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Notes

Sunday 30 May 2021 - Saturday 5 June 2021

[Notebook: DB 86: Hilbert / Minkowski]

[page 245]

Sunday 30 May 2021

Some might see raking over the Summa as an exercise in anachronism, as though theology, religion and the Catholic Church have totally changed in the interim, but I feel that actually doing a job on the Summa, backed by more recent documentation from the Church and other religious institutions

[page 256]

particularly the extremist and militarist wings of all religions, will show that the revolution in theology has not really started. In particular, I hold out come hope that the quantum mechanical input into theology will clarify our understanding of the universe and our place within it. My hope is to capitalize on the work I have done since my decision in 1961 to join the Dominican Order. Dominicans: Order of Preachers

Monday 31 May 2021

The Son is the Father's image of himself and so we might say that they are inside the Father within the initial singularity, constrained by the fixed point theorem to be a finite particle, within which the next layer of the universe is formed rather like the Russian dolls growing inside the Russian dolls. Brouwer fixed point theorem - Wikipedia

Divine Universe is not eternal, tota simul, in fact the time rate of change of the Universe is its energy, measured by the rate of succession of local spacelike slices.

We might think that linear systems cannot create particles but when two lines cross they identify a point. Every angel is a separate species and we may think of them as existing in the amplitude realm and when they meet they exchange specific messages which we in the word call a particle or an observation.

Tuesday 1 June 2021

[page 247]

Wednesday 2 June 2021
Thursday 3 June 2021

Quid est hoc quod est esse? The easy Christian answer – it is all in God's hands. More complex answer: evolution and our own role in our creation.

Aquinas's treatment of the Trinity is strongly logical and borders on inconsistency as he tries to reconcile the scutum trinitatis three identical divine personalities which are nevertheless both one god and orthogonal to one another. I am looking at it carefully to see if I can use the same framework to explain a transfinity within one divine universe [one fixed point per mapping; number of possible mappings is proportional to the number of permutations of the set mapped onto itself??]. The answer I glimpse is that God (= the Universe) is essentially one and dynamic. On the other hand Quantum field theory seems to skirt very closely to inconsistency and so I am looking to use the Thomistic view of God to purify physics, although from an empirical [modern] point of view his physics is way off. It seems in a way that we can see Hilbert space as the angelic heart of the physical universe. Shield of the Trinity - Wikipedia

Thomas says that the final cause is the first of causes, whereas in an evolving Universe it is the last.

Aquinas's work is heavy on logic and linguistic distinctions and these technologies play the part for him that mathematics plays in physics. Mathematics has gained a central position because of measurement and quantification, but it sometimes seems that logical consistency has to be sacrificed to get the mathematics to work.

[page 248]

Friday 4 June 2021

Although Aquinas was my favourite author I have never read the Summa through and I see that the next two years writing quantum theology as my apprenticeship for becoming a public commentator on the state of theology.

Action plus fixed point theory does it all. Outside the universe is contradiction. Fixed points require recursion.

Inertial motion is the basic stance of the dynamic universe: stasis and acceleration require cause [ie relative stasis requires binding/communication]. But all inertial motion at less than c has a rest frame.

In the Aquinas commentary I use the first person as he does, although I am a bit shy about it it is probably more modest and responsible than the royal we!

Theology and religion have two aims — peace and harmony between people and within individuals, ie all pairs of people and within all people [ie sufficient communication to establish stable relationships].

Saturday 5 June 2021

On with the Aquinas job. Sometimes it is so far away from me that there is not much connection, but it is slowly slipping into the motivation for a short essay on each article based on

[page 249]

the points of doctrine in it. Currently up to article number 251 in the Pauline edition. So should end the first [exploratory] run through the Prima Pars by the end of this month [and then settle down to along period of steady writing]. Thomas Aquinas; Summa Theologiae

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Further reading

Books

Aquinas, Thomas, Summa Theologiae, Editiones Paulinae 1962 back

Cantor, Georg, Contributions to the Founding of the Theory of Transfinite Numbers (Translated, with Introduction and Notes by Philip E B Jourdain), Dover 1895, 1897, 1955 Jacket: 'One of the greatest mathematical classics of all time, this work established a new field of mathematics which was to be of incalculable importance in topology, number theory, analysis, theory of functions, etc, as well as the entire field of modern logic.' 
Amazon
  back

