Natural Theology

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Notes DB 90: Psychogenesis_2024

Sunday 17 March 2024 - Saturday 23 March 2024

[page 247]

Sunday 17 March 2024

A tale of two spaces. I have been struggling to find the end of cognitive cosmology and it came to me this morning in crystal clarity after it had spent more than fifty years lurking in the shadows of my mind. Lonergan's massive tome on insight and transcendental knowledge never had a word to say about brain and body which explains the working of our minds in exquisite detail. On the other hand, quantum field theory, which is based on a very ad hoc union of quantum mechanics and reality totally overlooks the psychological role of quantum [physics]. Since I decided possibly about four years ago to make Hilbert space independent of Minkowski space it has gradually taken on, in my mind, the space of the mind of the Universe. So I am now free to reject the botched job of uniting quantum mechanics and relativity through continuity and renormalization and replacing it with the von Neumann vacuum, evolution with variation and natural selection that has built the world from an ignorant and omnipotent god whose methods have brought us civilization in a manner similar to the ignorant and omnipotent empire builders who have made our world.

[page 248]

Auyang page 34: ' The strong interaction is the strongest of the fundamental interactions. It also happens to have the highest symmetry.' Break in symmetry introduces new features, ie zero sum bifurcation of gravitation to potential and kinetic energy, PE + KE = 0: Principle 2: Zero sum complexification. Sunny Auyang (1995): How is Quantum Field Theory Possible?

page 37: Wigner: 'two characteristics of elementary particles under relativistic transformation, mass and spin': pure relativistic considerations single out mass and spin as indices for the classification of various free elementary particles and put certain constraints on their values. Wigner's classification - Wikipedia

page 38: All relativistic quantum field theories are invariant under CPT. CPT Symmetry - Wikipedia

There are three symmetry principles in physics: special + general relativity and local symmetry or the gauge principle. 'All four interations are all field theories with local symmetries.' But are they field theories if spacetime is not continuous but made of particles, fermions and bosons → 3 + 1 Minkowski.

Each theory of a fundamental interaction has a spatio-temporal group and a local group

page 39: gauge field theories control orientation of tangent Minkowski spaces.

Generalizations simplify life. So we reject spacetime continuity and restrict the dimensions of Hilbert space to countable infinity. This solves everything and deletes quantum field theory, but opens the way to discrete transfinity (complexity, not continuity) by combination and permutation made possible by the principle of individuation, putting angels in different places.

[page 249]

Auyang page 39 cont: 'Position has always been the natural parameter that appears explicitly in physical theories. NO. There is no position in Hilbert space, only phase, fixed and variable. All that counts is relative phase, ie relative 'position' in Hilbert space, the metric (f, g). Inner product space - Wikipedia

page 40: covariance means reality is independent of points of view, ie coordinates. Quantum theory says particles observe one another, acting as local frames of reference for one another. The energy of interaction totally outweighs any gravitation interaction by a factor of 1040, but particles can draw or deposit energy from [/ into] gravitational potential.

page 41: 'As a result of the equivalence principle there exists at each point a tiny Minkowski space. Spaces are disjoint and rotate freely of one another (tetrads)' [spacetime pixellated in terms of angular momentum by quantum of action].

page 42: Connection gives global invariance in the face of local variance, gravitation acting as photons do in em. This energy banking is important where E = mv2 = mc2.

page 43; 'New form of matter', the em field? No, it is photons.

page 48: 'A field ψ (t, x) is a dynamic variable for continuous systems whose points are indexed by the parameters t and x.' These do not exist, they are particulate

Hilbert space is like a field but it is INSIDE the particles.

[page 250]

Monday 18 March 2024

Traditionally we are a compound of mind and body, or maybe body and soul. The Catholic Church has told us that as a consequence of original sin the body no longer obeys the mind, or as Paul of Tarsus puts it, the flesh wars against the spirit. In more modern terminology we might say that the mind adds a new degree of freedom to the mind/body composite. A few year ago I began to see that we can apply this paradigm to the whole Universe, proposing quantum theory operating in Hilbert space as the mind of the Universe and Einsteins dynamism expressed in Minkowski space as the body of the Universe. Two spaces, two degrees of freedom. I then began to think in Trinitarian and evolutionary terms and proposed to myself that Hilbert space and quantum mechanics are in effect the realm of variation, the realm of possibility, and Minkowski space is the realm of selection, picking the ideas that work by being able to reproduce themselves. This paradigm appeared to be universal. Mobile phones, for instance, are a product of imaginations like Steve Jobs, and they have now been able, through the application of their specific technology and the technology necessary to reproduce them, to become ubiquitous on the planet. Paul the Apostle: Galatians, chapter 5, USCCB

[page 251]

Many people love them. Many people are afraid of them and they have had a deep epistemological impact on the deepest and most comprehensive realm of human behaviour, our collective decisions about what to do, politics.

