Natural Theology

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Notes

Sunday 1 January - Saturday 7 January 2023

[Notebook: DB 88 Salvation]

[page 230]

Sunday 1 January 2023

Some radical errors in [Catholic] theology listed in the park:

1. Information / intelligence is spiritual
2. Potential cannot actualize itself
3. Creation can be deterministic

[here we change from errors to assertions!]

4. Symmetry = law is not deterministic but enables enables probability as eg fair dice.
5. Personal communications are not deterministic, so that general covariance does not hold in the quantum regime.
6. Nevertheless Shannon theory shows how to achieve error free communication
7. Continua cannot carry information so quantization is necessary
8. Cantor's theorem + Turing's theorem guarantees large spaces in incomputability and therefore uncertainty
9. Gödel's theorem is the foundation of requisite variety.
10. Infallibility is consequently impossible
11. Entropy is the key to stability so educated democracy is the most stable form of government
12. The Universe is the Leviathan
13. Autocratic infallibility is the recipe for death [look at what is happening to Putin's Russia Holly Ellyatt: ‘Losing is not an option’: Putin is ‘desperate’ to avoid defeat in Ukraine as anxiety rises in Moscow]

Reformation question; sola fide vs good works. Faith vs charity (meditaed by hope.

My reformation: sola scriptura vs scientific reading of the divine universe [direct interface with god].

Priesthood of all believers → we are all literally children of god.

[page 231]

The most important element of humanity is the collective state of mind which decides who is to be saved and who is to be killed in wars of religion such as that currently being wagedt against Ukraine by Patriarch Kirill and Vladimir Putin. Patriarch Kirill of Moscow - Wikipedia

The Reformation sola scripture was possibly motivated by the creative work of Aquinas and others who injected Aristotelian ideas into theology to produce a new model of god. Scripture remained the specifically theological source of data, representing the facts known to the blessed with a vision of god and particularly emphasized by Lonergan in his Trinity books. Bernard Lonergan (2009): The Triune God: Doctrines

My feeling is that we can bypass the scriptural source by making the Universe divine so that we have a real scientific entree into theology and the basis of my approach is the concept of structureless initial singularity, action and evolution that start from Aristotle and Aquinas and, using quantum mechanics and the ideas of cognitive cosmology, generate the mind of god [ie the Universe] with the slogan 'Trinity to Transfinity'.

There is a subtle difference between addition and multiplication between real and complex numbers. In real numbers, multiplication can be understood as repeated addition but this is not so in complex numbers. This makes it possible for the dimensions of Hilbert space to be orthogonal in terms of multiplication but nevertheless additive when it comes to superposition. Check this.

Monday 2 January 2023

From cave to cathedral to convert to cosmos.

Eventually I have to make a performance [but a website observed is a performance].

Tuesday 3 January 2023

Omnes page 32: Newton's universal principles: three laws. Roland Omnes (2002): Quantum Philosophy: Understanding and Interpreting Contemporary Science

Can we understand these in terms of my (?) first principle: information is physical?

1. Inertial motion: no message, no change
2. a = F/m: rate of change (a) = communication rate (F) divided by total body of data (m).
3. Equal and opposite - full duplex.

[page 232]

Omnes page 35: 'unconsciously shifting from intuitive science, where everything could be visualized . . . toward a science involving formal element that are essentially unintelligible'.

The notion of action is central here. Unlike the concepts employed by Newton, this notion is purely mathematical, without any intuitive visual or analogical content. The action is the integral over time of the difference between potential and kinetic energy. We can surely make sense of their sum—it is the total energy— but their difference? What is more action means nothing by itself, it is only an intermediary [maybe like a complex number in algebra?]: actual motion has a kind of magical property which is to minimize [extremalize] the action (the principle of [stationary] action. Why a minimum or even a maximum? We can only wonder, without expecting to understand, without "seeing" anything because we do not know what "action" is or where it comes from [maybe the potential/action thing is something inherent in quantum theory and Aristotle's first glimpse of complex numbers?].

Pendulum rising: kinetic → potential; pendulum falling: potential → kinetic.

Omnes page 35: 'More efficient calculations do not entail higher conceptual content.' [so you say].

Rocket up; rising potential; rocket coming down: falling potenial.

Perhaps the world is calculating itself using an algorithm [based on] the principle 'time is of the essence' [see Cognitive Cosmology page 12: The quantum creation of Minkowski space].

Omnes page 46: 'In fact, after Maxwell, physics is no longer something one can visualize with the imagination and communicate in ordinary language. Its concepts cannot be completely rendered without at least the help of mathematical language [which implies quantification; what are we quantifying? entropy, communication rate, computation rate ???].

