governor-General
By Her Excellency’s Command
Prime Minister back |
Calla Wahlquist, Evidence of 250 massacres of Indigenous Australian mapped, 'There have been as many as 500 massacres of Aboriginal and Torres Strait Islander peoples in Australia. And mass killings occurred well into the middle of the 20th century, researchers have said.
The disturbing revelations were released by the University of Newcastle on Friday as part of the second stage of its online massacre map, which now covers frontier violence that occurred from the arrival of the first fleet in 1788 to the colonisation of the Northern Territory, South Australia and remote Queensland up to 1930.
The map now details about 250 massacres that meet strict criteria of standards of proof, covering every state except Western Australia.
The estimated death toll from those incidents is about 6,200 Aboriginal and Torres Strait Islander peoples and fewer than 100 colonists, with an average of 25 Indigenous people killed in every massacre.' back |
Catherine Pepinster, Pope Francis has utterly failed to tackle church's abuse scandal, 'The election of Francis in 2013 prompted hopes of a much-needed change in culture. He soon created an advisory commission on the protection of minors, appointing lay people such as British psychiatrist Lady Sheila Hollins and also victims. But the commission has foundered and the victims have quit, frustrated at lack of progress.
The pope has been up against an intransigent church bureaucracy. Vatican officials have proved unwilling to cooperate with the commission; nor has it been furnished with enough resources. But above all, there has been cultural resistance within the church over abuse. The clerical caste is one shaped by obedience and a deep fear of sullying the reputation of the church.' back |
Colin Marshall, Hannah Arendt's Original Articles on "The Banality of Evil" in the New Yorker Archive, 'We've all heard the phrase "the banality of evil." Some of us even know which political theorist to attribute it to, and among those, a few have even read it in context. Hannah Arendt most memorably employed it in both the subtitle and closing words of Eichmann in Jerusalem: A Report on the Banality of Evil, her book on the trial of Nazi lieutenant-colonel Adolf Eichmann. To Arendt's mind, Eichmann willingly did his part to organize the Holocaust — and an instrumental part it was — out of neither anti-semitism nor pure malice, but out of a non-ideological, entirely more prosaic combination of careerism and obedience.' back |
Differentiable manifold - Wikipedia, Differentiable manifold - Wikipedia, the free encyclopedia, 'In mathematics, a differentiable manifold is a type of manifold that is locally similar enough to a linear space to allow one to do calculus. Any manifold can be described by a collection of charts, also known as an atlas. One may then apply ideas from calculus while working within the individual charts, since each chart lies within a linear space to which the usual rules of calculus apply. If the charts are suitably compatible (namely, the transition from one chart to another is differentiable), then computations done in one chart are valid in any other differentiable chart. back |
Digital philosophy - Wikipedia, Digital philosophy - Wikipedia, the free encyclopedia, 'Digital philosophy is a new direction in philosophy and cosmology advocated by certain mathematicians and theoretical physicists, e.g., Gregory Chaitin, Edward Fredkin, Stephen Wolfram, and Konrad Zuse (see his Calculating Space).
Digital philosophy grew out of an earlier digital physics (both terms are due to Fredkin), which proposes to ground much of physical theory in cellular automata. Specifically, digital physics works through the consequences of assuming that the universe is a gigantic Turing-complete cellular automaton.' back |
Elmo Benedetto, Review Article: Lie Group of Spacetime, 'Symmetry is one of the most fundamental properties of nature. The branch of mathematics dealing with symmetry is the group theory. Lie groups lie at the intersection of these two fundamental fields of mathematics: algebra and geometry. A Lie group is first of all a group, and secondly it is a differentiable manifold. A Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the differential structure.' back |
Emily Flittdr, decade After Crisis, 1 $600 Trillion Msrkey Temains Murky to Regulators, 'In the maze of subsidiaries that make up Goldman Sachs Group, two in London have nearly identical names: Goldman Sachs International and Goldman Sachs International Bank.
Both trade financial instruments known as derivatives with hedge funds, insurers, governments and other clients.
United States regulators, however, get detailed information only about the derivatives traded by Goldman Sachs International. Thanks to a loophole in laws enacted in response to the financial crisis, trades by Goldman Sachs International Bank don’t have to be reported.
A decade after a financial crisis fueled in part by a tangled web of derivatives, regulators still have an incomplete picture of who holds what in this $600 trillion market.' back |
Fixed point theorem - Wikipedia, Fixed point theorem - Wikipedia, the free encyclopedia, 'In mathematics, a fixed point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some conditions on F that can be stated in general terms. Results of this kind are amongst the most generally useful in mathematics.
