Notes
Sunday 24 May 2020 - Saturday 30 May 2020
[Notebook: DB 84 Pam's Book]
[page 315]
Sunday 24 May 2020
I know the case I want to make: that much of modern physics is based on a platonic misunderstanding of representation resulting in mathematical fictions being given ontological roles in the explanation of the fundamental structure of the world and further fictions being used to correct the unnatural consequences of the initial fictions. The initial fiction relates to the role of virtual particles in field theory whose domain is considered to be a geometrical continuum measured by real numbers and the corrective fiction is the process of renormalization which is itself based on the renormalization group which is based on scale changes as the theory reaches down into the infinitesimal regime whose existence depends upon the real numbers. In both cases the theory overlooks the fact that reality is pixellated by the quantum of action and that the proof for the existence of real numbers is circular, being based on the epsilon-delta argument which itself depends on the assumption that ε and δ are real numbers. The question is is this critique true, and does my proposal to produce a logical model of the world based on the idea that every logical operation is measured by a quantum of action provide a way to correctly model the world? The first step in this direction is to suggest a network interpretation of the Hilbert space approach to quantum mechanics, the differentiable
[page 316]
manifold approach to relativity and the neural network approach to mind and cognition. Can I pull this off (A Fish Called Wanda). This project has theological consequences and I would dedicate it to my beloved mother who suffered much at the hands of the Roman Catholic Church. A Fish Called Wanda - Wikipedia
Implicit in this approach is the assumption that we cannot look inside the quantum of action [since we assume it is analogous to god or the initial singularity, the structureless starting point of everything] in the same way as we cannot look inside a logical argument to see how it actually works but we just have to take it on faith and assume that what does on in there is analogous to a computation as modelled by a Turing machine. In a way the ancient argument from continuity is an effort to overcome this hiatus, but it does not get us far on the ground that a continuum carries no information because it contains no marks to represent information.
James Brown James Brown - Wikipedia
SPACE = POTENTIAL
The special feature of the network proposal is the same as in my thesis, that every interaction involves an integral number of quanta of action without inquiring into what exactly is involved in that interaction. Jeffrey Nicholls: Prolegomenon to Scientific Theology
I am making a very minimal change demanding only that all quantum interactions involve an integral number of quanta of action, regardless of the content of that action.
[page 317]
A set is an act. The empty set is a continuum {——}, the next set is {not} and so on to the {ℵ0 = Turing machine} eg {Little Drummer Girl}. The Little Drummer Girl - Wikipedia
Monday 25 May 2020
von Neumann - Preface:
page vii: 'This new quantum mechanics has in recent years achieved in its essential parts what is presumably its definitive form, the so-called "transformation theory" (Dirac). Therefore the principal emphasis shall be placed on the general and fundamental questions which have arisen in connection with this theory. In particular the difficult problems of interpretation, many of which are not fully resolved, will be examined in detail. John von Neumann: Mathematical Foundations of Quantum Mechanics, Paul Dirac: The Principles of Quantum Mechanics (4th ed)
page viii: 'The method of Dirac, mentioned above . . . in no way satisfies the requirements of mathematical rigor — not even if these are reduced in a natural and proper fashion to the extent common in theoretical physics. For example, the method adheres to the fiction that every self-adjoint operator can be put in diagonal form. . . . In the case of those operators for which this is not actually the case, this requires the introduction of "improper" functions with self contradictory properties . . . It should be pointed out that the quantum mechanical "transformation theory" can be established in a manner which is just as clear and unified, but which is without mathematical objection. . . . . it requires a procedure differing from the very beginning, namely the reliance on the Hilbert theory of operators.'
[page 318]
At the root of the network model lies the assumption that such realisable operators can be implemented using finite means of computation, and in fact that quantum mechanics is in itself isomorphic to the well known [universal] Turing machine (I wish). Universal Turing Machine - Wikipedia
von Neumann page 6: "In order to obtain a preliminary view of the problem, let us set forth briefly the basic structure of the Heisenberg-Born-Jordan "matrix mechanics" and the Schrödinger "wave mechanics".'
A bit of perverse psychology: we are inclined to treat the people we are using (eg the slaves) [badly] because it points to our own inadequacy.
von Neumann page 21: 'The fundamental problem for the matrix theory is the solution of the eigenvalue equation Hψ = λψ.
page 22: All of vN's discussion is based on classical space and time using the traditional Hamiltonian as its foundation.
page 23: 'integral equations" Courant and Hilbert. Courant & Hilbert: Methods of Mathematical Physcis (2 volumes)
The use of real numbers in physics brings about an enormous simplification by compressing detailed physical considerations to simple algorithms like F = ma which owe their power to the symmetry of continuity, in effect a direct application of the foundation of Noether's theory. Dwight Neuenschwander: Emmy Noether's Wonderful Theorem
page 25: Dirac's δ, since somewhat accepted into mathematical society.
[page 319}
von Neumann page 28: The equivalence of the two theories arises because in both cases the set of solution |&psi|2 must sum to 1, whether we consider this value the integral of a continuous function or the sum of a discrete function. Here we depend upon normalization which later turns out to be a problem in quantum field theory.
page 31: Z and Ω are very different and to set up direct relationships between them must lead to great mathematical difficulties. On the other hand, FZ and FΩ are isomorphic . . . and since they . . . are the real analytical substrate of the matrix and wave theories, this isomorphism mean that the two theories must always yield the same numerical results.'
page 33: '. . . a unified theory, independent of the accidents of the formal framework selected at the time, and exhibiting only really essential elements of quantum mechanics will be achieved if we do this: Investigate the intrinsic properties (common to FZ and FΩ) of these two theoriers, and choose these properties as a starting point. The system FZ is generally known as Hilbert space.