'In the final years of the nineteenth century there are other foretelling signs of intuition slowly going blind.' What is happening here is that the [age] of spatial intuition is over and we are moving into the era of communication, gossip software, quantum mechanics, entropy, counting quanta and so on. I now have to think more in terms of cognitive cosmology, beginning with the quantum theory of the Trinity.

page 57: ' In mathematics what matters is not the nature of things but the relationships between them. Same also in physics [and it is the relationships between things which reflect their natures, fermions are defined by the bosons that they exchange and vice versa]. Fermion - Wikipedia, Boson - Wikipedia

God is real and a quantum of action is a real event, a unit of information, a physical entity [but maybe in some sense incomplete like a complex number or a boson].

[page 233]

In my early greenie days I spent a lot of time writing critiques of environmental impact statements, pointing out falsehoods, miscalculations and other inconsistencies. I am now preparing to apply the same methodology to the Catholic Church, criticizing its claims to be a force for salvation, beginning with the idea that the salvation it is offering is purely fiction.

Wednesday 4 January 2023

The first page of the God of Aquinas (part of physicaltheology.com) shows beyond [reasonable] doubt that the completely simple God of Aquinas lacks the entropy necessary to deterministically create the universe that we inhabit. This argument is couched in terms of information theory and cybernetics and holds also for the classical initial singularity proposed by Penrose, Hawking and Ellis. Hawking & Ellis (1975); The Large Scale Structure of Space-Time

The classical initial singularity, on the other hand, has no creative power whereas the quantum singularity modelled on the God of Aquinas, being pure act, is capable of action, albeit random, since the action of action is to act. So it has the first prerequisite for evolution. The corresponding selective power arises from the limitation on divine omnipotence that they cannot create a contradiction. We apply these ideas in the first instance to a treatment of the Trinity, and then go further to imagine the extension to a transfinite system.

My fear here is that these ideas are too outrageous but I see no alternative and so will stick by it this year, revising cognitive cosmology as I develop lust for life.

Omnes page 81: Part 2; The Fracture. "The fracture is nevertheless there in the fact that these laws are, when seen through the eyes of the average intelligence or classical philosophy, absolutely incomprehensible.

page 122: ' Present day physics is based on objects that cannot be conceived as elements of a set from which subsets can be formed.' This is to overlook that fact that in the real world the elements of interest are events and a large event has subsets. We describe events by recipes or algorithms, starting from the initial singularity and building up to a transfinite computational (algorithmic) network.

page 125: 'space-time totally inaccessible to intuition' ? We live in it and deal with it all the time, measuring times and distances to get to work on time, to meet one another, et etc.

[page 234]

I last read Omnes in 2009 after I got it in 2007. Why am I reading it now? Because lately I have been thinking about action and somewhere in the back of my mind there was something about the difficulties Omnes had with action, his "fracture", so I went looking for it and am reading my marginal noted to see if I have learnt anything about action in the last 13 years.

Ones page 139: Omnes caught in a classical footprint. Classics is preoccupied with energy, but the important point of the [atomic] orbital transition is the quantum of action which annihilates the electron in one state and creates it in another.

Thursday 5 January 2023

Left the Order of Preachers on 4 January 1967.

Getting a slight grip on the idea that action is the enabling intermediary in the universal process rather like the role of the complex numbers in algebra. This may explain the essential role of complex numbers in quantum theory and force me to study them a bit more closely. I am vaguely hoping that some sentence in Omnes will lead me further along this path and make it possible for me to write coherent quantum mechanical theory of the Trinity as the atom of universal communication, Father and Son are fermions, the Spirit is a boson. A corollary to all this might be derivation of Shannon's communication in the presence of noise using complex function space of rings, a la von Neumann.

A complex number is a vector, more complex and versatile than a real number. Maybe its physical representation a la Landauer is action. As act, we have said, is an event that changes some p into some not-p. So do we need to talk about complex logic, which would seem to be analogous to the rotation of wave functions?

Omnes 149: Translation between theory and observation, a codec in other words. Interpretation of Christianity attempts to derive rules of behaviour (eg no sex unless intention to reproduce) out of doctrine (eg Church has infallible communication with God).

'It is clear that the wrong . . . that interpretation seeks to right stems from the formal [written] character of science from the fact that its initial concepts are not accessible to imagination.' Your imagination, maybe, but any of us can imagine [intersecting] waves and see the complex vector representation of superposition which covers both phase and amplitude.

[page 235]

' [need for interpretation] is definitely manifest in the theory of relativity.' Why? All it says is leave early if you want to get there on time.

Omnes page 150: - we interpret quantum mechanics as s conversation (noted 2009!)

Computation of eigenvalues is deterministic, ie actual symbols exchange in computation, ie the source alphabet. What is probabilistic, as in communication theory, is the normalized rate of occurrence of [particular] letters of the alphabet. Each letter is a precisely defined act, a transition in the source from letter a to letter b.

'no cause is at work to make an excited atom decay at some specific moment.' In a sense this is caused by a universal process just as I utter certain words at certain appropriate moments in a conversation.

page 156: Greek philosophy would repudiate Δp . Δx ≈ h. Why? 'Because momentum is proportional to velocity [p = mv]. This is a classical spacetime version of momentum. In the information theoretical view momentum is the content of memory, a body of data whose content is changed by addition and subtraction by the information analogue of force, ie flow of data.