Chaitin, Gregory J, Information, Randomness & Incompleteness: Papers on Algorithmic Information Theory, World Scientific 1987 Jacket: 'Algorithmic information theory is a branch of computational complexity theory concerned with the size of computer programs rather than with their running time. . . . The theory combines features of probability theory, information theory, statistical mechanics and thermodynamics, and recursive function or computability theory. ... [A] major application of algorithmic information theory has been the dramatic new light it throws on Goedel's famous incompleteness theorem and on the limitations of the axiomatic method. . . .' 
Amazon
  back

Feynman (1988), 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.' 
Amazon
  back

Gardner, Erle Stanley, The Case of the Singing Skirt, Fawcett 1992 From the Inside Flap 'Ellen Robb does more than just sing for her supper -- she also dances and sells cigarettes in a two-bit gambling parlor in a one-horse town. But when she hits a sour note with her scheming employer by refusing to help fleece a fat-cat customer in a crooked card game, she finds herself out of all three jobs. That's when she sings her song of woe to Perry Mason, who promises to turn her blues into greenbacks with the help of his crack team, Della Street and Paul Drake, and a hefty lawsuit. Things are humming along just fine -- until murder interrupts the merry melody of Mason's crafty legal maneuvers. When the vindictive wife of Ellen Robb's not-so-secret lover turns up shot to death, Mason is certain it's a frame-up -- and that his songbird client's belligerent boss is to blame. Until his own gun is found at the scene. The cocksure Mason will have to change his tune -- and do some quick thinking -- or else this case could be his swan song.' 
Amazon
  back

Higman, Bryan, Applied Group-Theoretic and Matrix Methods, Dover Publications Jacket: '... This work, a comprehensive, thoroughly reliable exposition of the basic ideas of group theory (realized through matrices) and its applications to various areas of physics and chemistry, systematically covers this important ground for the first time. ... Although [it] deals basiclaly with advanced level material, the unusually clear exposition provides much valuable insight and fruitful suggestion for student and specialist alike. Chemists, physicists, mathematicians, and others who would like an idea of the applications and methods of group and matrix theory in the physical sciences will profit greatly from this book. ...'back

Jech, Thomas, Set Theory, Springer 1997 Jacket: 'This book covers major areas of modern set theory: cardinal arithmetic, constructible sets, forcing and Boolean-valued models, large cardinals and descriptive set theory. . . . It can be used as a textbook for a graduate course in set theory and can serve as a reference book.' 
Amazon
  back

Kuhn, Thomas S, Black-Body Theory and the Quantum Discontinuity 1894-1912, University of Chicago Press 1987 Jacket: '[This book] traces the emergence of discontinuous physics during the early years of this century. Breaking with historiographic tradition, Kuhn maintains that, though clearly due to Max Planck, the concept of discontinuous energy change does not originate in his work. Instead it was introduced by physicists trying to understand the success of his brilliant new theory of black-body radiation.' 
Amazon
  back

Lonergan, Bernard J F, Insight: A Study of Human Understanding (Collected Works of Bernard Lonergan : Volume 3), University of Toronto Press 1992 '. . . Bernard Lonergan's masterwork. Its aim is nothing less than insight into insight itself, an understanding of understanding' 
Amazon
  back

Misner, Charles W, and Kip S Thorne, John Archibald Wheeler, Gravitation, Freeman 1973 Jacket: 'Einstein's description of gravitation as curvature of spacetime led directly to that greatest of all predictions of his theory, that the universe itself is dynamic. Physics still has far to go to come to terms with this amazing fact and what it means for man and his relation to the universe. John Archibald Wheeler. . . . this is a book on Einstein's theory of gravity. . . . ' 
Amazon
  back

Nixon, Richard Milhous, The Memoirs of Richard Nixon, Buccaneer Books 1994 Amazon editorial review: 'Former President Richard Nixon's bestselling autobiography is an intensely personal examination of his life, public career, and White House years. With startling candor, Nixon reveals his beliefs, doubts, and behind-the-scenes decisions, and sheds new light on his landmark diplomatic initiatives, political campaigns, and historic decision to resign from the presidency. Throughout his career, Richard Nixon made extensive notes about his ideas, conversations, activities, and meetings. During his presidency, from November 1971 until April 1973, and again in June and July 1974, he kept an almost daily diary of reflections, analyses, and perceptions. These notes and diary dictations, which are quoted throughout this book, provide a unique insight into the complexities of the modern presidency and the great issues of American policy and politics.' 
Amazon
  back

