Notes DB 92: Physical Theology II - 2025
Sunday 18 May 2025 - Saturday 24 May 2025
[page 157]
Sunday 18 May 2025
Naked gravitation is the necessary being, essence identical to existence. So we identify the initial singularity with the Thomisitc God and with naked gravitation.
Physical evidence for theology, a final run through?
[page 158]
In effect Einstein used differential geometry
‘All that I have written seems like straw [chaff] compared to what has been revealed to me’ [perhaps he saw that the universe itself is divine?]. Marjorie O'Rorke Boyle (1997): Chaff: Thomas Aquinas's Repudiation of His Opera omnia
Thales: “The world is full of gods; Aristotle on Thales: On the Soul, 411a7-8
Aquinas: “god is not of this world”; Augustine “there are three discrete persons in god”; Nicholls: “god is part of the world’; back to Thales: “every quantum of action in the world is a god. controlling what we experience. The world is full of gods.
Pasnau: Aquinas: “On the eternity of the world: the key is to see where philosophy can be of service, and where it must give way to revealed doctrine.” In fact all possible revelation is physical. Robert Pasnau (Stanford Encyclopedia of Philosophy): Thomas Aquinas, Thomas Aquinas: Opusculum: De Aeternitate Mundi
Particulate approach to spacetime: Aristotle / Aquinas “space is nothing but the existence of bodies”. God omnipresent and eternity means present at every moment of space and time a la Newton Scholium. Isaac Newton (1729): 'General Scholium' from the Mathematical Principles of Natural Philosophy (1729)
Aquinas: ‘The created world has a ongoing cause ha conserves it.’ This description fits gravitation as eternal creator and conserver.
Now every creature may be compared to God, as the air is to the sun which enlightens it. For as the sun possesses light by its nature, and as the air is enlightened by sharing the sun's nature; so God alone is Being in virtue of His own Essence, since His Essence is His existence; whereas every creature has being by participation, so that its essence is not its existence. Aquinas, Summa, I, 104, 1: Do creatures need to be kept in being by God?
This description fits gravitation as eternal creator and conservator.
Glory of god: Aquinas, Summa, I, 65, 2: Were corporeal things created on account of God's goodness?
Angels: Aquinas, Summa, I, 50, 5: Are angels are incorruptible?
Pasnau: §9 Aquinas’ Influence:
For the quarter century after Aquinas’s death, scholasticism took shape around his Dominican supporters snd his Franciscan critics.
I was fortunate
[page 159]
to begin by getting to know Thomas to give a firm foundation to my departure from the Church he served by perverting Aristotle a little [Aristotle’s unmoved mover is part of the universe, but Aquinas interpreted Aristotle’s proof to mean that his God is outside the universe].
Franciscan opponents Scotus and Ockham. Duns Scotus - Wikipedia, William of Ockham - Wikipedia
Pasnau: ‘Dominicans statutorially required to promote [Aquinas’s] teaching. In 1567 Pope Pius made him Doctor of the Church.
In 1879 Pope Lei XIII revived Aquinas with a definitive edition of his work. This led to the work of Jacques Maritain, Etienne Gilson, Gertrude Anscombe and Alasdaire Macintyre. Pope Leo XIII: Aeterni Patris: On the Restoration of Christian Philosophy, Jacques Maritain - Wikipedia, Etienne Gilson - Wikipedia, G. E. M. Anscombe - Wikipedia,
Pasnau: ‘Aquinas today, viewed as a philosopher looks not so much as the culmination of an era, but rather like the brilliant beginning of Europe’s philosophical renaissance’. We really owe this to Aristotle.
Can we say that gravitation is substantial and it can serve as a carrier of abstract formal states? When the abstract quantum states become real [by the acquisition of energy from the zero sum bifurcation of naked gravitation into ℏpotential and kinetic incited by a self adjoint or hermitian operator] we have a particle whose personality is represented by that operator, ie the particle is a basis state of a dynamic Hilbert space. So much to read about QM but I will just plough through [the idea here may be that the basis state of the primordial Hilbert space are the elementary particles which are by definition orthogonal to one another (like individual photons or electrons) but are in effect transformed into one another by rotations in some Hilbert space as, eg, an electron can be rotated into two photons. Following Feynman, first we have to have the idea and then we can attach mathematical symbolism to various bits of it].
I just plough on in my own little furrows. ℏ is an operator which converts energy into frequency, E = ℏω [inverse time], momentum into [inverse space and we imagine that in Hilbert space the quantum of action is a logical invariant].
[page 160]
Diagram illustrating pythogorean relationship E2 = pc2 + (m0c2)2.