The ancient belief that the world was a perfect system made by a perfect god has tried to apply the mind / body dichotomy to the whole of reality and found it necessary, to achieve completeness, to introduce powers of evil in the form of Satan and a cohort of fallen angels working against the plans of the perfect god and achieving temporary hegemony over the perfect world by the introduction of death, work, pain and evil. The death of Jesus of Nazareth, they say, has fixed all this but we will not see the results and the return of perfection until the end of the world when it will be necessary to balance the books by consigning a large proportion of the human race to a hell of eternal punishment, for what, we are not sure, but it is deeply engrained in the human constituency to punish people that do not fit in as we see in the vast and profitable prison industry in the US. Prison-industrial complex - Wikipedia

I am trying to replace this old model with a new one which has involved destroying the old model of the perfect

[page 252]

creator, the fall, the redemption and the Apocalyptic end game. None of this seems to have the slightest connection to the world we see. The problem of evil is adequately explained by the random input to evolution necessary to secure the creative power that has brought us from the initial singularity to this point, but I am still in trouble with the body side of the picture, which has long been called the quantum measurement problem, the way that the Hilbert space maps onto the Minkowski space. To date I have found it necessary to reject the current standard model and the quantum field theories that have developed to explain the Hilbert . Minkowski interface. I feel strongly that the answer is on the tip of my mind and it is my intention to get the answer into words today [!!].

One of my ways of expressing the difference between Hilbert space and Minkowski space is to think of Hilbert space (and mathematics in general) as kinematic, unable to move itself but like computer generated imagery in the movies, able to do almost anything, not heavily constrained by laws like conservation of energy, which, from a Minkowski space point of view (and Noether's theorem), means invariance through time. Conservation of energy applies in Minkowski space and so phenomena like tunnelling in quantum mechanics which require

[page 253]

the system to play fast and loose with the conservation of energy through a sort of banking system which enables energy to be withdrawn if it is repaid again later to enable things to happen which could not otherwise happen and this facility is not available in Minkowski space [momentum???]. It is available human affairs, on the other hand, through the banking system and often has the effect of leading to catastrophe when borrowers cannot repay. In other words banking is a component of evolution which can lead to creation as well as disaster.

A major defect of field theory, known as the cosmological constant problem seems to point to a fatal flaw in quantum field theory which, in the words of Streater and Wightman, seems to be adequate to kill it. We must therefor give up on the other spurious idea that quantum uncertainty is a real dynamic source of energy. Cosmological constant problem - Wikipedia, Streater & Wightman (2000): PCT, Spin, Statistics and All That page 1

I have written a few pages now but do not feel any closer to the solution I seek between the kinematic mind and the dynamic world, but I already have it in a way in the assumption that the initial singularity is omnipotent, it is the divinity and the source of energy by its zero sum biurcation into potential energy and kinetic or dynamic energy . . . in the language of special relativity it is equivalent to mass, and so we must go

[page 254]

back and re-examine the derivation of E = mc2 through the operation of massless photons. So we turn to Kevin Brown's Reflections on Relativity. Kevin Brown (2018)

I find myself a very fearful and careful person who takes a long time to accept the obvious. When I look back on my refusal to bow to pressure in the Dominicans to revise my opinion and accept their version of the truth it seems to have been done without a qualm. I am having a bit more trouble rejecting quantum field theory and accepting my new model of the divine world, but when I sort out the kinematic / dynamic energy problem, ie E = hf vs E = mc2 all will be ready for publication.

An old idea still viable: The outcome of Turing (classical) computation processes is determined by the software, not by the rate of processing, so we get the same results regardless of the energy (operations per second) used by the machine. Does the same hold for quantum computation, so the actual outcome of quantum processes is indifferent to the period it takes to execute them, ie eg beta decay in different nuclei?

The quantum field theory crew seem to think that coupling constants scale with energy so they will all become algorithmically identical at some enormous energy. This contradicts the point above.