Operator changes a function, eg differentiation. Complementarity: ' [position] or [velocity / momentum] is in itself correct with no internal contradictions but it is impossible to confine them.' ie space / position resolution is limited to h as is energy / time

Quantum of action is a logical operator equivalent to not, and the symbol i is also an operator, changing a real number to a not real number so we can identify them, so i ≡ quantum of action. i establishes orthogonality, as in the complex plane [or Argand diagram]. Complex plane - Wikipedia

At the fundamental level of resolution wave and particle are indistinguishable so we are in a Wittgensteinian situation: Tractatus: what can be said can be said clearly and what we cannot talk about we must pass over in silence. The limits of language mean the limits of my world.' Biletski & Matar; Lunwig Wittgenstein

Friday 6 January 2023

Omnes page 164: 'There can be no doubt that the principles of quantum mechanics clash with common sense.' Yes, if you work in terms of deterministic space-time geometry, but no

[page 236]

if you think in terms of interpersonal relationships of communication and reasonable thought.

' Here the originality of our approach, to deduce the common sense from the quantum premises, including its limits – that is to demonstrate also under which condtions common sense is valid and what is its margin of error.'

Omnes page 165; For the time being we shall consider only those propositions concerning the position and velocity of a physical object at some instant of time.' I.e. an absolutely Newtonian approach which has nothing at all to do with the real flow of information at a noisy party.

page 166: starts with a pendulum, blah, blah, blah.

page 168: ' Formally an elementary proposition in dynamics is simply a proposition in kinematics in which time is implicitly mentioned.' ie frewquency, waves, the world of Hilbert space. Hilbert space - Wikipedia

'Classic determinism is a logical equivalence of two propositions 0f Newtonian dynamics with respect to two different instants of time' ie conservation of energy and Noether. Laplace's demon. Conservation of energy - Wikipedia, Noether's theorem - Wikipedia, Laplace's demon - Wikipedia

page 170: Reality is a form of thought governed by Gödel and Turing. Gödel's incompleteness theorems - Wikipedia, Turing machine - Wikipedia

So we use an angel expert in formalism who suffers the same limitations as God.

page 171: Observable = operator = matrix with eigenvectors which are letters in its alphabet whose total probability is normalized to 1.

Saturday 7 January 2023

Every bright idea has a downside. The new version of quantum Trinity has run aground, but hope springs eternal. The correlation between action and complex numbers looks fruitful and I am hoping for help from Omnes. If wishes were horses again. What I want is is clear link between Aristotle and Aquinas, actus purus and the quantum of action, the god in the machine. All lovely words, but what do they mean.

Living in the darkness before insight, the evil implicit in the evolutionary fact that creation requires a symmetry snd randomness. How does

[page 237]

the initial singularity become the initial duality? : acion + no-clonong.

Quantum mechanics is just sources talking to one another, increasing their initial complexity by sharing [duplicating] information, as happens to me when I watch the world around me. Quantum observation involves watching the conversations one letter at a time, each observer and observer are sources with an alphabet of "sounds" [phonemes] which they string together [linearly] to make a conversation. So what does god, the initial singularity, say to themself? It is a bit like this diary, me talking to myself as an example for you, the reader, of what I am thinking about physics → theology. It is all talk about the universe (of which I am an element) talking to itself [so consciousness is the source of creation in God?]. We organize all this talk with a hierarchical network, atoms talking, rabbits talking, galaxies talking, etc. Phoneme - Wikipedia

Omnes page 171: Omnes is locked on to the idea that common sense is identical to classical Newtonian physics [whereas it is far more concerned with interpreting all the gossip that surrounds each of us].

The invention of writing was the invention of formalism, the reduction of moving and passionate speech to a set of symbols (maybe a play by Shakespeare). The task of actors is to add in the elements that the playwright has abstracted out to represent the original reality captured by the writing [so an actor is just like the reader of Turing's paper, adding in the imagery that Turing is representing].

page 173; A random variable: the unpredictable (but practically constrained) thing I am going to do next (make another cup of coffee and eat my corn flakes while reading some fiction, How to Stage a Coup. Also pick some flowers and think about fixing some broken branches on a rose bush. Also how to deal with alcoholic landlady - fix rose bush with old bike tube). Rory Cormac (2022): How to Stage a Coup

Omnes page 175: God is the operator, ie the universe operates itself by talking to itself, as I do [being an image of god].

page 176: 'Therefore in quantum mechanics there are propositions that can be expressed in ordinary language but which have no meaning because of the underlying formalism.' Δx . Δp ≈ ΔE . Δt ≈ h: quantum mechanics is so simple because it is prior to space-time and its projectors cannot embrace both space and time at once. Cognitive Cosmology: page 12: The quantum creation of Minkowski space

von Neuman: Birkoff and vN then wondered whether the logic of the quantum world did not after all obey laws that were different from—and less restrictive than— the sacred ones of Aristotelian logic. Yes, all polynomials have solutions in the complex field.