The Banach fixed point theorem gives a general criterion guaranteeing that, if it is satisfied, the procedure of iterating a function yields a fixed point.
By contrast, the Brouwer fixed point theorem is a non-constructive result: it says that any continuous function from the closed unit ball in n-dimensional Euclidean space to itself must have a fixed point, but it doesn't describe how to find the fixed point (See also Sperner's lemma).' back |
George F. Will, Our socialist president, 'Concerning Johnson’s observation, the Hoover Institution’s John H. Cochrane, who blogs as the Grumpy Economist, says actually, it’s worse than that: “It’s a darker system, which leads to crony capitalism.” Cochrane is just slightly wrong: Protectionism, and the promiscuous and capricious government interventions that inevitably accompany it, is , always and everywhere, crony capitalism.' back |
Group (mathematics) - Wikipedia, Group (mathematics) - Wikipedia, the free encyclopedia, 'In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. To qualify as a group, the set and the operation must satisfy a few conditions called group axioms, namely closure, associativity, identity and invertibility. Many familiar mathematical structures such as number systems obey these axioms: for example, the integers endowed with the addition operation form a group. However, the abstract formalization of the group axioms, detached as it is from the concrete nature of any particular group and its operation, allows entities with highly diverse mathematical origins in abstract algebra and beyond to be handled in a flexible way, while retaining their essential structural aspects. The ubiquity of groups in numerous areas within and outside mathematics makes them a central organizing principle of contemporary mathematics.' back |
Hannah Arendt (film) - Wikipedia, Hannah Arendt (film) - Wikipedia, the free ecyclopedia, 'Hannah Arendt is a 2012 German-Luxembourgish-French biographical drama film directed by Margarethe von Trotta and starring Barbara Sukowa. The film centers in the life of German-Jewish philosopher and political theorist Hannah Arendt. . . .
German director von Trotta's film centers on Arendt's response to the 1961 trial of Nazi Adolf Eichmann, which she covered for The New Yorker. Her writing on the trial became controversial for its depiction of both Eichmann and the Jewish councils, and for its introduction of Arendt's now-famous concept of "the banality of evil".' back |
Hans-Thomas Janka, Collapsing stars, supernovae, and gamma ray bursts, 'When massive stars die, they don't just fade away. Their lives end in the most spectacular and most luminous explosions that we know. For weeks they can become nearly as bright as a whole galaxy. The stellar debris is expelled with velocities up to ten percent of the speed of light and an energy of motion that equals the radiation of the Sun during its whole life. In rare cases this amount of energy can even be released in an enormously intense flash of gamma radiation. Such a gamma-ray burst outshines all stars of the universe for a period of seconds to many minutes and can be accompanied by a stellar explosion ten or even fifty times more energetic than usual.' back |
John Braithwaite, The shaky case for prosecuting Witness K and his lawyer in the Timor-Lest spying scandal, 'The reason people are worried about the case is that it has the appearance of state revenge against Witness K, who complained through proper channels about the illegality of the bugging he was asked to do, but a decade on served the public interest by blowing the whistle.
Alexander Downer was foreign minister when our international intelligence services were moved away from their counter-terrorism work to focus on commercial espionage on behalf of oil magnates who later offered him a lucrative consultancy. Witness K went public after Downer started working for the consultancy.' back |
John L Bell, Continuity and Infinitesimals - Stanford Encyclopedia of Philosophy, 'The usual meaning of the word continuous is “unbroken” or “uninterrupted”: thus a continuous entity—a continuum—has no “gaps.” We commonly suppose that space and time are continuous, and certain philosophers have maintained that all natural processes occur continuously: witness, for example, Leibniz's famous apothegm natura non facit saltus—“nature makes no jump.” In mathematics the word is used in the same general sense, but has had to be furnished with increasingly precise definitions. So, for instance, in the later 18th century continuity of a function was taken to mean that infinitesimal changes in the value of the argument induced infinitesimal changes in the value of the function. With the abandonment of infinitesimals in the 19th century this definition came to be replaced by one employing the more precise concept of limit.' back |
Motorola 6809 - Wikipedia, Motorola 6809 - Wikipedia, the free encyclopdia, 'The Motorola 6809 is an 8-bit (with some 16-bit features) microprocessor CPU from Motorola, designed by Terry Ritter and Joel Boney and introduced 1978. It was a major advance over both its predecessor, the Motorola 6800, and the related MOS Technology 6502.' back |
NASA, Jupiter, Hubble Space Telescope best colour image of Jupiter's Little Red Spot back |
NIST, Fundamental Physical Constants from NIST, 'Founded in 1901, NIST is a non-regulatory federal agency within the U.S. Commerce Department's Technology Administration. NIST's mission is to promote U.S. innovation and industrial competitiveness by advancing measurement science, standards, and technology in ways that enhance economic security and improve our quality of life.' back |
PDG - U of California, Particle Data Group, 'The Particle Data Group is an international collaboration charged with summarizing Particle Physics, as well as related areas of Cosmology and Astrophysics. In 2006, the PDG consists of 166 authors from 100 institutions in 19 countries.