Pais, Abraham, 'Subtle is the Lord...': The Science and Life of Albert Einstein, Oxford UP 1982 Jacket: In this . . . major work Abraham Pais, himself an eminent physicist who worked alongside Einstein in the post-war years, traces the development of Einstein's entire ouvre. . . . Running through the book is a completely non-scientific biography . . . including many letters which appear in English for the first time, as well as other information not published before.' 
Amazon
  back

Yourgrau, Wolfgang, and Stanley Mandelstam, Variational Principles in Dynamics and Quantum Theory, Dover 1979 Variational principles serve as filters for parititioning the set of dynamic possibilities of a system into a high probability and a low probability set. The method derives from De Maupertuis (1698-1759) who formulated the principle of least action, which states that physical laws include a rule of economy, the principle of least action. This principle states that in a mathematically described dynamic system will move so as to minimise action. Yourgrau and andelstam explains the application of this principle to a variety of physical systems.  
Amazon
  back

Papers

Bouwmeester, Dick, "High NOON for photons", Nature, 429, 6989, 13 May 2004, page 139-141. 'Entangled photons conspire to create interference patterns that would normally be associated with a wavelength much smaller than that of the individual photons, beating the diffraction limit.'. back

Szathnary, Eors, Peter Hammersetin, "John Maynard-Smith (1920-2004)", Nature, 429, 6989, 20 May 2004, page 258-259. 'John Maynard-Smith ... made crucial contributions to several debates in evolutionary theory: the levels -- genes, the individual organism, and so on -- at which natural selection operates effectively; the maintenance of sex as a costly mode of reproduction; the use of game theory for biological analysis of conflict and cooperation; the characteristics of major evolutionary transitions, such as the origin of multicellularity; and the logic of animal signalling. ... Maynard-Smith observed succinctly that twentieth-century biology is more about the role of information in biology than about anything else. The terminology of molecular biology (transcription, translation, proofreading and so on), the concept of positional information in embryology, the nervous system as information processor and the questions on animal signalling (about which he published his last book just a few months ago) all confirm the validity of this point. ... '. back

Tschumperlin, Daniel J, et al, "Mechanotransduction through growth-factor shedding into the extracellular space", Nature, 429, 6987, 6 May 2004, page 83-86. 'Physical forces elicit biochemical signalling in a diverse array of cells, tissues and organisms, helping to govern fundamental biological processes. Several hypotheses have been advanced that link physical forces to intracellular signalling pathways, but in most cases the molecular mechanisms of mechanotransduction remain elusive. Here we find that compressive stress shrinks the lateral intercellular space surrounding epithelial cells and triggers cellular signalling via autocrine binding of epidermal growth factor family ligands to the epidermal growth factor receptor.'. back

Walther, Philip, et al, "De Broglie wavelength of a non-local four-photon state", Nature, 429, 6989, 13 May 2004, page 158-161. 'Superposition is one of the most distinctive features of quantum theory and has been demonstratred in numerous single particle interference experiments. Quantum entanglement, the coherent superposition of states in multi-particle systems, yields more complex phenomena. One important type of multi-particle experiment uses path entangled number states, which exhibit pure higher order interference and potential for applications in metrology and imaging; ... It has been generally understood that in optical implemetations of such schemes, lower order interference effects always decrease the overall performance at higher particle numbers. ... Here we have overcome this limitation, demonstrating a four-photon inteferometer based on linear optics. ... We anticipate that this scheme should be extendable to arbitrary photon numersa, holding promise for realizable applications with entanglement-enhanced performance.'. back

Links

Anne Hyland, It’s a gas, gas, gas: How Aussie richlisters plan to unlock a fracking fortune in the NT, ' The government further claims that gas is necessary to drive a manufacturing-led recovery in Australia. However, this has been disputed by bodies such as the Grattan Institute, which says gas does not stack up as a transition fuel. Grattan’s energy director Tony Wood, a former Origin executive, in a report last year, argued: “Even if the government could significantly reduce gas prices, the benefits to manufacturing are overstated. The companies that would benefit most contribute only about 0.1 per cent of gross domestic product.” ' back

Brouwer fixed point theorem - Wikipedia, Brouwer fixed point theorem - Wikipedia, the free encyclopedia, ' Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after Luitzen Brouwer. It states that for any continuous function f with certain properties there is a point x0 such that f(x0) = x0. The simplest form of Brouwer's theorem is for continuous functions f from a disk D to itself. A more general form is for continuous functions from a convex compact subset K of Euclidean space to itself.' back