[page 255]

Another thing to bear in mind is that the power of quantum computation lies in parallel processing so one hermitian operator can have a large number of eigenvectors and eigenvalues depending on the dimension of the space in which it is working and the probabilities of observng these is determined by their distance apart in Hilbert space.

High energy accelerator collisions produce more bits and pieces but does the energy change the actual quantum process that occurs by, for instance, carrying out the interactions across a wider spectrum of eigenvalues of the colliding particles, or is it just same particles, same algorithm, faster process, higher energy output of particles?

Tuesday 19 March 2024

Can we say that the dynamics can drive kinematic, and not vice versa, but that dynamics can read kinematics, as I can read this kinematic writing produced by my dynamic body, but the writing can only move me through my mind when I read it, as we can experience deep emotion when watching and listening to the kinema.

The next bit to write out is Dirac's account of observables and the intelligent insight of quantum mechanics solving the eigenvalue problem kinematically driven by the dynamic energy it derives from gravitation.

[page 256]

The idea that quantum mechanics is a theory 0f communication and computation leads us to think of the fundamental interactions as codecs represented by Hermitian operators which have been discovered through an evolutionary process. So proponents of unified field theory feel that at sufficiently high energy all the three forces described by quantum field theory will become one. The energy scale is predicted to be enormously greater than the energy that will ever be available to us in our laboratories, but may have been the case in the first moments of the big bang when temperatures correspond to the [Planck time]: Page 18.2: Fixed Points—Motion and stillness: Parmenides vs Heraclitus . This unification seems unlikely if the interactions are in fact quantum codecs. We know that the operation of classical codecs remains constrained by software snd so the outcomes are identical [and independent] of the speed of the machine on which it is executed. We expect the same to be true with quantum codecs imagined as fixed algorithms whose rate of execution is a function of the energy of interaction so that the effect of the codec will be independent of the temperature of interaction which is a proxy for the energy of interaction.

Wednesday 20 March 2024

Woke up this morning feeling radical. Ditch Catholic theology and quantum field theory and

[page 257]

replace them completely with my story based on the intelligence of quantum mechanics and evolution. The final page becomes quantum chromodynamics explained by quantum mechanics as the software of the Universe explained by suitably complex operators of the same cardinality as the Turing computable functions, the mapping based on the cardinal of the natural numbers obeyed by the digital logical machinery and the complexity of the Universe by the digital transfinite numbers. So I will have gone all the way to complete my monastic intuition and my construction reflected the political consequences of such an evolving system. So I will have exposed my full intuition emerging from my quantum brain.

My Auntie has had another fall, perhaps an expression of her wish to fall off her perch and be with her husband. What is the deep meaning of life and death [accumulation of errors and rebuild from form preserved in genes / memory. As 80 approaches my body begins to stiffen!]

Quantum chromodynamics becomes page 24, the last gasp of the old theory whose stupidity has been made clear by Wilczek's rather hubristic book and my equally hubristic story is completed by a methodological essay, the answer to Lonergan, c25_theology_physics. Getting happier all the time as I finally discard the myths and become my real self. Lonergan (1992): Insight: A Study of Human Understanding

[page 258]

Field theory is a computational process that yields precise results in quantum mechanics but this does not necessarily mean that it represents reality. The presence of infinity and infinitesimals in a quantized universe means that it misses some points. The linear operators that lie at the heart of quantum mechanics are functions of vectors rather than numbers so they provide a spectrum of answers to any question, rather like the multi-armed advisor who tells us on the one hand . . . and on the other . . . etc etc.

Thursday 21 March 2024

A good morning. I am happy with my work and will finish cc23_insight_beliefg today and then just cc24_fields_end and cc25_physics_theology to go of the main body and cc27_conclusiob to round it iff. The killer argument in cc24_fields_end is Wilczek's book which multiplies the cosmological constnt problem n-fold.

Oscar Wilde on me and my family: "What seems to us as bitter trials are often blessings in disguise."

Friday 22 March 2024

cc24_fields_end. What is my case against field? The world is empty vs the world is full? The world is logical vs the world is forceful? The world is top down vs the world is bottom up / I observe that I am free

[page 259]

in x and y, constrained by gravity in z [and constrained by ?? in t.

The world started as an omnipotent empty set which still exists as the initial singularity and initial singularity of the Universe.

Wilczek promotes the grid and then computes its mass to be absurdly large another version of the cosmological constant problem which, if we take it seriously, completely removes the idea of quantum fluctuations.