The summaries are published in even-numbered years as a now 1200-page book, the Review of Particle Physics, and as an abbreviated version (320 pages), the Particle Physics Booklet.' back |
Peter Weinberger, Revisiting Louis de Broglie's famous 1924 paper in the Philosophical Magazine, 'De Broglie's contribution in the Philosophical Magazine from 1924 is fascinating from many standpoints for its moderate use of mathematics the close connection
to Einstein's special theory of relativity, and of course for the proposal of matter waves. We revisit this mostly speculative publication, which contributed crucially to the birth of quantum mechanics.' back |
Propositional Calculus - Wikipedia, Propositional Caluclus - Wikipedia, the free encyclopedia, 'In logic and mathematics, a propositional calculus (or a sentential calculus) is a formal system in which formuae representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules allows certain formulae to be established as "theorems" of the formal system. . . . Many different formulations exist which are all more or less equivalent but differ in the details of (1) their language, that is, the particular collection of primitive symbols and operator symbols, (2) the set of axioms, or distinguished formulae, and (3) the set of inference rules.' back |
Ravit Hecht, Does Iran Really Want to Nuke Israel: Is Israel Stronger than Iran? A Top Security Expert Explains, 'Israel is closer than ever to war with Iran, warns former deputy national security adviser Eran Etzion – an exceptional voice among Israel’s security experts.' back |
Russell Goodman (Stanford Encyclopedia of Philosophy), William James, 'William James was an original thinker in and between the disciplines of physiology, psychology and philosophy. His twelve-hundred page masterwork, The Principles of Psychology (1890), is a rich blend of physiology, psychology, philosophy, and personal reflection that has given us such ideas as “the stream of thought” and the baby’s impression of the world “as one great blooming, buzzing confusion” (PP 462). It contains seeds of pragmatism and phenomenology, and influenced generations of thinkers in Europe and America, including Edmund Husserl, Bertrand Russell, John Dewey, and Ludwig Wittgenstein.' back |
Team America: World Police - Wikipedia, Team America: World Police - Wikipedia, the free encyclopedia, 'Team America: World Police is a 2004 American-German adult animated puppet satirical action comedy film produced by Scott Rudin, Matt Stone, and Trey Parker, written by Parker, Stone and Pam Brady and directed by Parker, all of whom are also known for the popular animated television series South Park. The film stars Parker, Stone, Kristen Miller, Masasa Moyo, Daran Norris, Phil Hendrie, Maurice LaMarche, Chelsea Marguerite, Jeremy Shada, and Fred Tatasciore, and is a satire of big-budget action films and their associated clichés and stereotypes, with particular humorous emphasis on the global implications of the politics of the United States.' back |
William James - Wikipedia, William James - Wikipedia, the free encyclopedia, 'William James (January 11, 1842 – August 26, 1910) was an American philosopher and psychologist, and the first educator to offer a psychology course in the United States. James was one of the leading thinkers of the late nineteenth century and is believed by many to be one of the most influential philosophers the United States has ever produced, while others have labeled him the "Father of American psychology".' back |
Yang-Mills theory - Wikipedia, Yang-Mills theory - Wikipedia, the free encyclopedia, 'Yang–Mills theory is a gauge theory based on the SU(N) group, or more generally any compact, reductive Lie algebra. Yang–Mills theory seeks to describe the behavior of elementary particles using these non-Abelian Lie groups and is at the core of the unification of the electromagnetic force and weak forces (i.e. U(1) × SU(2)) as well as quantum chromodynamics, the theory of the strong force (based on SU(3)). Thus it forms the basis of our understanding of the Standard Model of particle physics.' back |
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