All this is [dynamic, living] Minkowski stuff. We want to couple it to [kinematic, formal], quantum mechanics.
Potential energy corresponds to negative mass: potential energy + kinetic energy = 0. E = mc2 + − mc2 = 0. For naked gravitation, something to do with antiparticles [eg electron + positron = massless photons, must be something to do with photon being a piece of Hilbert space loose in Minkowski space. We know energy and momentum are conserved across the border from massive to massless but charge is neutralized. The transformation from Minkowski to Hilbert neutralizes spacetime: is spacetime like a charge? (note added in transcription)]
Monday 19 May 2025
Can we balance the political power of religion against the truth and verifiability of the underlying theology. From the evidence based theological point of view the facts and the truth must take precedence and even if they are politically unpalatable they will become a force moving the religion in the right direction [toward conformity with the reality]. The root particular failure in Catholicism is the exclusion of women from priestly roles most recently emphasized by Pope Paul VI Inter Insigniores. Second Vatican Presbyteriorum Ordines and Optatum Totius. John Paul II Ordinatio Saceedotalis, Wikipedia Ordination of Women. This position means that the Catholic Church fails a reasonable qualification for a Social Licence to Operate [and this error goes right down to the failure to realize that divinity is material, insofar as the old story is that the male proves the form and the female provides the matter]. Pope Paul VI (1976_10_15): Inter Insigniores: On the question of admission of women to the ministerial priesthood, Holy See: Pope Paul VI (1965_12_07): Presbyteriorum ordinis: Decree on the ministry and life of priests, Holy See: Pope Paul VI (1965_10_28): Optatam Totius: Decree on Priestly Training, Ordination of women and the Catholic Church - Wikipedia
[page 161]
We might guess that the principal input into religion and politics is value and a powerful role of science is to teach us what to value by showing us directions in which we would do well to evolve, basically toward peace and productivity while reducing our footprint on the system that sustains us. A complex set of constraints, apparent in our evolution from simians to Homo. Liaoyi Xu et al (2025_04_06): The genetic architecture of and evolutionary constraints on the human pelvic form
Looking for insight into quantum theory to include in frontiers: physical evidence for theology where we are following the line that the invisible underpinning of the universe traditionally attributed to god is in fact a combination of bare gravitation and quantum mechanics which are inside the universe rather than outside, in other words we are saying that an omnipotent, eternal structureless initial singularity can make a universe.
I like to think that I can write an article in a day but this frontiers piece has been going since 11 May and is starting to get very interesting as I explore the consequences of making Hilbert space fundamental. Now I am reading old paper by Kronz and Lupher on von Neumann vs Dirac looking to get to the bottom of my intuition about Hilbert and Minkowski spaces which is now probably about three years old and although I have said it again and again and even put it in my book I am beginning to see I have a long
[page 162]
a long way to go and the result might be quite exciting. As I dig deeper I see that I have skimmed over many debates that may have made incremental progress in my direction but he root of my program is the conceptual leap from physics to psychology incorporated in cognitive cosmogenesis and I am now down to bridging the gaps that I previously skated over. Fred Kronz & Tracy Lupher (Stanford Encyclopedia of Philosophy): Quantum Theory and Mathematical Rigor
Look at Stanford Quantum Logic / Bohmian Mechanics. Alexander Wilce (Stanford Encyclopedia of Philosophy): Quantum Logic and Probability Theory
Bohmian Mechanics:
[Conceptual difficulties have plagued quantum mechanics since its inception, despite its extraordinary predictive successes. The basic problem, plainly put, is this: It is not at all clear what quantum mechanics is about. What, in fact, does quantum mechanics describe? Sheldon Goldstein (Stanford Encyclopedia of Philosophy): Bohmian Mechanics:
In Bohmian mechanics the wave function, obeying Schrödinger’s equation, does not provide a complete description or representation of a quantum system. Rather, it governs the motion of the fundamental variables, the positions of the particles: In the Bohmian mechanical version of nonrelativistic quantum theory, quantum mechanics is fundamentally about the behavior of particles; the particles are described by their positions, and Bohmian mechanics prescribes how these change with time. In this sense, for Bohmian mechanics the particles are primary, or primitive, while the wave function is secondary, or derivative.]
Quantum-Bayesian and Pragmatist Views of Quantum Theory Richard Healey (Stanford Encyclopedia of Philosophy): Quantum-Bayesian and Pragmatist Views of Quantum Theory
Rings of Operators ⇆ von Neumann algebra Von Neumann algebra - Wikipedia
My fundamental feeling is that all this is getting too complex for description of a baby universe one step beyond the initial singularity.