'We wish then to describe the abstract Hilbert space and prove rigourously the following points:
1. abstract Hilbert space is characterized uniquely by the properties specified
2. the properties belong to both FZ and FΩ
The actual logical behaviour of a computer is invariant with respect to clock frequency which is analogous to energy whereas particle physics appears to be energy dependent largely due to relativistic effects. We might expect the computer network model to provide an underlying symmetry here which might only need to be tweaked to yield the changes arising from location of systems at different point on the energy scale [since as we go up the scale we reveal the deeper and deeper processes that contribute to the structure of the universe, like the processes associated with the strong force in baryons and mesons].
[page 319]
I am beginning to think of this project as the PhD work that did not get to do after my honours, so I can allow myself three years to complete it. The opening salvo, so to speak, is the current essay e30: Quantum field theory is impossible: an introduction to cognitive cosmology.
Ariana Grande Manchester Ariana Grande
A Hilbert space is a musical instrument for playing the music of the spheres going from note to note via unitary operators carrying us through time [although it cannot be always unitary because entropy is increasing (due to communication = "measurement"] ) Wojciech Hubert Zurek: Quantum origin of quantum jumps: breaking of unitary symmetry induced by information transfer and the transition from quantum to classical
Being emotional is very natural and in a way to easy because true freedom comes from going deeper and getting to the rational foundation of what is going on penetrating through the superficial layers to the deep meaning [??].
Tuesday 26 May 2020
von Neumann page 89: Quantum mechanics only linear operators. And only operators whose domains are everywhere dense. Operator (mathematics) - Wikipedia, Dense set - Wikipedia
Am I at my limit? Can I do any better? Can I try harder? On the whole I think not. I am with John Prine's dear Abby, I am what I am and I'm not what I'm not. I feel that I am doing the best I can. It might be said that I should get more help, but my experience is that it is not available. The established theologians and evangelists are established and not going to
[page 321]
change. The other side think that theology and religion are an anachronism. I feel that my position is valid. To build a history, to embrace the wisdom of the past and trace it to its source, the divine universe that made us. The main problem is the deeply ingrained gnostic belief that we and the universe are evil and we should put our hope in a total and fictitious apocalyptic remake of the system. An impossible fantasy, very common to revolutionaries who feel that a better system will miraculously emerge if we destroy what we already have [which might be why destroyers like President Trump are so closely tied to fundamentalist Christians].
The limiting factor, for me, would seem to be the flow of ideas and insights. I have a fair grasp of progress in this direction, and try to seek out the most creative ideas in the business, but there is a limit to my rate of discovery and documentation, and I feel that I am up against it, sparing no effort to make the next step.
How do we get from probability amplitudes to particles? Energy.
The amplitude representation, form embedded in energy (the post Aristotelian version of matter); nec quid, nec quale, nec quantum nec aliquid eorum quibus ens determinatur. But [energy is] the input into quantum mechanics via linear superposition.
Are virtual particle off the mass shell still associated with the quantum of action. And if not, can they be considered real? On shell and off shell - Wikipedia
How am I to prove quantum field theory impossible? Because it does not represent anything because it is just formal mathematics? Because it involved contradictions and so it is not even formal mathematics? Because it contradicts physical reality? How do we introduce representation into applied mathematics? And what is the value of messing with physics
[page 322]
from a theological and political point of view? It will not have much of an effect if it is not as new and exciting as special relativity, and how can that be? By making the material universe intelligent, as it has already done itself by evolving into our alleged intelligent minds.
Everything is made of energy which is made of action, the heart of our divinely dynamic universe. Action is both eternal and dynamic insofar as it has no specific properties at all, like Pseudo-Dionysius' god, but it is something, a being trivially identical with its essence insofar as its essence is to be. We cannot really improve at all on all this old mythological / mystical / theological / Zen / etc etc stuff. Aquinas, Summa, I, 3, 4: Are essence and existence the same in God?
Music is represented by waves in the air, ripples in the vinyl, digits on a disk. The world is represented by waves in energy, explained by quantum mechanics. Relativity has two inputs here. First, once space comes into existence the limited velocity of light has an effect on phase, and the relation between mass and energy gives us particles, fixed point in energy space [whose interactions eg in atoms, give us fixed point in spectral (photon) space].
My guess is that most of the problems in quantum field theory will be solved when we understand how quantum mechanics creates space-time. Given time we will capture the music of the universe in the physics, god singing to us. Wild flowers don't care were they grow. The quantum representation of space. This idea seems to be the solution to al these problems. Just have to put it together. An exciting idea, but I have been prone to dream about exciting impossibilities before, but cannot think
[page 323]
of much more impossible that the current concept of an electron, a particle with zero size but a large amount of mass-energy and charge. As I see my theology being a serious improvement on Catholic mythology I might see my physics as a radical improvement on the modern set of impossible dreams about how the world began from a geometric point containing possibly infinite energy. Parton, Ronstadt & Harris: Wildflowers
Wednesday 27 May 2020
The creative view, from a quantum mechanical point of view is observation or measurement which is seen to break the unitarity of quantum evolution, but we might just as well see it as the spread of possibilities represented by the wave function which is normalized to one by the unitarity of the time evolution operator U being collapsed into one possibility with a probability 1, which is equivalent to it actually happening, and from the |ψ|2 point of view, which is the observational p0int of view, there has been no breach of unitarity. See Zurek, who in effect explains this on the grounds that the limited bandwidth of the communication associated with measurement forces the choice [selection] of one signal out of the infinity of possibilities. The situation here seems to parallel von Neumann's unification of Heisenberg and Schroödinger on the ground that they both yield the same numerical result. Some might think that s measurement requires the presence of a physicist, but the reality is that particles are always observing one another and in the process, if there is to be real communication, sharing an eigenfunction that is one code (language, [basis] ).