I suppose that from my point of view of field theory is that it is a theory of control which might be extended from fundamental physics to the social realm. By filling space with a massive but imperceptible grid one gets the feeling that there is some sort of agenda in Wilczek's view of the world that seems to be behind his acceptance of rather silly ideas, a bit like an internet conspiracy theory. My feeling about the initial singularity that it is the empty space that gives us freedom [and if there is any field we carry it within ourselves, as is the case of all other particles, and this interior state has some control over how particles (sources, persons) react when they meet]. I am keen to see any real argument in favour of the fact that quantum fluctuations cause mass and energy, because I am keen to see that my own understanding of bottom up creation can serve as an argument against top down control [which is why I love my totally ignorant god].

I have bitten off quite a mouthful with fields_end but I feel that a coupling of the cosmological constant problem and

[page 260]

the kinematic/dynamic distinction are quite telling and if I can find a strong argument against fields I think it might tell us something about the totalitarian field that infects some parts of humanity. The free particles moving inertially in space are in a way an optimum model for humanity if we avoid wars, which are the analogue of back holes where the binding force becomes stronger than the structure can bear.

Meanwhile lubricate the mind with Christie's Dead Mans Folly

I am beginning to think, as I look back on my life, that I never did take anything very seriously but aways slightly apart, observing. This seemed to be my way of dealing with monastic life and most of my attention was taken up with theological thoughts that not only fascinated me but seemed quite stupid which is why I found no trouble in insisting to L. P. Fitzgerald, Master of Studies, that he ought to be able to understand that the world is divine, but of course his whole life depended on believing otherwise and I am beginning to learn from the banality of evil and other sources that people will believe anything if it helps them fit in and do well. A survival mechanism that most of us learn in infancy, but not all.

The idea must be to falsify the whole of Wilczek's book, including the field theoretical explanation of hadrons by the fact that quarks and gluons cannot exist

[page 261]

separately, explaining it all in the only way available to me, by quantum mechanics, self-adjoint operators and evolution. I do not need to explain exactly how it works, but that it does and Gross and Wilczek have come to it in terms of a false explanation in terms of Yang-Mills theory, renormalization, screening, antiscreening, all of these things being open to explanation by quantum algorithms embedded in linear operators and solutions to the associated eigenvalue problems. These [might be] be turned into Turing computable algorithms by Fourier transforms, so solving the problem of why it takes months of super computation to imitate what a proton does in femtoseconds. All a big ask, beyond me but worth a try exploiting the principle of symmetry with respect to complexity.

Agatha: the denouement; for me Wilczek spills all the beans and 't Hooft, and Veltman and Yang-Mills are co-conspirators. I do not know any of this but I am a poet and can say what I feel without evidence in the last two pages of cognitive cosmology and then write the theology book and spend the rest of my life getting the physics right. Gerardus 't Hooft (1999): Nobel Lecture 1999: A Confrontation with Infinity, Martinus J G Veltman (1999): Nobel Lecture 1999: From weak interactions to gravitation, Yang-Mills theory - Wikipedia

Clockwork Orange: Burgess: 'I think it is not only the right but the duty of an artist to shock if he think this is needed to make us think seriously about humanity and its destiny. A Clockwork Orange (novel) - Wikipedia

[page 262]

What I an trying to say is that the quantum field theories have missed the point of the world just as badly as the theologians who have missed thr point of god,

Crime and punishment: God punishes us much more violently than the crimes we commit: eat the apple and get an eternity of pain. Anthony Burgess: Catholic behaviour is evil. Benoit Felici & Elisa Mantin: Clockwork Orange: The Prophecy

Ai Wei Wei: Torture the dissenters.

Saturday 23 March 2024

Crime, punishment and absolute control. Field is the paradigm of absolute control. The divine field has providence over everything, that is absolute control, and the slightest deviation has to be punished by some violent horrendous evil, like hanging, drawing and quartering. Aquinas, Summa, I, 22, 3: Does God have immediate providence over everything?, Hanged, drawn and quartered - Wikipedia

[page 263]

Chugging along: Critique of Wilczek pp 32-111 all about the massive condensates. Pure bullshit that indicates the rate of quantum fluctuations on GFT. Check Kuhlman. Then quantum mechanics and evolution. 25.5 Physics is tge basic empirical foundation of theology. Meinard Kuhlmann (Stanford Encyclopedia of Philosophy): Quantum Field Theory