'Underlying formalism is mathematical hence Aristotelian'. No, complex numbers open up a new world of algebraic completeness [which increases the space of consistent mathematical statements far beyond the Aristotelian imagination].

[page 238]

Omnes page 176 (continued): 'The quantum non-Aristotelian component would therefore be flanked by the mathematical (Aristotelian) and empirical (also Aristotelian) ones. Another indigestible "sandwich".

page 177: 'We shall therefore abandon it, to insist on the advantages of sticking to the more conventional—more rational in fact—logical forms.' Probably a mistake.

Histories: '. . . Griffith proposed considering what amounts to a history of the physical system. . . ' that is looking at the sentence rather than one phoneme?

Veltman says a Hilbert space is a history; page 33 "dogs and cats" Martinus Veltman (1994): Diagrammatica: The Path to the Feynman Rules

page 178: Probabilities . . . lie at the very heart of the theory, and their role goes far beyond the mere description of chance.' Probabilities deal with complete systems of events. Collectively exhaustive events - Wikipedia

page 179; Probability of a history (ie a sequence of elementary events). Consistent histories are normalized just as elementary events are normalized [clearly described by Feynman: Richard Feyman: Feynman Lectures on Physics vol III lecture 1; Quantum Behaviour.]

Omnes page 280; Bayes conditional probability. If we do not know which slit the particle went through we get interference. Bayes' theorem - Wikipedia

page 186: Complex numbers are not observable. Are there 4i eggs in this basket?

page 191: 'classical determinism is approximate.' Not in s halting Turing Machine.

page 193: 'common sense confirms the quantum nature of the laws governing the material world.' Tell that to the two slit experiment!

page 194: All our knowledge machinery has been created by evolution in a quantum world.

'Common sense, thus reappraised and with its scope circumscribed no longer applies to the universe at large.' Of course it does, when we consider the

[page 239]

universe to be a society of sources beginning with the Father and the Son.

Omnes page 199; Decoherence.

page 222: Bohr: ' "[Quantum mechanics] requires a renunciation of the classical idea of causality and a radical revision of our idea of physical reality".' At the most elementary level, change requires annihilation and creation because entities are to small to change within themselves. The elements of a particular set of creations and annihilations are members of a symmetry like the faces of a die. As the die spins, one fact is annihilated and another appears but all six of them are elements of a complete system of events so the sum of the probabilities is normalized to 1, some face always appears when it comes to rest.

Polya: Vectors are symmetrical with respect to displacement. Polya & Latta (1974); Complex Variables

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Further reading

Books

Cormac (2022), Rory, How to Stage a Coup, Atlantic Books 2022 ' Cormac combines the best true life spy stories with thoughtful analysis of the perils of covert government operations. So full is it of fascinating and acutely examined examples of these murky practices that you wouldn't want this book to fall into the wrong hands.' 
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Hawking (1975), Steven W, and G F R Ellis, The Large Scale Structure of Space-Time, Cambridge UP 1975 Preface: Einstein's General Theory of Relativity . . . leads to two remarkable predictions about the universe: first that the final fate of massive stars is to collapse behind an event horizon to form a 'black hole' which will contain a singularity; and secondly that there is a singularity in our past which constitutes, in some sense, a beginning to our universe. Our discussion is principally aimed at developing these two results.' 
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Lonergan (2009), Bernard J F, and Robert M Doran and H Daniel Monsour (eds), The Triune God: Doctrines (Volume 11 of Collected Works), University of Toronto Press 2009 Bernard Lonergan (1904-1984), a professor of theology, taught at Regis College, Harvard University, and Boston College. An established author known for his Insight and Method in Theology, Lonergan received numerous honorary doctorates, was a Companion of the Order of Canada in 1971 and was named as an original members of the International Theological Commission by Pope Paul VI. 
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Omnes (2002), Roland, and Arturo Sangalli (translator), Quantum Philosophy: Understanding and Interpreting Contemporary Science, Princeton University Press 2002 From Booklist 'Einstein and Aristotle meet and shake hands in this illuminating exposition of the unexpected return of common sense to modern science. A companion volume to Omnes' earlier Understanding Quantum Mechanics (1999), this book recounts—with mercifully little mathematical detail—how this century's pioneering researchers severed the ties that for millennia had anchored science within the bounds of clear and intuitive perceptions of the world. As an abstruse mathematical formalism replaced the visual imagination, scientists jettisoned normal understandings of cause and effect, of coherence and continuity, setting science adrift from philosophical conceptions going back as far as Democritus. But when theorists recently began to weigh the "consistent histories" of various quantum events, the furthest frontiers of science became strangely familiar, as rigorous logic revalidated much of classical physics and many of the perceptions of common sense. With a contagious sense of wonder, Omnes invites his readers, who need no expertise beyond an active curiosity, to share in the exhilarating denouement of humanity's 2,500-year quest to fathom the natural order. And in a tantalizing conclusion, he beckons readers toward the mystery that still shrouds the origins of formulas that physicists love for their beauty even before testing them for their truth. An essential acquisition for public library science collections.' Bryce Christensen 
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Polya (1974), George, and Gordon Latta, Complex Variables, John Wiley & Sons Inc 1974 Preface: 'After having lectured for several decades on complex variables to prospective engineers and physicists, I have definite and, I hope, not unrealistic ideas about their requirements and preferences. . . .
I hope that this book is useful not only to future engineers and physicists, but also to future mathematicians. Mathematical concepts and facts gain in vividness and clarity if they are well connected with the world around us and with general ideas, and if we obtain them by our own work through successive stages instead of in one lump.' 
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Veltman (1994), Martinus, Diagrammatica: The Path to the Feynman Rules, Cambridge University Press 1994 Jacket: 'This book provides an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics. The aim is to make clear what the physical foundations of present-day field theory are, to clarify the physical content of Feynman rules, and to outline their domain of applicability. ... The book includes valuable appendices that review some essential mathematics, including complex spaces, matrices, the CBH equation, traces and dimensional regularization. . . .' 
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Links