This little bit of progress relaxes me enough to listen to the flowers.
[page 324]
Von Neumann page 73: 'We now desire to go further into the geometric analysis of Hilbert space, and to investigate in detail the closed linear manifolds which play in the M∞ a role analogous to that played by straight lines, planes etc in the Rn (ie the Mm, m ≤ n).
As von Neumann points out, Hilbert space is closely analogous to infinite dimensional Euclidean space. There are a few interesting features because the domain is the field of complex numbers, but both the domain and the functions (operators) on it mapping it onto itself are continuous and the only disjoint feature, as in Euclidean space, is the orthogonality of the dimensions, but the metric, via the inner product goes toward erasing this discreteness by effectively superposing all the dimensions in a linear way so that we can define unitary transformations that rotate the basis states into one another while preserving the abstract structure of the space and the probabilities that one derives from it. My question then, is how is the quantization of quantum dynamics reflected in the structure of the space, or how can it be reflected. I hope I can find the answer in vN's book.
Thursday 28 May 2020
Here we get to the crux of the matter. Hilbert space is a formal mathematical structure, something very close to a platonic form whose basic claim to existence is that it is a logically consistent structure which obeys the classical notions of continuity developed in the nineteenth century from the need to put differential and integral calculus on a firm footing and to respect our natural feeling for the continuity of motion. Unfortunately it may be
[page 325]
that the quantization of nature reveals all this work to be a delusional dream when it comes to representing the world in mathematics. It seems to me that this delusion lies at the heart of the difficulties that plague quantum field theory, particularly its relationship to gravitation and the vast differences between the observed and computed values of the cosmological constant which cast a shadow of doubt over the whole physical enterprise. On the whole technology leads science, so we built nuclear weapons long before we had the nuclear understanding yielded by quantum chromodynamics. At a less esoteric level we use quantum mechanics for almost all our chemistry, electronics and molecular biology, but we still do not have a clear understanding of how the mathematics of quantum theory applies to reality. Cosmological constant problem - Wikipedia, Quantum chromodynamics - Wikipedia, Measurement problem - Wikipedia
We begin with 0 dimensional Hilbert space which represents the initial singularity of pure act, |ψ| = 1, |ψ| 2 = 1, probability = 1, exists and therefore eternal. The we imagine the tensor product of this space with itself to give us 1D Hilbert space, equivalent to a line in Euclidean space, maybe practically indistinguishable from 0 dimension. Not sure of there is any meaning here. Fun starts at 2D, two basis states |0> and |1> whose superposition gives us energy states [the vectors] a|0> + b|1>, a2 + b2 = 1 acting as a harmonic oscillator between a = 0 b = 1 and a = 1 b = 0, the origin of energy.
So we may understand the complexification of the universe in terms of increasing the dimension of its Hilbert space. We want to introduce bosons and fermions by mapping this idea onto the transfinite computer network [which is big enough to represent a complete Hilbert space]. Complete metric space - Wikipedia
[page 325]
Friday 29 May 2020
von Neumann page 87: 'An operator R is a function defined in a subset of ℜ with values from ℜ, ie a relation which establishes a correspondence between certain elements of ℜ and elements Rf of ℜ. Only linear [operators considered in this book], page 89.
page 96: Hermitian operator is its own adjoint, A = A*.
Unitary if UU* = U*U = 1, ie U* = U-1.
page 97: (Uf, Ug) = (f, g)
page 98: A hermitian, arbitrary X, XAX* is hermitian.
page 99: 'The continuity of operators, just as in the case of numerical functions, is of basic importance.'
Momentum works a bit like the uncertainty principle enabling us to do things which would otherwise be impossible like driving in a nail. It is a form of capital. So just now I had only one hand free because I was sholding a tin of cat food in the other so I flicked the lid of the wheelie bin up and while it was in the air threw the lid of the tin in before the lid of the bin came down. Such a long sentence here to describe a very simple action [which involved, in fact, trillions of trillions of quanta of action].
page 102: Eigenvalue problem: 'We have now come far enough that we can consider in the abstract Hilbert space that problem which was of central importance in quantum mechanics, in its relationship to the special cases FZ and FΩ: the solution of . . . the eigenvalue
[page 327]
problem E: HΦ = λΦ.
Saturday 30 May 2020
The Hilbert space corresponding to a geometric line has transfinite dimensions each corresponding to a point in the line. We see the line expanded into a universe [rather like the series of transfinite numbers, where adding 1 to ℵn is equivalent to creating the set of all permutations of ℵn to give ℵn+1]. Each point in this scheme is orthogonal to all the others [reflecting the "fact" that the points are independent] and we can imagine that [physically] mapping one point to another takes a quantum of action, but this does seem a bit weird converting one Euclidean dimension into transfinite Hilbert dimensions [although it may reflect the real underlying complexity of the universe]. Maybe by the time I understand this my copy of von Neumann will be thoroughly dog eared,
von Neumann page 219 (2018 edition page 136) '. . . we admit as a fact tht the natural laws which govern the elementary processes (ie the laws of quantum mechanics) are of a statistical nature.' John von Neumann: The Mathematical Foundations of Quantum Mechanics
page 136: 'This concept of quantum mechanics, which accepts its statistical expression as the actual form of the laws of nature and which abandons the principle of causality [while accepting the principle of symmetry, as in dice] is the so called statistical interpretation. It is due to M. Born, and is the only consistently enforceable interpretation of quantum mechanics today — ie the sum of our experiences relative to the elementary processes. It is this interpretation to which we shall conform in the following (until we can proceed to a detailed and fundamental discussion of this situation). ' Born rule - Wikipedia
This has an informational basis which I explain in my essay on invincible ignorance. The meaning of a message is a structure which is invisible in the message itself [see Feynman on addition of amplitudes and possibilities, page 74] Jeffrey Nicholls: Is the whole truth inacessible? A case for invincible ignorance, Richard Feynman; Feynman's Thesis: A New Approach to Quantum Mechanics
[page 328]
von Neumann page 212 (1955 ed): Compton experiment: x-ray photons and electrons collide elastically. Outcome cannot be predicted in advance but measurement reveals that it is causal.