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Further reading

Books

Auyang (1995), 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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Brown (2018), Kevin, Reflections on Relativity, 2018 ' . . . general relativity teaches us that the principles of special relativity are applicable only over infinitesimal regions in the presence of gravitation, so in a sense the general theory restricts rather than generalizes the special theory. However, we can also regard special relativity as a theory of flat four-dimensional spacetime, characterized by the Minkowski metric (in suitable coordinates), and the general theory generalizes this by allowing the spacetime manifold to be curved, as represented by a wider class of metric tensors. It is remarkable that this generalization, which is so simple and natural from the geometrical standpoint, leads almost uniquely to a viable theory of gravitation.' (page 700) 
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Lonergan (1992), Bernard J F, Insight: A Study of Human Understanding (Collected Works of Bernard Lonergan : Volume 3), University of Toronto Press 1992 '. . . Bernard Lonergan's masterwork. Its aim is nothing less than insight into insight itself, an understanding of understanding' 
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Streater (2000), Raymond F, and Arthur S Wightman, PCT, Spin, Statistics and All That, Princeton University Press 2000 Amazon product description: 'PCT, Spin and Statistics, and All That is the classic summary of and introduction to the achievements of Axiomatic Quantum Field Theory. This theory gives precise mathematical responses to questions like: What is a quantized field? What are the physically indispensable attributes of a quantized field? Furthermore, Axiomatic Field Theory shows that a number of physically important predictions of quantum field theory are mathematical consequences of the axioms. Here Raymond Streater and Arthur Wightman treat only results that can be rigorously proved, and these are presented in an elegant style that makes them available to a broad range of physics and theoretical mathematics.' 
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Links

A Clockwork Orange (novel) - Wikipedia, A Clockwork Orange (novel) - Wikipedia, the free encyclopedia, ' Clockwork Orange is a dystopian satirical black comedy novella by English writer Anthony Burgess, published in 1962. It is set in a near-future society that has a youth subculture of extreme violence. The teenage protagonist, Alex, narrates his violent exploits and his experiences with state authorities intent on reforming him. The book is partially written in a Russian-influenced argot called "Nadsat", which takes its name from the Russian suffix that is equivalent to '-teen' in English. According to Burgess, the novel was a jeu d'esprit written in just three weeks.' back

Aquinas, Summa, I, 22, 3, Does God have immediate providence over everything?, ' I answer that, Two things belong to providence—namely, the type of the order of things foreordained towards an end; and the execution of this order, which is called government. As regards the first of these, God has immediate providence over everything, because He has in His intellect the types of everything, even the smallest; and whatsoever causes He assigns to certain effects, He gives them the power to produce those effects. Whence it must be that He has beforehand the type of those effects in His mind. As to the second, there are certain intermediaries of God's providence; for He governs things inferior by superior, not on account of any defect in His power, but by reason of the abundance of His goodness; so that the dignity of causality is imparted even to creatures.' back

Benoit Felici & Elisa Mantin, Clockwork Orange: The Prophecy, ' Examines and re-evaluates the 60-year history and cultural impact of A Clockwork Orange, as a novel, movie and stage play, with the help of archival content and interviews with important creative figures.' back