Aakar Patel , India is weaponising FATF recommendations against civil society, ' The October 3 raids on the news website “NewsClick” and the arrest of its founder, Prabir Purkayastha and human resources head, Amit Chakravarty, are the latest attempts by the Indian government to decimate independent and critical media in the country. The use of draconian anti-terror laws against the media organisation and its journalists is an alarming reminder of the Indian government’s determination to crack down on free press and systematically stifle dissenting voices. . . . .. It targeted many media outlets and non-profits, including Amnesty International, which I represent, with these laws under the guise of fulfilling India’s membership commitments to the Financial Action Task Force (FATF), an intergovernmental body mandated to curb global money laundering and terrorism financing.. . .. FCRA is another piece of legislation that has been used as a tool to quash dissent. Non-governmental organisations in India require a “foreign contribution licence” to access foreign funds as established by the Foreign Contribution (Regulation) Act (FCRA). The introduction of this bill in 2006 coincided with India becoming an observer state of the FATF. Later in 2010, to improve India’s “non-compliant” status, amendments were made to the act which gave wide-ranging powers to the Ministry of Home Affairs to suspend and cancel an NGO’s registration. Since then, and especially in the last 10 years, more than 20,600 NGOs have had their licences cancelled with nearly 6,000 of these cancellations occurring since the beginning of 2022, according to government data. The vague reasonings and arbitrary nature of these cancellations have led to thousands of job cuts and massively shrunk the sector, resulting in a great loss to a wide number of public interest goals in India, from public health to poverty alleviation, to human rights advocacy.' back

Andrew E. Kramer, With Speeches to Ukraine, and the World, Zelensky Shapes Narrative of the War, ' His New Year’s Eve address to the nation on Saturday night offered another opportunity for him to depict the war in a way that rallied his fellow citizens behind the army, using the electric moment before midnight to give the speech a special significance. “This year began on Feb. 24,” he said, the date Russia first invaded Ukraine. “It can still be dark, loud and complicated for us. But we will definitely never be afraid again.” The year, he said, was “our year. The year of Ukraine. The year of Ukrainians".' back

Bayes' theorem - Wikipedia, Bayes' theorem - Wikipedia, the free encyclopedia, 'IIn probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule) describes the probability of an event, based on conditions that might be related to the event. . . .Bayes' theorem is named after Rev. Thomas Bayes (1701–1761), who first provided an equation that allows new evidence to update beliefs. It was further developed by Pierre-Simon Laplace, who first published the modern formulation in his 1812 Théorie analytique des probabilités. Sir Harold Jeffreys put Bayes' algorithm and Laplace's formulation on an axiomatic basis. Jeffreys wrote that Bayes' theorem "is to the theory of probability what the Pythagorean theorem is to geometry".' back

Biletski & Matar (Standord Encyckopedia of Philosophy), Ludwig Wittgenstein, 'Considered by some to be the greatest philosopher of the 20th century, Ludwig Wittgenstein played a central, if controversial, role in 20th-century analytic philosophy. He continues to influence current philosophical thought in topics as diverse as logic and language, perception and intention, ethics and religion, aesthetics and culture.' back

Boson - Wikipedia, Boson - Wikipedia, the free encyclopedia, 'In particle physics, bosons are particles with an integer spin, as opposed to fermions which have half-integer spin. From a behaviour point of view, fermions are particles that obey the Fermi-Dirac statistics while bosons are particles that obey the Bose-Einstein statistics. They may be either elementary, like the photon, or composite, as mesons. All force carrier particles are bosons. They are named after Satyendra Nath Bose. In contrast to fermions, several bosons can occupy the same quantum state. Thus, bosons with the same energy can occupy the same place in space.' back

C. Uday Bhaskar, Attack on US Capitol: two security time bombs for America revealed by committee, 'As committee chairman Bennie Thompson noted in his foreword: “If this Select Committee has accomplished one thing, I hope it has shed light on how dangerous it would be to empower anyone whose desire for authority comes before their commitment to American democracy and the Constitution.” Expressing faith that “most Americans will turn their backs on those enemies of democracy”, he noted that “some will rally to the side of the election deniers”, including “white supremacists”, “violent extremists” and “groups that subscribe to racism, anti-Semitism and violent conspiracy theories”.' back