page 223: Each step between the elements of a pure discrete spectrum correspond to a quantum of action and although mathematically, through the fiction of continuity, we can allow for continuous spectra, these may not actually exist in reality but arise from the imperfections of measurement. Here we get to the root of the quantum mechanical problem, the allegedly logically demonstrative proof of continuity via the circular ε, δ argument.
page 398: 'Although our entropy expression, as we saw, is completely analogous to the classical entropy, it is still surprising that it is invariant in the normal evolution in time of the system (process 2, [unitary, page 351]) and only increases with measurements (process 1) — in the classical theory (where the measurement in general played no role) it increased as a rule even with the ordinary mechanical evolution in time of the system. It is therefore necessary to clear up this apparently paradoxical situation.'
This 'paradox' indicates that measurement (ie communication) is in effect the act of creation that increases entropy, as I have thought in the past.
page 417: The Measurement Process
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Further readingBooks
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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Clark, Ronald, The Life of Bertrand Russell, Bloomsbury Reader 1973, 2012 Preface: '. . . Russell's letters to Lucy Donelly. to Lady Contance Malleson and above all the Lady Ottoline Morrell wikk, when pubkished in full, reveal the deep emotionak complexities of a man to whm no venture was too dangerous, no exploration too unlikely. It will eventually be possible to describe in greater some aspects of Russell's later life although it now seems conclusive — at least to the oreset writer — that these details will not materially alter the picture it is possible to draw today.' (1974)
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Courant, Richard, and David Hilbert, Methods of Mathematical Physcis (Volume 1), John Wiley and Sons 1989 Publisher: 'This classic work is now available in an inexpensive unabridged paperback edition. Since the first volume of this work came out in Germany in 1924, this book has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volumes represent Richard Courant's second and final revision of 1953.'
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Dirac, P A M, The Principles of Quantum Mechanics (4th ed), Oxford UP/Clarendon 1983 Jacket: '[this] is the standard work in the fundamental principles of quantum mechanics, indispensible both to the advanced student and the mature research worker, who will always find it a fresh source of knowledge and stimulation.' (Nature)
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Exodus, and Alexander Jones (editor), in The Jerusalem Bible, Darton Longman and Todd 1966 Introduction to the Pentateuch: 'Exodus is occupied with two primary themes: The Deliverance from Egypt ... and the Sinaitic Covenant. A secondry theme, the journey through the wilderness, connects the two. Moses leads the liberated Israelites to Sinai where God's incommunicable name, 'Yahweh', had been revealed to him. Against the background of a majestic theophany, God concludes an alliance with the people and proclaims his laws. ...'
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Feynman, Richard, QED: The Strange Story of Light and Matter, Princeton UP 1988 Jacket: 'Quantum electrodynamics - or QED for short - is the 'strange theory' that explains how light and electrons interact. Thanks to Richard Feynmann and his colleagues, it is also one of the rare parts of physics that is known for sure, a theory that has stood the test of time. . . . In this beautifully lucid set of lectures he provides a definitive introduction to QED.'
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Feynman, Richard Phillips, Feynman's Thesis: A New Approach to Quantum Mechanics, World Scientific Publishing Company 2005 Amazon editorial review: 'Editorial Reviews
Review
'The young Feynman revealed here was full of invention, verve, and ambition. His new approach to quantum mechanics, after simmering for decades beneath the surface of theoretical physics, burst into new prominence in the 1970s. Now its influence is pervasive, and still expanding. Feynman's original presentation is not only uniquely clear, but also contains insights and perspectives that are not widely known, and might well provide ammunition for another explosion or two.' Frank Wilczek
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Hobson, M P, and G. P. Efstathiou, A. N. Lasenby, General Relativity: An Introduction for Physicists, Cambridge University Press 2006 Amazon Editorial Reviews
Book Description
'After reviewing the basic concept of general relativity, this introduction discusses its mathematical background, including the necessary tools of tensor calculus and differential geometry. These tools are used to develop the topic of special relativity and to discuss electromagnetism in Minkowski spacetime. Gravitation as spacetime curvature is introduced and the field equations of general relativity derived. After applying the theory to a wide range of physical situations, the book concludes with a brief discussion of classical field theory and the derivation of general relativity from a variational principle.'
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John, and Alexander Jones (editor), in The Jerusalem Bible, Darton Longman and Todd 1966 Introduction to Saint John: '[This] gospel has a complex literary form: it is akin to the earliest Christian preaching, and yet at the same time it gives the final results of a quest ... for a deeper and more rewarding apprehension of the mystery of Jesus. Each of the evangelists has his own approach to Christ's person and mission. For St John, he is the Word made flesh, come to give life to men, 1:14,and this, the mystery of the Incarnation, dominates the whole of John's thought.' p 140.