Bernie Sanders (2024), A Revolution in American Foreign Policy: Replacing Greed, Militarism, and Hypocrisy With Solidarity, Diplomacy, and Human Rights, ' I wish I could say that the foreign policy establishment in Washington learned its lesson after the failures of the Cold War and the global war on terror. But, with a few notable exceptions, it has not. Despite his promise of an “America first” foreign policy, President Donald Trump increased unrestricted drone warfare around the world, committed more troops to the Middle East and Afghanistan, ramped up tensions with China and North Korea, and nearly got into a disastrous war with Iran. He showered some of the most dangerous tyrants in the world—from the United Arab Emirates to Saudi Arabia—with weapons. Although Trump’s brand of self-dealing and corruption was new, it had its roots in decades of U.S. policy that prioritized short-term, unilateral interests over long-term efforts to build a world order based on international law. And Trump’s militarism wasn’t new at all. In the past decade alone, the United States has been involved in military operations in Afghanistan, Cameroon, Egypt, Iraq, Kenya, Lebanon, Libya, Mali, Mauritania, Mozambique, Niger, Nigeria, Pakistan, Somalia, Syria, Tunisia, and Yemen. The U.S. military maintains around 750 military bases in 80 countries and is increasing its presence abroad as Washington ramps up tensions with Beijing. Meanwhile, the United States is supplying Netanyahu’s Israel with billions of dollars in military funding while he annihilates Gaza. U.S. policy on China is another illustration of failed foreign policy groupthink, which frames the U.S.-Chinese relationship as a zero-sum struggle. For many in Washington, China is the new foreign policy bogeyman—an existential threat that justifies higher and higher Pentagon budgets. There is plenty to criticize in China’s record: its theft of technology, its suppression of workers’ rights and the press, its enormous expansion of coal power, its repression of Tibet and Hong Kong, its threatening behavior toward Taiwan, and its atrocious policies toward the Uyghur people. But there will be no solution to the existential threat of climate change without cooperation between China and the United States, the two largest carbon emitters in the world. There will also be no hope for seriously addressing the next pandemic without U.S.-Chinese cooperation. And instead of starting a trade war with China, Washington could create mutually beneficial trade agreements that benefit workers in both countries—not just multinational corporations.' 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 the observed values of vacuum energy density (the small value of the cosmological constant) and theoretical large value of zero-point energy suggested by quantum field theory. Depending on the Planck energy cutoff and other factors, the discrepancy is as high as 120 orders of magnitude, a state of affairs described by physicists as "the largest discrepancy between theory and experiment in all of science" and "the worst theoretical prediction in the history of physics".' back

CPT Symmetry - Wikipedia, CPT Symmetry - Wikipedia, the free encyclopedia, ' Charge, parity, and time reversal symmetry is a fundamental symmetry of physical laws under the simultaneous transformations of charge conjugation (C), parity transformation (P), and time reversal (T). CPT is the only combination of C, P, and T that is observed to be an exact symmetry of nature at the fundamental level.The CPT theorem says that CPT symmetry holds for all physical phenomena, or more precisely, that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry.' back

Gerardus 't Hooft (1999), Nobel Lecture 1999: A Confrontation with Infinity, ' Early attempts at constructing realistic models of the weak interaction were offset by the emergence of infinite, hence meaningless expressions when one tried to develop radiative corrections. When models based on gauge theories with Higgs mechanism were discovered to be renormalizable, the bothersome infinities disappeared - they cancelled out. If this success seemed to be due to sorcery, it may be of interest to explain the physical insights on which it is actually based.' back

Hanged, drawn and quartered - Wikipedia, Hanged, drawn and quartered - Wikipedia, the free encyclopedia, ' To be hanged, drawn and quartered became a statutory penalty for men convicted of high treason in the Kingdom of England from 1352 under King Edward III (1327–1377), although similar rituals are recorded during the reign of King Henry III (1216–1272). The convicted traitor was fastened to a hurdle, or wooden panel, and drawn by horse to the place of execution, where he was then hanged (almost to the point of death), emasculated, disembowelled, beheaded, and quartered. His remains would then often be displayed in prominent places across the country, such as London Bridge, to serve as a warning of the fate of traitors. For reasons of public decency, women convicted of high treason were instead burned at the stake. back

Inner product space - Wikipedia, Inner product space - Wikipedia, the free encyclopedia, 'In mathematics, an inner product space is a vector space of arbitrary (possibly infinite) dimension with additional structure, which, among other things, enables generalization of concepts from two or three-dimensional Euclidean geometry. The additional structure associates to each pair of vectors in the space a number which is called the inner product (also called a scalar product) of the vectors. Inner products allow the rigorous introduction of intuitive geometrical notions such as the angle between vectors or length of vectors in spaces of all dimensions. It also allows introduction of the concept of orthogonality between vectors. Inner product spaces generalize Euclidean spaces (with the dot product as the inner product) and are studied in functional analysis. An inner product space is sometimes also called a pre-Hilbert space, since its completion with respect to the metric induced by its inner product is a Hilbert space.' back

Kashgarian, Lusuegro & Siddique (2024), The Warfare State: How Funding for Militarism Compromises Our Welfare, ' In FY 2023, out of a $1.8 trillion federal discretionary budget, $1.1 trillion— or 62% — was for militarized programs that use violence or the threat of violence or imprisonment, including war and weapons, law enforcemen and mass incarceration, and detention and deportation. . . .. The U.S. spent $16 on the military and war for every $1 that was spent on diplomacy and humanitarian foreign aid. The vast majority of militarized pending was for weapons, war and the Pentagon, at $920 billion. Only 56 billion was spent for international affairs, diplomacy, and humanitarian foreign aid. . . . . The U.S. federal budget allocated twice as much for federal law enforcement, which includes federal prisons, the FBI and other law enforcement agencies $31 billion), as for child care and early childhood education programs ($15 billion).' back