Christopher Ruddy, Benedict's theological legacy, ' Now the last surviving major participant at Vatican II is gone. An ecclesial era has ended. The man who grew up under Nazism, who resisted Marxism and theological liberalism, has passed. There are new movements in the world and in the Church, new signs of the times, for good and for ill. Still, I am convinced that the stature of this “mustard seed” theologian and hierarch will grow over the coming decades and bear much fruit.' back

Collectively exhaustive events - Wikipedia, Collectively exhaustive events - Wikipedia, the free encyclopedia, ' In probability theory and logic, a set of events is jointly or collectively exhaustive if at least one of the events must occur. For example, when rolling a six-sided die, the events 1, 2, 3, 4, 5, and 6 balls of a single outcome are collectively exhaustive, because they encompass the entire range of possible outcomes.' back

Complex plane - Wikipedia, Complex plane - Wikipedia, the free encuclopedia, ' In mathematics, the complex plane is a geometric representation of the complex numbers established by the real axis and the orthogonal imaginary axis. It can be thought of as a modified Cartesian plane, with the real part of a complex number represented by a displacement along the x-axis, and the imaginary part by a displacement along the y-axis.' back

Conservation of energy - Wikipedia, Conservation of energy - Wikipedia, the free encyclopedia, 'In physics, the law of conservation of energy states that the total energy of an isolated system cannot change—it is said to be conserved over time. Energy can be neither created nor destroyed, but can change form, for instance chemical energy can be converted to kinetic energy in the explosion of a stick of dynamite. back

Costica Bradatan, I Know What Savage Fear Really Lies at the Heart of the American Dream, ' The Romanian state did everything — from the repression and surveillance to the police beatings and windows broken in the middle of the night — in the name of the working class. The regime was called “the dictatorship of the proletariat,” but that must have been a grammatical error: It was most obviously a dictatorship over the proletariat. The workers were kept deep in misery, ignorance and poverty. They were treated like beasts of burden and told that they were lucky, that under capitalism, their lives would be so much worse. In school, many subjects were covered, but the discipline most widely taught was the art of cognitive dissonance: how to look at all of this and pretend to see none of it. If you mastered the craft, you could survive, even though you were left seriously broken inside. I lived in “1984,” knew it like the back of my hand, long before I discovered the book.' back

Fermion - Wikipedia, Fermion - Wikipedia, the free encyclopedia, 'In particle physics, fermions are particles with a half-integer spin, such as protons and electrons. They obey the Fermi-Dirac statistics and are named after Enrico Fermi. In the Standard Model there are two types of elementary fermions: quarks and leptons. . . . In contrast to bosons, only one fermion can occupy a quantum state at a given time (they obey the Pauli Exclusion Principle). Thus, if more than one fermion occupies the same place in space, the properties of each fermion (e.g. its spin) must be different from the rest. Therefore fermions are usually related with matter while bosons are related with radiation, though the separation between the two is not clear in quantum physics. back

Gödel's incompleteness theorems - Wikipedia, Gödel's incompleteness theorems - Wikipedia, 'Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible, giving a negative answer to Hilbert's second problem. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (i.e., any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency.' back

Hilbert space - Wikipedia, Hilbert space - Wikipedia, the free encyclopedia, ' The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It extends the methods of vector algebra and calculus from the two-dimensional Euclidean plane and three-dimensional space to spaces with any finite or infinite number of dimensions. A Hilbert space is a vector space equipped with an inner product, an operation that allows defining lengths and angles. Furthermore, Hilbert spaces are complete, which means that there are enough limits in the space to allow the techniques of calculus to be used.' back

Holly Ellyatt, ‘Losing is not an option’: Putin is ‘desperate’ to avoid defeat in Ukraine as anxiety rises in Moscow, ' As the weather turns cold once again, and back to the freezing and muddy conditions that Russia’s invading forces experienced at the start of the conflict, Moscow faces what’s likely to be months more fighting, military losses and potential defeat. That, Russian political analysts say, will be catastrophic for Putin and the Kremlin, who have banked Russia’s global capital on winning the war against Ukraine. They told CNBC that anxiety was rising in Moscow over how the war was progressing. “Since September, I see a lot of changes [in Russia] and a lot of fears,” Tatiana Stanovaya, a nonresident scholar at the Carnegie Endowment for International Peace and founder and head of political analysis firm R.Politik, told CNBC. back

José Paulo Florenzano , Pelé was ensnared by ‘Brazilian-style racism’ but stood firm as dictatorship tried to keep him playing , ' Pelé’s trajectory reveals that soccer can be transformed into a space for the anti-racist struggle. In steadfastly refusing to be seen as simply a soccer player and in pursuing a career away from the pitch, Pele exerted a right that Afro-Brazilians not be excluded from activities historically monopolised by the more privileged white groups. The historical significance of Pelé chimes with the present context Brazil finds itself in. After four years of an extreme right-wing government, the return of a government not inclined to diminishing democracy, and committed to the anti-racist struggle, represents the resumption of a trajectory for Brazil that Pelé’s own journey illustrated. back