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Kung, Hans, The Church, Search Press 1971 Preface to the English Edition: 'Though there is much talk nowadays about the Church in the secular world, there is not a corresponding awareness of what the Church is. One can only know what the Church should be if one also knows what the Church was originally. This means knowing what the Church of today wshould be in the light of the Gospel. It is the purpose of this book to answer that question.'
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Neuenschwander, Dwight E, Emmy Noether's Wonderful Theorem, Johns Hopkins University Press 2011 Jacket: A beautiful piece of mathematics, Noether's therem touches on every aspect of physics. Emmy Noether proved her theorem in 1915 and published it in 1918. This profound concept demonstrates the connection between conservation laws and symmetries. For instance, the theorem shows that a system invariant under translations of time, space or rotation will obey the laws of conservation of energy, linear momentum or angular momentum respectively. This exciting result offers a rich unifying principle for all of physics.'
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Russell, Betrand, Mysticism and Logic, Including A Free Man's Worship, Routledge 1986 'This collection of essays is concerned with different ways of knowing; the particular problems of philosophy; and the ultimate nature of matter. They reveal Russell's lifelong preoccupation: the disentanglement with ever-increasing precision of what is subjective or intellectually cloudy from what is objective or capable of logical demonstration. In them we can see the Russell method in operation: intellectual analysis dissecting a problem to its bare bones. Also included is Bertrand Russel's celebrated essay "A Free Man's Worship". In it he maintains that a new and deeper faith can be constructed, not faith in a theological sense but faith in the power of reason; his faith in man's capacity to create his own world through his own effort.'
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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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Links
A Fish Called Wanda - Wikipedia, A Fish Called Wanda - Wikipedia, the free enycylopedia, ' A Fish Called Wanda is a 1988 heist comedy film directed by Charles Crichton and written by John Cleese. It stars Jamie Lee Curtis, Kevin Kline and Michael Palin as a gang of diamond thieves who double-cross one another to find stolen diamonds hidden by the gang leader. A barrister (Cleese) becomes a central figure as femme fatale Wanda (Curtis) uses him to locate the loot. It was Crichton's last film. ' back |
Aquinas, Summa, I, 3, 4, Are essence and existence the same in God?, 'I answer that, God is not only His own essence, as shown in the preceding article, but also His own existence. This may be shown in several ways.
First, whatever a thing has besides its essence must be caused either by the constituent principles of that essence (like a property that necessarily accompanies the species--as the faculty of laughing is proper to a man--and is caused by the constituent principles of the species), or by some exterior agent--as heat is caused in water by fire. Therefore, if the existence of a thing differs from its essence, this existence must be caused either by some exterior agent or by its essential principles. Now it is impossible for a thing's existence to be caused by its essential constituent principles, for nothing can be the sufficient cause of its own existence, if its existence is caused. Therefore that thing, whose existence differs from its essence, must have its existence caused by another. But this cannot be true of God; because we call God the first efficient cause. Therefore it is impossible that in God His existence should differ from His essence.' back |
Aquinas, Summa, I, 3, 4, Are essence and existence the same in God?, ' I answer that, God is not only His own essence, as shown in the preceding article, but also His own existence. This may be shown in several ways.
First, whatever a thing has besides its essence must be caused either by the constituent principles of that essence (like a property that necessarily accompanies the species — as the faculty of laughing is proper to a man — and is caused by the constituent principles of the species), or by some exterior agent — as heat is caused in water by fire. Therefore, if the existence of a thing differs from its essence, this existence must be caused either by some exterior agent or by its essential principles. Now it is impossible for a thing's existence to be caused by its essential constituent principles, for nothing can be the sufficient cause of its own existence, if its existence is caused. Therefore that thing, whose existence differs from its essence, must have its existence caused by another. But this cannot be true of God; because we call God the first efficient cause. Therefore it is impossible that in God His existence should differ from His essence.' . . . back |
Ariana Grande, One Love Manchester (June 4th 2017), '
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back |
Born rule - Wikipedia, Born rule - Wikipedia, the free encyclopedia, 'The Born rule (also called the Born law, Born's rule, or Born's law) is a law of quantum mechanics which gives the probability that a measurement on a quantum system will yield a given result. It is named after its originator, the physicist Max Born. The Born rule is one of the key principles of the Copenhagen interpretation of quantum mechanics. There have been many attempts to derive the Born rule from the other assumptions of quantum mechanics, with inconclusive results. . . . The Born rule states that if an observable corresponding to a Hermitian operator A with discrete spectrum is measured in a system with normalized wave function (see bra-ket notation), then
the measured result will be one of the eigenvalues λ of A, and
the probability of measuring a given eigenvalue λi will equal <ψ|Pi|ψ> where Pi is the projection onto the eigenspace of A corresponding to λi'. back |
Calla Wahlquist, Rio Tinto blasts 46,000-year-old Aboriginal site to expand iron ore mine, ' A sacred site in Western Australia that showed 46,000 years of continual occupation and provided a 4,000-year-old genetic link to present-day traditional owners has been destroyed in the expansion of an iron ore mine.
The cave in Juukan Gorge in the Hammersley Ranges, about 60km from Mt Tom Price, is one of the oldest in the western Pilbara region and the only inland site in Australia to show signs of continual human occupation through the last ice age. It was blasted along with another sacred site on Sunday.' back |
Calla Wahlquist, Juukan Gorge: Rio Tinto blasting of Aboriginal site prompts calls to change antiquated laws, ' A 46,000-year-old Aboriginal heritage site destroyed by Rio Tinto this month is one of more than 463 sites that mining companies operating in Western Australia have applied for permission to destroy or disturb since 2010.