Martinus J G Veltman (1999), Nobel Lecture 1999: From weak interactions to gravitation, ' This lecture is about my contribution to the renormalizability of gauge theories. There is of course no perfectly clear separation between my contributions and those of my co-laureate 't Hooft, but I will limit mysef to some brief comments on those publications that carry only his name. An extensive review on the subject including detailed references to contemporary work can be found elsewhere. As is well known, the work on renormalizability of gauge theories caused a complete change in the landscape of particle physics.' back

Meinard Kuhlmann (Stanford Encyclopedia of Philosophy), Quantum Field Theory, ' Quantum Field Theory (QFT) is the mathematical and conceptual framework for contemporary elementary particle physics. In a rather informal sense QFT is the extension of quantum mechanics (QM), dealing with particles, over to fields, i.e. systems with an infinite number of degrees of freedom. (See the entry on quantum mechanics.) In the last few years QFT has become a more widely discussed topic in philosophy of science, with questions ranging from methodology and semantics to ontology. QFT taken seriously in its metaphysical implications seems to give a picture of the world which is at variance with central classical conceptions of particles and fields, and even with some features of QM.' back

Michael C.Davis, What Article 23 means for the future of Hong Kong and its once vibrant pro-democracy movement, ' The legislation expands the potential use of incarceration with both lengthy sentences upon conviction and longer holding of suspects before trial. Article 23 also intensifies scrutiny of “foreign influence” – making working with outsiders risky for Hong Kong citizens. The draft legislation speaks disparagingly of activism under the guises of fighting for or monitoring human rights and is critical of “so-called” nongovernmental organizations. All of this makes working with or supporting international human rights organizations perilous. In short, in the space of two decades, Hong Kong’s liberal constitutional order has been transformed into a national security order with weak or no protections for basic freedoms. What is the wider context to Article 23? To understand this legislation, one must appreciate the Chinese Communist Party’s deep hostility to liberal values and institutions, such as the rule of law, civil liberties, independent courts, a free press and public accountability. Such liberal ideas are viewed as an existential threat to party rule. This mindset has led to a dramatic expansion of the party’s national security agenda under current leader Xi Jinping.' back

Paul the Apostle, Galatians, chapter 5, USCCB, ' 16 I say, then: live by the Spirit and you will certainly not gratify the desire of the flesh. For the flesh has desires against the Spirit, and the Spirit against the flesh; these are opposed to each other, so that you may not do what you want. But if you are guided by the Spirit, you are not under the law. Now the works of the flesh are obvious: immorality, impurity, licentiousness, idolatry, sorcery, hatreds, rivalry, jealousy, outbursts of fury, acts of selfishness, dissensions, factions, occasions of envy, drinking bouts, orgies, and the like. I warn you, as I warned you before, that those who do such things will not inherit the kingdom of God. ' back

Prison-industrial complex - Wikipedia, Prison-industrial complex - Wikipedia, the free encyclopedia, ' The prison-industrial complex (PIC) is a term, coined after the "military-industrial complex" of the 1950s] used by scholars and activists to describe the many relationships between institutions of imprisonment (such as prisons, jails, detention facilities, and psychiatric hospitals) and the various businesses that benefit from them. . . . Proponents of this concept, including civil rights organizations such as the Rutherford Institute and the American Civil Liberties Union (ACLU), believe that the economic incentives of prison construction, prison privatization, prison labor, and prison service contracts have transformed incarceration into an industry capable of growth, and have contributed to mass incarceration. These advocacy groups note that incarceration affects people of color at disproportionately high rates.' back

Wigner's classification - Wikipedia, Wigner's classification - Wikipedia, the free encyclopedia, ' In mathematics and theoretical physics, Wigner's classification is a classification of the nonnegative ( E ≥ 0 ) energy irreducible unitary representations of the Poincaré group which have either finite or zero mass eigenvalues. (These unitary representations are infinite-dimensional; the group is not semisimple and it does not satisfy Weyl's theorem on complete reducibility.) It was introduced by Eugene Wigner, to classify particles and fields in physics—see the article particle physics and representation theory. It relies on the stabilizer subgroups of that group, dubbed the Wigner little groups of various mass states.' ' 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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