Dominicans, Order of Preachers, '... the official international Web site of the Order of Preachers (the Dominicans). The branches of the Dominican family are multiple: brothers, contemplative nuns, congregations of contemplative and apostolic sisters, lay persons in fraternities or secular institutes, secular priests in fraternities.' back

Emma Christopher, From the Caribbean to Queensland: re-examining Australia’s ‘blackbirding’ past and its roots in the global slave trade, ' If Pacific labour is seen not as an Australian peculiarity but instead as part of the global slave trade, it becomes far easier to grasp the scope of the grief and disadvantage that Australian South Sea Islanders are still dealing with. As Pacific Islanders have been demanding for some time, we need to examine and confront this history before we can move forward.' back

Erik P Verlinde, The Origins of gravity and the Laws of Newton, 'Starting from first principles and general assumptions Newton's law of gravitation is shown to arise naturally and unavoidably in a theory in which space is emergent through a holographic scenario. Gravity is explained as an entropic force caused by changes in the information associated with the positions of material bodies. A relativistic generalization of the presented arguments directly leads to the Einstein equations. When space is emergent even Newton's law of inertia needs to be explained. The equivalence principle leads us to conclude that it is actually this law of inertia whose origin is entropic.' back

Faha Katun, Holy Rights, 'Safia, a deeply religious Muslim woman from Bhopal in Central India, driven by her belief that because of the patriarchal mindset of the interpreters of ‘Sharia’, Muslim women are denied equality and justice in the community. She joins a program that trains women as Qazis, (Muslim clerics who interpret and administer the personal law), which is traditionally a male preserve.' back

Haidar Eid, In this confrontation with apartheid Israel, the Palestinians won, 'Edward Said once said that the intellectual is supposed to be, “someone who cannot easily be co-opted by governments or corporations, and whose raison d’etre is to represent all those people and issues that are routinely forgotten or swept under the rug.” back

Haidar Eid, B’Tselem’s ‘bombshell’ apartheid report: Stating the obvious, ' The International Convention on the Suppression and Punishment of the Crimes of Apartheid (ICSPCA), Article 2, Part 3, defines apartheid as: “Any legislative measures and other measures calculated to prevent a racial group or groups from participation in the political, social, economic and cultural life of the country and the deliberate creation of conditions preventing the full development of such a group or groups, in particular by denying to members of a racial group or groups basic human rights and freedoms, including the right to work, the right to form recognized trade unions, the right to education, the right to leave and to return to their country, the right to a nationality, the right to freedom of movement and residence, the right to freedom of opinion and expression, and the right to freedom of peaceful assembly and association.” ' back

Jennifer Kahn, The Disease Detective, ' The practice that DeRisi helped pioneer to skirt this problem is known as metagenomic sequencing. . . . Metagenomic sequencing is especially good at what scientists call “environmental sampling”: identifying, say, every type of bacteria present in the gut microbiome, or in a teaspoon of seawater. Such studies have revealed just how vast the microbial world is, and how little we know about it. One study found more than 1,000 different kinds of viruses in a tiny amount of human stool; another found a million in a couple of pounds of marine sediment. And most were organisms that nobody had seen before. ' back

Joseph W. Tobin, The Long Game: Pope Francis’s vision of synodality, ' When I say “conversion,” I’m talking about the Church’s own conversion, a new way in understanding and approaching how we carry out our mission. Francis has rightly decried the mindset of “But we’ve always done it this way.” John XXIII famously said that we in the Church are not called to guard a museum but to tend to a flourishing garden of life. The same goes for a synodal Church. You can’t show up with an imperious attitude, as if you have all the answers.' back

Massimo Faggioli, Germany Takes a Synodal Path, ' Does the Church have the power to bless same-sex unions? That was the question posed in a dubium submitted to the Congregation for the Doctrine of Faith in February, and the answer that was made public some weeks later is by now well known: no. That the response received the assent of Pope Francis also received a lot of attention, much of it negative, especially in the secular, liberal-progressive circles of the West. . . . But maybe the most interesting reaction came out of Germany, where, on May 10, about a hundred Catholic churches around the country held blessing ceremonies for same-sex couples.' back