None of those applications have been refused. And under the state’s 48-year-old Aboriginal heritage laws, only the land or lease holder has the right to appeal – traditional owners do not.
The figures show that the shocking destruction of the sites in the Juukan Gorge in the western Pilbara was not unique.
The conflict between mining companies and Aboriginal heritage, particularly in mineral-rich areas such as the iron ore-rich Hamersley range of the Pilbara, has spawned a system of suffocating bureaucracy and lopsided agreement-making that privileges development over protecting sacred spaces and leaves traditional owners with no legislative power, and very little institutional power, to fight back. back |
Charlie Warzel, What Would Happen if Twitter Banned Trump?, ' Every few months the same debate re-emerges: Should Twitter ban Donald Trump? Usually, it’s because of something particularly egregious, conspiratorial, untrue or geopolitically reckless that the president tweeted. Many of these tweets would result in a takedown or a temporary suspension if they came from a normal user’s account, but Twitter has made an exception for heads of state, citing a “newsworthiness” clause that allows the company to evade responsibility.' back |
Clive Irving, From Vietnam to COVID-19, the Arrogance f Ignorance Keeps killing Americans, ' Of course, blind support of a catastrophic war did not stop with Vietnam. But it is that conflict which, in its numerous escalations and miscalculations, best reveals the persistent flaw in American political leadership—in both parties—that curses us to this day: the multiplication of error, the doubling down on mistakes.
In Robert Asprey’s masterful 1975 analysis of guerrilla wars, War in the Shadows, he called this the "arrogance of ignorance compounded by arrogance of power.” And what we have learned this year is that the arrogance of ignorance can be every bit as dangerous in a "war" against a pandemic as it was in wars against guerrillas.' back |
Complete metric space - Wikipedia, Complete metric space - Wikipedia, the free encyclopedia, ' In mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M or, alternatively, if every Cauchy sequence in M converges in M.
Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary). For instance, the set of rational numbers is not complete, because e.g. √2 is "missing" from it, even though one can construct a Cauchy sequence of rational numbers that converges to it (see further examples below). It is always possible to "fill all the holes", leading to the completion of a given space, . . . ' back |
Cosmological constant problem - Wikipedia, Cosmological constant problem - Wikipedia, the free encyclopedia, 'In cosmology, the cosmological constant problem or vacuum catastrophe is the disagreement between measured values of the vacuum energy density (the small value of the cosmological constant) and the zero-point energy suggested by quantum field theory.
Depending on the assumptions[which?], the discrepancy ranges from 40 to more than 100 orders of magnitude, a state of affairs described by Hobson et al. (2006) as "the worst theoretical prediction in the history of physics." ' back |
Dense set - Wikipedia, Dense set - Wikipedia, the free encyclopediaa, 'In topology and related areas of mathematics, a subset A of a topological space X is called dense (in X) if every point x in X either belongs to A or is a limit point of A; that is, the closure of A is constituting the whole set X.[1] Informally, for every point in X, the point is either in A or arbitrarily "close" to a member of A — for instance, the rational numbers are a dense subset of the real numbers because every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine approximation). ' back |
Dolly Parton, Linda Ronstadt & Emmylou Harris, Wildflowers,
' The hills were alive with wildflowers and I
Was as wild, even wilder than they
For at least I could run
They just died in the sun
And I refused to just wither in place
Just a wild mountain rose
Needing freedom to grow
So I ran fearing not where I'd go
When a flower grows wild
It can always survive
Wildflowers don't care where they grow
And the flowers I knew
In the fields where I grew
Were content to be lost in the crowd
They were growing too close
I had no room for growth
I wanted so much to get out
So I uprooted myself from my home ground and left
Took my dreams and I took to the road
When a flower grows wild
It can always survive
Wildflowers don't care where they grow
I grew up fast and wild
And I never felt right
In a garden so different from me
I just never belonged
I just longed to be gone
So the garden one day set me free
Hitched a ride with the wind
And since he was my friend
I just let him decide where we'd go
When a flower grows wild
It can always survive
Wildflowers don't care where they grow
Just a wild rambling rose seeking mysteries untold
No regret for the path that I chose
When a flower grows wild
It can always survive
Wildflowers don't care where they grow
Wildflowers don't care where they grow
back |
Dorothy Parker, 'If you want to know . . . ', Misattributed: 'If you want to know what the Lord God thinks of money, just look at those to whom he gives it.
Man and the Gospel (1865) by Thomas Guthrie "and you may know how little God thinks of money by observing on what bad and contemptible characters he often bestows it."
“We may see the small Value God has for Riches, by the People he gives them to.” -- Alexander Pope (1727).'
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Exodus, Exodus, King James Version, Exodus 3:7 'And the LORD said, I have surely seen the affliction of my people which are in Egypt, and have heard their cry by reason of their taskmasters; for I know their sorrows;
And I am come down to deliver them out of the hand of the Egyptians, and to bring them up out of that land unto a good land and a large, unto a land flowing with milk and honey; unto the place of the Canaanites, and the Hittites, and the Amorites, and the Perizzites, and the Hivites, and the Jebusites.' back |
Integral equation - Wikipedia, Integral equation - Wikipedia, the free encyclopedia, ' In mathematics, integral equations are equations in which an unknown function appears under an integral sign.