Rigged Hilbert space: - dual pair of Hilbert paces generated from separable Hilbert space neither of which is a Hilbert space because it does not have an inner product. Rigged Hilbert space - Wikipedia
Jennan Ismael: What have I got? Cognitive cosmology: We have to get into the logic of quantum mechanics. It is a life’s work. Isi t worth it. Jennan Ismael (Standord Encyclopedia of Philosophy): Quantum Mechanics, Nielsen & Chuang (2016): Quantum Computation and Quantum Information
We go back to describing quantum mechanics as superposition choosing stationary nodes in the chaotic Hilbert space of the initial singularity which like gravitation is everywhere creating and annihilating particles in the same way as biological evolution continues non-stop everywhere.
[page 163]
The notion that the essence of quantum mechanics is captured by the difference between real and complex numbers gathers weight. From a kinematic point of view the complex numbers are dynamic and from the fact that the self-adjoint values in a matrix, the solutions to a polynomial, suggests that the basis states of Hilbert space should be complex numbers and therefore waves which by superposition can create nodes which are the stationary points, the basis vectors of a Hilbert space which have real statinary eigenvalues which are observable. In this way the selection of elementary particles becomes clear and I must learn enough about it to write it into phyical theology.
I does sound a bit too simple to be true but the real key is to study the qubit |Ψ〉 = a|boson〉 + b|fermion〉 which could be the foundation of Minkowski space, [the physical equivalent of the last universal common ancestor]. We work it out from the Schrödinger equation and its transformation into the Dirac equation. These ideas to be added to the notion that Hilbert space is as Aristotle might say, space ≡ bodies, ie the container of bodies. These thoughts excite me although when I come to work them out in detail I feel very average. The idea would be to write all this as I have done to encourage some real physicists to work on it. Let the heuristic of simplicity [symmetry] be my guide, my shield and my salvation.
[page 164]
Tuesday 20 May 2025
How do we express the digitization of the quantum of action in Hilbert space? It is a feature of a basis state which is an entity selected by a hermitian operator in a quantum measurement, ie a quantum communication, which we understand by Zurek’s article on breaking unitary symmetry, that is to say, in effect, that unitary symmetry never existed in reality in the first place, only in the minds of mathemticians like Dedekind and other prophets of continuity defending the honour of calculus with the doctrine of limits.
An orgasm is a stationary point like an insight or the outcome of a quantum interaction as described by Zurek.
Wednesday 21 May 2025
Beginning to feel that I have got physical theology in the bag, at least for myself, which is all I can go by until I can get something published and get a bit of feedback. Being happy with my own effort is the best payoff, probably a bit like god felt when she first created the world before the angels and humans ruined everything.
My notion of the heuristic of simplicity has
[page 165]
the effect of restricting the options at the beginning to the four binary logical operators, identity, and, or, not which can all be implemented in quantum mechanics (see Nielsen + Chuang), each represented by a matrix representing the superposition of vectors in a complex space. This observation may be taken as the reason for the fact that Hilbert space is complex, to achieve both algebraic and logical completeness along von Neumann’s line toward quantum logic. Is this true, or just an example of my Trumpian tendency to wing things to get the answers I want: basically the idea that all the possibilities are on the table in a universe that begins as an eternal, structureless, omnipotent initial singularity which we identify as bare or naked gravitation, a sexy starting point that supports reproduction as the central selective element in evolution. This passage my sere as a logical abstrct of my essay. Mission possible achieved, just have to write it down and make the movie. It is now 10 days since I started this essay on mother;s day 2025 - for my mother. Ultimately I just love doing what I do and work at a leisurely pace about 16 hours per day,
Austin Macauley contract signed 18 September 2024, Final complete revised MS delivered 30 September 2024. This plus 290 days = 17 July 2025
Can we say particles are the interface between logic and physics
[page 166]
because they are physical objects (substances) carrying a logical personality which is a hermitian operator. In the Zurek mode particles interact logically through their associated operators which are their quantum of action as the highest level of human interaction is controlled by their mental states. A quantum of action is a logical / mental state which may comprise many quantum subroutines, as is required, for instance to walk from A to B. At the simplest level cognitive cosmogenesis must explain the interface between logic and physics and the simplest level is the creation of physical space by the interaction of fermions and bosons creating Minkowski space.