Laplace's demon - Wikipedia, Laplace's demon - Wikipedia, the free encyclopedia, ' We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.' A Philosophical Essay on Probabilities, Essai philosophique dur les probabilites introduction to the second edition of Theorie analytique des probabilites based on a lecture given in 1794. back

Matthew Smaltz, Pope Benedict XVI: A man at odds with the modern world who leaves a legacy of intellectual brilliance and controversy , ' Most recently, a January 2022 report on sexual abuse in the diocese of Munich criticized Ratzinger’s “inaction” regarding four cases of sexual abuse during his period as archbishop from 1977 to 1982. In reaction to the report, the pope emeritus apologized but did not admit to any administrative failures. Benedict XVI’s writings will be relevant decades from now, but his pontificate will inevitably be associated with controversies. As for his own personal legacy, that will likely be defined by the one issue that concerned Benedict the most: how the Catholic Church can still make a difference in the modern world.' back

Noether's theorem - Wikipedia, Noether's theorem - Wikipedia, the free encyclopedia, 'Noether's (first) theorem states that any differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proved by German mathematician Emmy Noether in 1915 and published in 1918. The action of a physical system is the integral over time of a Lagrangian function (which may or may not be an integral over space of a Lagrangian density function), from which the system's behavior can be determined by the principle of least action.' back

Patriarch Kirill of Moscow - Wikipedia, Patriarch Kirill of Moscow - Wikipedia, the free encylopedia, ' Kirill or Cyril (Russian: Кирилл, secular name Vladimir Mikhailovich Gundyayev, Russian: Владимир Михайлович Гундяев; born 20 November 1946) is a Russian Orthodox bishop. He became Patriarch of Moscow and all Rus' and Primate of the Russian Orthodox Church on 1 February 2009. Prior to becoming Patriarch, Kirill was Archbishop (later Metropolitan) of Smolensk and Kaliningrad beginning on 26 December 1984, and also Chairman of the Russian Orthodox Church's Department for External Church Relations and a permanent member of the Holy Synod beginning in 1989.' back

Phoneme - Wikipedia, Phoneme - Wikipedia, the free encyclopedia, 'A phoneme is one of the units of sound (or gesture in the case of sign languages, see chereme) that distinguish one word from another in a particular language. The difference in meaning between the English words kill and kiss is a result of the exchange of the phoneme /l/ for the phoneme /s/. Two words that differ in meaning through a contrast of a single phoneme form a minimal pair. In linguistics, phonemes (established by the use of minimal pairs, such as kill vs kiss or pat vs bat) are written between slashes like this: /p/, whereas when it is desired to show the more exact pronunciation of any sound, linguists use square brackets, for example [pʰ] (indicating an aspirated p).' back

Pope John Paul II: Joseph Cardinal Ratzinger (1984), Congregation for the Docrine of the Faith: Instruction on Certain Aspects of the "Theology of Liberation", ' Liberation is first and foremost liberation from the radical slavery of sin. Its end and its goal is the freedom of the children of God, which is the gift of grace. As a logical consequence, it calls for freedom from many different kinds of slavery in the cultural, economic, social, and political spheres, all of which derive ultimately from sin, and so often prevent people from living in a manner befitting their dignity. To discern clearly what is fundamental to this issue and what is a by-product of it, is an indispensable condition for any theological reflection on liberation. . . . The present Instruction has a much more limited and precise purpose: to draw the attention of pastors, theologians, and all the faithful to the deviations, and risks of deviation, damaging to the faith and to Christian living, that are brought about by certain forms of liberation theology which use, in an insufficiently critical manner, concepts borrowed from various currents of Marxist thought.' back

Pope John Paul II: Joseph Cardinal Ratzinger (1984), Congregation for the Docrine of the Faith: Letter to the Bishops of the Catholic Church on the Pastoral Care of Homsexual Persons, ' 12. What, then, are homosexual persons to do who seek to follow the Lord? Fundamentally, they are called to enact the will of God in their life by joining whatever sufferings and difficulties they experience in virtue of their condition to the sacrifice of the Lord's Cross. That Cross, for the believer, is a fruitful sacrifice since from that death come life and redemption. While any call to carry the cross or to understand a Christian's suffering in this way will predictably be met with bitter ridicule by some, it should be remembered that this is the way to eternal life for all who follow Christ.' back

Pope John Paul II: Joseph Cardinal Ratzinger (1984), Congregation for the Docrine of the Faith: Notification in te book "Jesus Symbol of God" by Father Roger Haight S. J., ' In publishing this Notification, the Congregation for the Doctrine of the Faith is obliged to declare that the above-mentioned assertions contained in the book Jesus Symbol of God by Father Roger Haight S.J. are judged to be serious doctrinal errors contrary to the divine and catholic faith of the Church. As a consequence, until such time as his positions are corrected to be in complete conformity with the doctrine of the Church, the Author may not teach Catholic theology.' back