There is a close connection between differential and integral equations, and some problems may be formulated either way. See, for example, Green's function, Fredholm theory, and Maxwell's equations.' back |
James Brown, Please Please Please, '
willcat
2 years ago
This is JAMES BROWN & THE FAMOUS FLAMES (Bobby Byrd, Bobby Bennett, and Lloyd Stallworth)...not just 'James Brown"
Too many people today try to play the role of "History Revisionist" by giving JAMES BROWN sole credit...as if he were always a "solo artist", (which he WASN'T) instead of crediting THE ENTIRE GROUP. Without BOBBY BYRD & the FAMOUS FLAMES, there would BE no 'James Brown. He would have never gotten out of prison in the FIRST PLACE. It was BOBBY that first recognized Brown's talent , and persuaded his parents to sponsor Brown's release...and it was BOBBY that CHANGED his focus AWAY from crime to MUSIC...AND RECRUITED him for his singing group, THE FAMOUS FLAMES . Today, THE FAMOUS FLAMES are in THE ROCK AND ROLL HALL of FAME.
It's HIGH-TIME that people STOPPED IGNORING THE FLAMES...and STARTED GIVING THEM THEIR PROPS !!! back |
James Brown - Wikipedia, James Brown - Wikipedia, the free encyclopedia, ' James Joseph Brown (May 3, 1933 – December 25, 2006) was an American singer, songwriter, dancer, musician, record producer and bandleader. A progenitor of funk music and a major figure of 20th century music and dance, he is often referred to as the "Godfather of Soul" and "Soul Brother No. 1". In a career that lasted over 50 years, he influenced the development of several music genres.' back |
Jeffrey Frankel, Is China overtaking the US as a financial and ecoomic power?, ' For now, China has far less clout than the US at the IMF. But under President Donald Trump, the US is surrendering its influence in multilateral organisations such as the World Trade Organization, Nato, and the World Health Organization (even in the midst of a pandemic). It should surprise no one that China is filling the vacuum.
The US does not lack the economic or financial power to sustain its 75-year leadership of the international order. But under Trump, it has forgotten why that leadership position is important, and is flushing its power – and its reputation – down the drain.' back |
Jeffrey Nicholls, Prolegomenon to Scientific Theology, ' This thesis is an attempt to carry speculative theology beyond the apogee it reached in the medieval work of Thomas Aquinas into the world of empirical science (Aquinas 2019). Since the time of Aquinas, our understanding of the Universe has increased enormously. The ancient theologians not only conceived a perfect
God, but they also saw the world as a very imperfect place. Their reaction was to place God outside the world.
I will argue that we live in a Universe which approaches infinity in size and complexity, is as perfect as can be, and fulfils all the roles traditionally attributed to God, creator, lawmaker and judge.' back |
Jeffrey Nicholls, Is the whole truth inacessible? A case for invincible ignorance, ' I argue in this essay that there is a logical limit to our knowledge of the world which is implicit in the scientific method of hypothesis and testing. We make hypotheses about what is happening in regions where we cannot see, and test them by exploring their consequences to see if they correctly predict phenomena that we can see. A successful test does not necessarily guarantee a correct hypothesis but a failed test tells us that the hypothesis must be revised.' back |
John von Neumann, The Mathematical Foundations of Quantum Mechanics, ' MATHEMATICAL FOUNDATIONS OF QUANTUM MECHANICS by John von Neumann NEW EDITION translated from the German by ROBERT T. BEYER edited by Nicholas A. Wheeler
PRINCETON UNIVERSITY PRESS PRINCETON & OXFORD
This content downloaded from 129.127.145.240 on Sat, 30 May 2020 22:38:31 UTC
All use subject to https://about.jstor.org/terms
Copyrightc © 1955, 1983, 2018 by Princeton University Press Published by Princeton University Press, 41 William Street,Princeton, New Jersey 08540 All Rights Reserved ISBN: 978-0-691-17856-1 ISBN (pbk.) 978-0-691-17857-8 Library of Congress Control Number: 2017949631 ' back |
K J Cronin, Exodus 3:14 - An Explanation of its Meaning, 'A website devoted to the interpretation of Exodus 3:14: The published content of this website is based upon a paper written on the subject of the divine name in Exodus 3:14, and specifically on the subject of its meaning. Although written to a high standard of scholarship, it has not been written with only scholars in mind. Its subject-matter is relevant to all who are engaged in serious theological exploration, and I believe that what follows will be of interest to all dedicated religious thinkers, irrespective of their religious affiliation or educational background.' back |
Matthew 26:40-43, The spirit is willing but the flesh is weak, '40 Then he returned to his disciples and found them sleeping. “Couldn’t you men keep watch with me for one hour?” he asked Peter. 41 “Watch and pray so that you will not fall into temptation. The spirit is willing, but the flesh is weak.”
42 He went away a second time and prayed, “My Father, if it is not possible for this cup to be taken away unless I drink it, may your will be done.”
43 When he came back, he again found them sleeping, because their eyes were heavy.' back |
Max Born, The statistical interpretation of quantum mechanics, Nobel Lecture, December 11, 1954 back |
Measurement problem - Wikipedia, Measurement problem - Wikipedia, the free encyclopedia, 'The measurement problem in quantum mechanics is the problem of how (or whether) wave function collapse occurs. The inability to observe this process directly has given rise to different interpretations of quantum mechanics, and poses a key set of questions that each interpretation must answer. The wave function in quantum mechanics evolves deterministically according to the Schrödinger equation as a linear superposition of different states, but actual measurements always find the physical system in a definite state. Any future evolution is based on the state the system was discovered to be in when the measurement was made, meaning that the measurement "did something" to the system that is not obviously a consequence of Schrödinger evolution.' back |
New York TimesEditorial Board, Why Does thr U.S. Military Celebrate White Supremacy?, ' By the time the federal government sought out military training facilities in the South in preparation for war abroad, the school of mythology known as the Lost Cause movement — forged by groups like The United Daughters of the Confederacy — had rewritten Civil War history. This telling valorized the Ku Klux Klan; cast even the most execrable Confederate officers as saints; and portrayed slavery as an idyll featuring loving masters who doted on happy black retainers. . . .