Thursday 22 May 2025
Reading the Stanford encyclopedia and a lot of other stuff I wonder why things as simple s gravitation, quantum mechanics and spacetime have become such complex subjects and I am always trying to exploit the axiom [heuristic] of simplicity to pick out the central point - dynamic naked gravitation, random fixed points, quantum selection, stationary forms becoming realized by the attachment of energy, the duality of fermions and bosons, Minkowski space, general relativity. On top of this we need charge, three further degrees of potential: electromagnetic, weak and strong. So I have a theory of spacetime. Now
[page 167]
which has its roots in two classes of particles, spin 1 and spin ½ Where does this come from? We see it in Minkowski space when we do the Stein-Gerlach experiment and electric charge becomes magnetism in the hands of special relativity. So the key is Schrödinger and Dirac to create spin 1 and spin ½. We begin with a 2D qubit. Now we go to 4D Minkowski, 3Ds of fermion. Entropy trying to increase. Fermions seeking room to move [by mutual exclusion]. What would god do? What would evolution do? Fundamental particles are ephemeral: permance comes from reproduction. Minkowski space is very strong and can only be crushed in a black hole.
How does the energy enter the form? Is the mass of a particle the measure of the rate of action within it? It must be. What is the difference between a massless photon and a massive electron of the same energy? How do charge and the photon a la Maxwell fit together [a la french for latin secundum].
Phone [Rosalie] 6a: Essay on mathematics and reality based on [Landauer] information is physical and the distinction between kinematic and dynamic. Naked gravitation, like traditional god, is structureless and dynamic, intellectual and part of the universe as Aristotle says of the first mover hence the name cognitive cosmogenesis. Rolf Landauer (1999): Information is a Physical Entity
Quantum fluctuations and the cosmological constant problem replaced by fixed point theorem applied to naked gravitation as a continuous empty set.
[page 168]
Complex numbers are observable as periodic events which may be kinematic (driven) or dynamic (driving, living, self moving)
Darwin took from 1831 when he left on the Beagle 22yo until 1859 when Origin was published to become certain of his position 28 years later. It has taken me from How Universal, 1965, 20 yo until 2025, 80 yo, 60 years to become convinced that I feel god in gravity. A slow thinker and writer.
Friday 23 May 2025
Toying with Bohmian mechanics; looking for better representation of QM than stones in a pond. Holland. Up in the air again seeking, like an AI machine, for the next sentence to write based on all the stuff I have “trained” on over the last 80 years. Unlike the machine I have some insight into all this selected training material so maybe my next sentence will make some logical connection to the one before it and not be just a sample of my training input. AI seems to be an bad joke because it is not intelligent, it does not know what it is saying and so the implications of its answers are often wrong, reflecting a feature of the random sample of its input. Peter Holland (1993): The Quantum Theory of Motion: An Account of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics
I am claiming that quantum mechanics is intelligent and it is the natural selector that has built a beautiful and consistent universe. How do I explain its difference from
[page 169]
statistical AI? This is the heart of my story. So far we have got past the cosmological constant problem. Check Stanford Richard Healy QBism: Born rule generally considered objective; QB: “QM is a “user’s manual’ that can help an agent make a wise decision in this world of inherent uncertainty”. How do we do this. With Born Rule. Back to psychophysics? Richard Healey (Stanford Encyclopedia of Philosophy): Quantum-Bayesian and Pragmatist Views of Quantum Theory
. . .
Cognitive cosmology: the link between oe and sex tells something about the lik between physics and theology.
Third round of revision of NICHOLLS – CognitiveCosmogenesis – PPDF (22_05_2025).pdf [posted today]
A countably infinite Hilbert space will have a countably infinite set of nodes and given that it can be continuously rotated in a ‘continuous’ space, an infinite set of countable infinite nodes [basis states].
So we continue to define quantum intelligence in tems of Lonergan's insight, the discoery of a fixed point in the mind which can be described by the paragraph above.
Quote Darwin Clark page 160: ‘How odd it is that anyone could not see that all observations must be before or against some view of it is to be of any service.’ Ronald Clark (1984): The Survival of Charles Darwin: A Biography of a Man and an Idea
[page 170]
Saturday 24 May 2025
Stalled on quantum intelligence. What do we mean by intelligence anyway? Lonergan, Insight: ‘get the point’, see how things fit together. Is this what quantum mechanics does. detecting many dimensions of nodes in a kinematic Hilbert space [by the superposition of kinematic vectors in many dimensions. Active and passive intelligence: make the point versus get the point. Why are the Trumpists against DEI (diersity, equity and Inclusion)? Because they think it discriminates against whites (Kassam). Ashifa Kassam (2025_01_25): What is DEI and why is Trump opposed to it?