Max Hastings, With Trump Gone, Diplomacy Is No Longer a Dirty Word, ' Diplomacy, one of the most unfashionable words of the Donald Trump era — alongside “ally” and “partner” — is making a comeback. President Joe Biden’s administration seeks to get the Israelis talking to the Palestinians again; to achieve serious speaking terms with China; and to rescue the State Department from the abandoned railyard where it languished during the past decade. . . . ' But the talking must happen, the attempts be made to find common ground even on lesser issues if the big ones are intractable. I once met a diplomat who spent much of the 1960s representing Britain at international arms-control talks in Geneva. He argued that, while superficially the interminable meetings were futile, with the Soviets churning out position papers that never seemed to change, the very fact of the meetings helped to avert war. ' I think he was right — the isolationists who seek simply to build walls and hide behind them put at risk any advance or even stability in human affairs. Fear has been the dominant motive in foreign affairs since the beginning of time. Dialogue — diplomacy — has a critical role to play in managing and dispelling it..' back

Michael Bradley, Friday essay: reckoning with an animal that sees us as prey — living and working in crocodile country, ' . . . crocodiles are a threat. Young salties eat fish and crabs. As they grow, they move on to larger prey — dogs, pigs, people, horses and buffalo. Our species fits comfortably in their diet, slipping into the line-up between pigs and horses. Crocodiles may be opportunistic hunters, but their encounters with prey aren’t chance. They think about it. They watch, and they learn. Wash your pots and pans on the riverbank every evening, and you are inviting an attack. For people along the coastline of the tropical arc between Eastern India and Australia, they colour the water’s edge with a lurking malice and the threat of a violent death.' back

Observer editorial, The Observer view on deadly government incompetence, ' That Boris Johnson lacks the leadership skills, capability and integrity to guide the country through a national emergency is not a new insight: it has been clear for months. But the significance of Dominic Cummings’ testimony to the House of Commons last week was that the prime minister’s former adviser provided more evidence of Johnson’s culpability for decisions that cost countless lives.' back

Ruth Schuster, World’s ‘First War’ 13,400 Years Ago Wasn't Isolated Episode but Series of Events , ' Humankind is a bellicose lot and probably always has been, yet evidence in prehistory that we used our stone tools not only to hunt prey but each other has been scanty. Then, in 2014, archaeologists deduced that a site discovered in Sudan decades before wasn’t a prehistoric cemetery on the bucolic banks of the Nile but the site where the victims of the world’s first organized war were interred. . . . ' The research for the paper published Thursday in Scientific Reports was done on remains preserved in the British Museum, Isabelle Crevecoeur and team clarify. . . . ' These disparate groups may have been fighting over resources in a time of frightening climate change, and it wasn’t an isolated spasm of rage.' back

Shield of the Trinity - Wikipedia, Shield of the Trinity - Wikipedia, the free encyclopedia, 'The Shield of the Trinity or Scutum Fidei is a traditional Christian visual symbol which expresses many aspects of the doctrine of the Trinity, summarizing the first part of the Athanasian Creed in a compact diagram. In late medieval England and France, this emblem was considered to be the heraldic arms of God (and of the Trinity).' back

Siddiqui, Hussein, Zaheer & Haddad, Infographic: What you need to know about Israel’s military, ' The US is by far the biggest supplier of military aid to Israel, providing the country with a total of $3.8bn in 2020 as part of a record $38bn deal across a 10-year period signed under former US President Barack Obama in 2016. . . . In comparison, the US allocated $19m in all forms of aid to the Palestinians in 2020, according to USAID, after the Trump administration suspended most funding to the Palestinian Authority as his government promoted a so-called “peace plan” that the Palestinians denounced as one-sided.' back

William Nash, ‘The Underground Railroad’ attempts to upend viewers’ notions of what it meant to be enslaved , ' Speaking on NPR’s Fresh Air, Barry Jenkins, the director of “The Underground Railroad,” noted that “before making this show … I would have said I’m the descendant of enslaved Africans.” “I think now that answer has evolved,” he continued. “I am the descendant of blacksmiths and midwives and herbalists and spiritualists.” As a scholar interested in how modern representations of enslavement shape our understanding of the past, I am struck by the ways Jenkins seeks to change the way viewers think about – and talk about – Black American history. In doing so, he takes the baton from scholars, activists and artists who have, for decades, attempted to shake up Americans’ understanding of slavery. Much of this work has centered on reimagining slaves not as objects who were acted upon, but as individuals who maintained identities and agency – however limited – despite their status as property.' back

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