Adolf Hitler himself took notice, praising the United States as the near epitome of the racist state. The Nazi movement normalized its agenda in Germany by pointing out that “racist policies and practices” had been successfully applied in the Southern United States.' back |
On shell and off shell - Wikipedia, On shell and off shell - Wikipedia, the free encyclopedia, ' In physics, particularly in quantum field theory, configurations of a physical system that satisfy classical equations of motion are called on shell, and those that do not are called off shell.
In quantum field theory, virtual particles are termed off shell because they do not satisfy the energy–momentum relation; real exchange particles do satisfy this relation and are termed on shell (mass shell). In classical mechanics for instance, in the action formulation, extremal solutions to the variational principle are on shell and the Euler–Lagrange equations give the on-shell equations. Noether's theorem regarding differentiable symmetries of physical action and conservation laws is another on-shell theorem.' back |
Operator (mathematics) - Wikipedia, Operator (mathematics) - Wikipedia, the free encyclopedia, ' In mathematics, an operator is generally a mapping or function that acts on elements of a space to produce elements of another space (possibly the same space, sometimes required to be the same space). There is no general definition of an operator, but the term is often used in place of function when the domain is a set of functions or other structured objects. Also, the domain of an operator is often difficult to be explicitly characterized (for example in the case of an integral operator), and may be extended to related objects (an operator that acts on functions may act also on differential equations whose functions are solutions).' back |
Quantum chromodynamics - Wikipedia, Quantum chromodynamics - Wikipedia, the free encyclopedia, ' In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks and gluons, the fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a type of quantum field theory called a non-abelian gauge theory, with symmetry group SU(3). The QCD analog of electric charge is a property called color. Gluons are the force carrier of the theory, like photons are for the electromagnetic force in quantum electrodynamics.' back |
Rolf Landauer, Information is a Physical Entity, 'Abstract: This paper, associated with a broader conference talk on the fundamental physical limits of information handling, emphasizes the aspects still least appreciated. Information is not an abstract entity but exists only through a physical representation, thus tying it to all the restrictions and possibilities of our real physical universe. The mathematician's vision of an unlimited sequence of totally reliable operations is unlikely to be implementable in this real universe. Speculative remarks about the possible impact of that on the ultimate nature of the laws of physics are included.' back |
Scientology - Wikipedia, Scientology - Wikipedia, the free encyclopedia, 'Scientology is a body of beliefs and related practices created by L. Ron Hubbard (1911–1986), starting in 1952, as a successor to his earlier self-help system, Dianetics.[1] Hubbard characterized Scientology as a religion, and in 1953 incorporated the Church of Scientology in New Jersey.' back |
Special relativity - Wikipedia, Special relativity - Wikipedia, the free encyclopedia, 'Special relativity . . . is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein (after the considerable and independent contributions of Hendrik Lorentz, Henri Poincaré and others) in the paper "On the Electrodynamics of Moving Bodies".
It generalizes Galileo's principle of relativity—that all uniform motion is relative, and that there is no absolute and well-defined state of rest (no privileged reference frames)—from mechanics to all the laws of physics, including both the laws of mechanics and of electrodynamics, whatever they may be. Special relativity incorporates the principle that the speed of light is the same for all inertial observers regardless of the state of motion of the source.' back |
The Little Drummer Girl - Wikipedia, The Little Drummer Girl - Wikipedia, the free encyclopedia, 'The Little Drummer Girl is a spy novel by John le Carré, published in 1983. The title suggests a word play on the Christmas carol The Little Drummer Boy. The story follows the manipulations of Martin Kurtz, an Israeli spymaster who intends to kill Khalil – a Palestinian terrorist who is bombing Jewish-related targets in Europe, particularly Germany – and Charlie, an English actress and double agent working on behalf of the Israelis. ' back |
The Prime Minister of Australia, The Hon Tony Abbott MP, 'New measures to strengthen Australian citizenship
The Commonwealth Government intends to update the Australian Citizenship Act 2007 so dual nationals who engage in terrorism can lose their citizenship.
The Minister for Immigration and Border Protection will be able to exercise these powers in the national interest where a dual citizen betrays our country by participating in serious terrorist-related activities.
The new powers will apply to dual citizens who fight with or support groups such as ISIL, or Daesh, as well as so-called ‘lone wolves’, whether in Australia or on foreign soil.'
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United States Government, Cyberspace Solarium Commission, back |
Universal Turing Machine - Wikipedia, Universal Turing Machine - Wikipedia, the free encyclopedia, 'Alan Turing's universal computing machine (alternately universal machine, machine U, U) is the name given by him (1936-1937) to his model of an all-purpose "a-machine" (computing machine) that could process any arbitrary (but well-formed) sequence of instructions called quintuples. This model is considered by some (for example, Davis (2000)) to be the origin of the stored program computer -- used by John von Neumann (1946) for his "Electronic Computing Instrument" that now bears von Neumann's name: the von Neumann architecture.
This machine as a model of computation is now called the Universal Turing machine.' back |
Uranium-238 - Wikipedia, Uranium-238 - Wikipedia, 'Around 99.284% of natural uranium[1] is uranium-238, which has a half-life of 1.41 × 1017 seconds (4.46 × 10E9 years, or 4.46 billion years).' 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. In quantum Darwinism, they are the progenitors of multiple copies spread throughout the environment -- the fittest quantum states that not only survive decoherence, but subvert it into carrying information about them -- into becoming a witness.' back |
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