Revision proceeds at Chapter 1 page 36. Only one error so far, page 26. Some progress in quantum intelligence via Dirac and eigenvalue equation.
1500: done to end of p 62 - snooze.
2030: beginning chapter 14 - must check all URLs in footnotes. Still happy with the book as I skate carefully around the thin ice [it is the first edition of an upcoming 20 year saga, until I die]
The quantum computationalists trying to isolate single states in single articles seem to have totally missed the point of the social nature of quantum theory based in its multidimensional linearity. I need to incorporate more of this in my story of quantum intelligence [based on my tendency to think of many things at once and frequently forget where I was].
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Further readingBooks
Clark (1984), Ronald W, The Survival of Charles Darwin: A Biography of a Man and an Idea, Random House 1984
Amazon
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Holland (1993), Peter R, The Quantum Theory of Motion: An Account of the de Broglie-Bohm Causal Interpretation of Quantum Mechanics, Cambridge University Press 1993 Jacket: 'This book presents the first comprehensive exposition of the interpretation of quantum mechanics pioneered by Louis de Broglie and David Bohm. . . . Developing the theme that a material system such as an electron is guided by a surrounding quantum wave, a detailed examination of the classic phenomena of quantum theory is presented . . . The theory provides a novel and satisfactory framework for analysing the classical limit of quantum mechanics and Heisenberg's relations, and implies a theory of measurement without wavefunction collapse. It also suggests a strikingly novel view of relativistic quantum theory, including the Dirac equation, quantum field theory and the wavefunction of the universe.'
Amazon
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Nielsen (2016), Michael A., and Isaac L Chuang, Quantum Computation and Quantum Information, Cambridge University Press 2016 Review: A rigorous, comprehensive text on quantum information is timely. The study of quantum information and computation represents a particularly direct route to understanding quantum mechanics. Unlike the traditional route to quantum mechanics via Schroedinger's equation and the hydrogen atom, the study of quantum information requires no calculus, merely a knowledge of complex numbers and matrix multiplication. In addition, quantum information processing gives direct access to the traditionally advanced topics of measurement of quantum systems and decoherence.' Seth Lloyd, Department of Quantum Mechanical Engineering, MIT, Nature 6876: vol 416 page 19, 7 March 2002.
Amazon
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Links
Adriel Trott (2020_01_23), Aristotle and gender: form s matter?, ' Even as strides toward gender equality have been made in the last century, the notion that gender is a binary divided between those who determine the social world – men – and those who need to be determined – women – remains well entrenched. Advertisements depict women as furniture, food and body parts. Assumptions that men are more rational and capable of being brilliant and women emotional and constrained by their bodies continue to affect elections, hiring practices and career advancement, in for example, the academy. But did you know that these ideas can be traced back to Aristotle? Aristotle saw gender – the opposition between men and women, male and female – as associated with an opposition between form and matter. Form and soul give shape to the world. Matter and body are the stuff that needs to be shaped and properly bounded.' back |
Alexander Wilce (Stanford Encyclopedia of Philosophy), Quantum Logic and Probability Theory, 'Mathematically, quantum mechanics can be regarded as a non-classical probability calculus resting upon a non-classical propositional logic. More specifically, in quantum mechanics each probability-bearing proposition of the form “the value of physical quantity AA lies in the range BB” is represented by a projection operator on a Hilbert space H. These form a non-Boolean—in particular, non-distributive—orthocomplemented lattice. Quantum-mechanical states correspond exactly to probability measures (suitably defined) on this lattice.' back |
Andrew Pask & Deidre Mattiske (2019_04_08), All female mammals have a clitoris – we’re starting to work out what that means for their sex lives, ' Amazingly, it was not until the late 1990s that the complete anatomy of the human clitoris was accurately described by Australia’s first female urologist, Helen O’Connell. Her work to understand the detailed form and function of the clitoris provides answers to some basic biological questions about sex.
Such research also has implications in pelvic area surgery, where doctors can use this knowledge to avoid any loss of sexual function. back |
Aquinas, Summa, I, 104, 1, Do creatures need to be kept in being by God?, ' Now every creature may be compared to God, as the air is to the sun which enlightens it. For as the sun possesses light by its nature, and as the air is enlightened by sharing the sun's nature; so God alone is Being in virtue of His own Essence, since His Essence is His existence; whereas every creature has being by participation, so that its essence is not its existence. back |
Aquinas, Summa, I, 50, 5, Are angels are incorruptible?, ' Now to be belongs to a form considered in itself; for everything is an actual being according to its form: whereas matter is an actual being by the form. Consequently a subject composed of matter and form ceases to be actually when the form is separated from the matter. But if the form subsists in its own being, as happens in the angels, as was said above (Article 2), it cannot lose its being. Therefore, the angel's immateriality is the cause why it is incorruptible by its own nature.