Pope John Paul II: Joseph Cardinal Ratzinger (1990), Congregation for the Docrine of the Faith: Donum Veritatis on the Ecclesial Vocation of the Theologian, ' 6. Among the vocations awakened in this way by the Spirit in the Church is that of the theologian. His role is to pursue in a particular way an ever deeper understanding of the Word of God found in the inspired Scriptures and handed on by the living Tradition of the Church. He does this in communion with the Magisterium which has been charged with the responsibility of preserving the deposit of faith. It is the theologian's task in this perspective to draw from the surrounding culture those elements which will allow him better to illumine one or other aspect of the mysteries of faith. This is certainly an arduous task that has its risks, but it is legitimate in itself and should be encouraged. 12. Freedom of research, which the academic community rightly holds most precious, means an openness to accepting the truth that emerges at the end of an investigation in which no element has intruded that is foreign to the methodology corresponding to the object under study.' In theology this freedom of inquiry is the hallmark of a rational discipline whose object is given by Revelation, handed on and interpreted in the Church under the authority of the Magisterium, and received by faith. These givens have the force of principles. To eliminate them would mean to cease doing theology. ' back

Pope John Paul II: Joseph Cardinal Ratzinger (2000), Congregation of the Doctrine of the Faith:Declaration "Dominus Jesus" on the Unicity and Salvific Universality of Jesus Christ and the Church, ' 3. In the practice of dialogue between the Christian faith and other religious traditions, as well as in seeking to understand its theoretical basis more deeply, new questions arise that need to be addressed through pursuing new paths of research, advancing proposals, and suggesting ways of acting that call for attentive discernment. In this task, the present Declaration seeks to recall to Bishops, theologians, and all the Catholic faithful, certain indispensable elements of Christian doctrine, which may help theological reflection in developing solutions consistent with the contents of the faith and responsive to the pressing needs of contemporary culture. ' back

Rafael M. Almeida et al, Floating solar power could help fight climate change — let’s get it right, ' For now, floatovoltaics make up a tiny part of the electricity picture. As of 2020, the global installed capacity of floating solar panels was just 3 GW11, compared with more than 700 GW for land-based solar systems12. But the potential for expansion is considerable, given the vast number of reservoirs worldwide — with a total area roughly equivalent to that of France. Covering 10% of the world’s hydropower reservoirs with floating solar panels would install nearly 4,000 GW of solar capacity9 — equivalent to the electricity-generation capacity of all fossil-fuel plants in operation worldwide.' back

Richard Feyman, FLP III_1: Quantum Behaviour, ' Summary: 1. The probability of an event in an ideal experiment is given by the square of the absolute value of a complex number ϕ which is called the probability amplitude:

P = probability, ϕ = probability amplitude, P = |ϕ|2
2. When an event can occur in several alternative ways, the probability amplitude for the event is the sum of the probability amplitudes for each way considered separately. There is interference:

ϕ = ϕ1 + ϕ2, P=|ϕ1+ϕ2|2
3. If an experiment is performed which is capable of determining whether one or another alternative is actually taken, the probability of the event is the sum of the probabilities for each alternative. The interference is lost.
,br> P = P1 + P2.' back

Rui, Mai & Zheng, For China’s intellectuals, restrictions started long before the pandemic and will continue after Covid is over , ' A literature teacher at a Guangzhou-based university surnamed Liu – who did not wish to give her full name due to the sensitivity of the subject – said at each faculty meeting she was reminded she was not supposed to talk to students about seven subjects. They include universal values, press freedom and civil rights. Those seven topics were designated taboo in college courses in 2013, the year Xi became president, and have since been established as a firm red line in ideology in Chinese universities.' back

Sara J. Brenneis, Spain’s new memory law dredges up a painful chapter of Spain’s often forgotten ties to Nazis, ' Walking down a tree-lined street in the Poble Sec neighborhood of Barcelona, one might easily miss a small bronze square set into the sidewalk. Stamped into the metal in the regional language of Catalan are the words: “Here lived Francesc Boix Campo, born 1920, exiled 1939, deported 1941, Mauthausen, liberated.” Holocaust memorials like this one – which honors a Spanish Nazi concentration camp survivor – are part of a project that started in Germany but has expanded over the past few years across Europe and the United States. These unassuming memorials hide a mighty purpose – making the victims of a traumatic past a visible and permanent part of the modern landscape.' back

Turing machine - Wikipedia, Turing machine - Wikipedia, the free encyclopedia, ' A Turing machine is a hypothetical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a computer. The "machine" was invented in 1936 by Alan Turingwho called it an "a-machine" (automatic machine). The Turing machine is not intended as practical computing technology, but rather as a hypothetical device representing a computing machine. Turing machines help computer scientists understand the limits of mechanical computation.' back

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