A token of this incorruptibility can be gathered from its intellectual operation; for since everything acts according as it is actual, the operation of a thing indicates its mode of being. Now the species and nature of the operation is understood from the object. But an intelligible object, being above time, is everlasting. Hence every intellectual substance is incorruptible of its own nature.' back |
Aquinas, Summa, I, 65, 2, Were corporeal things crested on account of God's goodness?, ' So, therefore, in the parts of the universe also every creature exists for its own proper act and perfection, and the less noble for the nobler, as those creatures that are less noble than man exist for the sake of man, whilst each and every creature exists for the perfection of the entire universe. Furthermore, the entire universe, with all its parts, is ordained towards God as its end, inasmuch as it imitates, as it were, and shows forth the Divine goodness, to the glory of God. Reasonable creatures, however, have in some special and higher manner God as their end, since they can attain to Him by their own operations, by knowing and loving Him. Thus it is plain that the Divine goodness is the end of all corporeal things. back |
Aristotle on Thales, On the Soul, 411a7-8, ' Certain thinkers say that soul is intermingled in the whole universe, and it is perhaps for that reason that Thales came to the opinion that all things are full of gods.' back |
Ashifa Kassam (2025_01_25), What is DEI and why is Trump opposed to it?, ' When American voters headed to the ballot box in November, polls suggested the cost of living, immigration and reproductive rights ranked among their biggest concerns.
But tucked within this week’s barrage of executive orders was an attack on an initiative that had in recent years become increasingly weaponised around the world: measures that sought to tackle discrimination.
Donald Trump signed two executive orders aimed at unwinding the federal government’s decades-long push to ensure an inclusive workplace that reflects American society.
The directives also instruct federal agencies to develop plans to deter diversity, equity and inclusion measures – often referred to as DEI – in the private sector, a move viewed by some as an attempt to ward off companies from addressing discrimination in their workplaces. [. . .]
In 2023, the US supreme court ruled against race-conscious admission programmes at colleges and universities, reversing decades of precedent. The decision emboldened conservatives and unleashed a flood of lawsuits aimed at dismantling policies designed to foster diversity, equity and inclusion
At the heart of these challenges was the argument that these anti-discrimination measures were in fact discriminatory towards the groups that had historically dominated workplaces, including white Americans. back |
Brian Murphy (2025_05_21), Peter Lax, mathematician who found order in the natural world, dies at 99, ' Peter Lax, an innovator in applied mathematics who left Hungary during World War II and worked on U.S. atomic bomb calculations as a college student while developing equations that would later influence fields such as medicine and weather forecasting, died May 16 at his home in Manhattan. He was 99.
The death was announced by the Norwegian Academy of Science and Letters, which in 2005 awarded Dr. Lax the Abel Prize, often called one of the mathematics equivalents of the Nobel Prize. No cause was given.
A mathematics prodigy, Dr. Lax began as a teenager to seek ways to express in numeric terms the movements of the natural world such as how a shock wave dissipates or how a ripple travels down a narrow canal. His equations to convey physical properties — including fluid and wave dynamics — helped provided a foundation for the age of computer modeling in engineering and science.
“I like to start with some phenomenon, the more striking the better, and then use mathematics to try to understand it,” he told the Simons Foundation, a private research group, in 2014.
His breakthroughs in translating aspects of physics into mathematical structure led to some of the most productive early interplays of human imagination and computing power. Dr. Lax used early mainframe systems to run his math through complex variations simulating the real world.
Dr. Lax — who spent nearly his entire career at the Courant Institute of Mathematical Sciences at New York University — once described the influence of computers in mathematics as profound as “the role of telescopes in astronomy and microscopes in biology.” back |
Duns Scotus - Wikipedia, Duns Scotus - Wikipedia, the free encycloepdia, ' John Duns Scotus OFM (1265/66 – 8 November 1308) was a Scottish Catholic priest and Franciscan friar, university professor, philosopher and theologian. He is considered one of the four most important Christian philosopher-theologians of Western Europe in the High Middle Ages, together with Thomas Aquinas, Bonaventure and William of Ockham.
Duns Scotus has had considerable influence on both Catholic and secular thought. The doctrines for which he is best known are the "univocity of being", that existence is the most abstract concept we have, applicable to everything that exists; the formal distinction, a way of distinguishing between different formalities of the same thing; and the idea of haecceity, the property supposed to be in each individual thing that makes it an individual (i.e. a certain “thisness”). back |
Etienne Gilson - Wikipedia, Etienne Gilson - Wikipedia, the free encyclopedia, 'Étienne Henri Gilson (13 June 1884 – 19 September 1978) was a French philosopher and historian of philosophy. A scholar of medieval philosophy, he originally specialised in the thought of Descartes; he also philosophized in the tradition of Thomas Aquinas, although he did not consider himself a neo-Thomist philosopher. [. . .]
Although Gilson was primarily a historian of philosophy, he was also at the forefront of the 20th century revival of Thomism, along with Jacques Maritain. His work has received critical praise from Richard McKeon.' back |
Fred Kronz & Tracy Lupher (Stanford Encyclopedia of Philosophy), Quantum Theory and Mathematical Rigor, ' An ongoing debate in the foundations of quantum physics concerns the role of mathematical rigor. The contrasting views of von Neumann and Dirac provide interesting and informative insights concerning two sides of this debate. Von Neumann’s contributions often emphasize mathematical rigor and Dirac’s contributions emphasize pragmatic concerns. The discussion below begins with an assessment of their contributions to the foundations of quantum mechanics. Their contributions to mathematical physics beyond quantum mechanics are then considered, and the focus will be on the influence that these contributions had on subsequent developments in quantum theorizing, particularly with regards to quantum field theory and its foundations. The entry quantum field theory provides an overview of a variety of approaches to developing a quantum theory of fields. The purpose of this article is to provide a more detailed discussion of mathematically rigorous approaches to quantum field theory, as opposed to conventional approaches, such as Lagrangian quantum field theory, which are generally portrayed as being more heuristic in character. The current debate concerning whether Lagrangian quantum field theory or axiomatic quantum field theory should serve as the basis for interpretive analysis is then discussed.' back |
G. E. M. Anscombe - Wikipedia, G. E. M. Anscombe - Wikipedia, the free encyclopedia, ' Gertrude Elizabeth Margaret Anscombe FBA (8 March 1919 – 5 January 2001), was a British analytic philosopher. She wrote on the philosophy of mind, philosophy of action, philosophical logic, philosophy of language, and ethics. She was a prominent figure of analytical Thomism, a fellow of Somerville College, Oxford, and a professor of philosophy at the University of Cambridge.
Anscombe was a student of Ludwig Wittgenstein and became an authority on his work and edited and translated many books drawn from his writings, above all his Philosophical Investigations. Anscombe's 1958 article "Modern Moral Philosophy" introduced the term consequentialism into the language of analytic philosophy, and had a seminal influence on contemporary virtue ethics. Her monograph Intention (1957) was described by Donald Davidson as "the most important treatment of action since Aristotle".' back |
G. E. M. Anscombe - Wikipedia, G. E. M. Anscombe - Wikipedia, the free encyclopedia, back |
Holy See: Pope Paul VI (1965_10_28), Optatam Totius: Decree on Priestly Training, ' 1. Since only general laws can be made where there exists a wide variety of nations and regions, a special "program of priestly training" is to be undertaken by each country or rite. It must be set up by the episcopal conferences, revised from time to time and approved by the Apostolic See. In this way will the universal laws be adapted to the particular circumstances of the times and localities so that the priestly training will always be in tune with the pastoral needs of those regions in which the ministry is to be exercised.' back |
Holy See: Pope Paul VI (1965_12_07), Presbyteriorum ordinis: Decree on the ministry and life of priests, ' 1. The excellence of the order of priests in the Church has already been recalled to the minds of all by this sacred synod. Since, however, in the renewal of Christ's Church tasks of the greatest importance and of ever increasing difficulty are being given to this order, it was deemed most useful to treat of the subject of priests at greater length and with more depth. What is said here applies to all priests, especially those devoted to the care of souls, with suitable adaptations being made for priests who are religious. Priests by sacred ordination and mission which they receive from the bishops are promoted to the service of Christ the Teacher, Priest and King. back |
Isaac Newton (1729), 'General Scholium' from the Mathematical Principles of Natural Philosophy (1729), ' This most beautiful System of the Sun, Planets and Comets, could only proceed from the counsel and dominion of an intelligent and powerful being. And if the fixed Stars are the centers of other like systems, these being form'd by the like wise counsel, must be all subject to the dominion <389> of One; especially, since the light of the fixed Stars is of the same nature with the light of the Sun, and from every system light passes into all the other systems. And lest the systems of the fixed Stars should, by their gravity, fall on each other mutually, he hath placed those Systems at immense distances one from another.
This Being governs all things, not as the soul of the world, but as Lord over all: And on account of his dominion he is wont to be called Lord God παντοκρáτωρ or Universal Ruler. back |
Jacques Maritain - Wikipedia, Jacques Maritain - Wikipedia. the free encyclopedia, ' Jacques Maritain (French: November 1882 – 28 April 1973) was a French Catholic philosopher. Raised as a Protestant, he was agnostic before converting to Catholicism in 1906. An author of more than 60 books, he helped to revive Thomas Aquinas for modern times, and was influential in the development and drafting of the Universal Declaration of Human Rights. Pope Paul VI presented his "Message to Men of Thought and of Science" at the close of Vatican II to Maritain, his long-time friend and mentor. The same pope had seriously considered making him a lay cardinal, but Maritain rejected it. Maritain's interest and works spanned many aspects of philosophy, including aesthetics, political theory, philosophy of science, metaphysics, the nature of education, liturgy and ecclesiology.' back |
Jennan Ismael (Standord Encyclopedia of Philosophy), Quantum Mechanics, ' Quantum mechanics is, at least at first glance and at least in part, a mathematical machine for predicting the behaviours of microscopic particles — or, at least, of the measuring instruments we use to explore those behaviours — and in that capacity, it is spectacularly successful: in terms of power and precision, head and shoulders above any theory we have ever had. Mathematically, the theory is well understood; we know what its parts are, how they are put together, and why, in the mechanical sense (i.e., in a sense that can be answered by describing the internal grinding of gear against gear), the whole thing performs the way it does, how the information that gets fed in at one end is converted into what comes out the other.
The question of what kind of a world it describes, however, is controversial; there is very little agreement, among physicists and among philosophers, about what the world is like according to quantum mechanics. Minimally interpreted, the theory describes a set of facts about the way the microscopic world impinges on the macroscopic one, how it affects our measuring instruments, described in everyday language or the language of classical mechanics. Disagreement centers on the question of what a microscopic world, which affects our apparatuses in the prescribed manner, is, or even could be, like intrinsically; or how those apparatuses could themselves be built out of microscopic parts of the sort the theory describes.
It is decribng an intelligent world: cognitie cosmogenesis back |
John Paul II (1994_05_22), Ordinatio Sacerdotalis, 22 May 1994: On reserving priestly ordination to men alone, '4. Although the teaching that priestly ordination is to be reserved to men alone has been preserved by the constant and universal Tradition of the Church and firmly taught by the Magisterium in its more recent documents, at the present time in some places it is nonetheless considered still open to debate, or the Church's judgment that women are not to be admitted to ordination is considered to have a merely disciplinary force.
Wherefore, in order that all doubt may be removed regarding a matter of great importance, a matter which pertains to the Church's divine constitution itself, in virtue of my ministry of confirming the brethren (cf. Lk 22:32) I declare that the Church has no authority whatsoever to confer priestly ordination on women and that this judgement is to be definitively held by all the Church's faithful.'
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Jonathan R Goodman (2025_05_18), Are we hardwired to fall for autocrats? , ' A recent piece of research commissioned by Channel 4 suggested that more than half of people aged between 13 and 27 would prefer the UK to be an authoritarian dictatorship.
The results shocked a lot of people concerned about the rising threat of autocracy across the world, including me. Yet, on reflection, I don’t think we should be surprised. The way we evolved predisposes us to place trust in those who often deserve it least – in a sense, hardwiring us to support the most machiavellian among us and to propel them into power. This seems like an intractable problem. But it’s what we do in the face of that knowledge that matters.' back |
Kyle Chan (2025_05_19), In the Future, China Will Be Dominant. The U.S. Will Be Irrelevant., ' For years, theorists have posited the onset of a “Chinese century”: a world in which China finally harnesses its vast economic and technological potential to surpass the United States and reorient global power around a pole that runs through Beijing.
That century may already have dawned, and when historians look back they may very well pinpoint the early months of President Trump’s second term as the watershed moment when China pulled away and left the United States behind.
It doesn’t matter that Washington and Beijing have reached an inconclusive and temporary truce in Mr. Trump’s trade war. The U.S. president immediately claimed it as a win, but that only underlines the fundamental problem for the Trump administration and America: a shortsighted focus on inconsequential skirmishes as the larger war with China is being decisively lost.' back |
Liaoyi Xu et al (2025_04_06), The genetic architecture of and evolutionary constraints on the human pelvic form, ' INTRODUCTION: Human pelvic shape has undergone significant evolutionary change since the divergence from the chimpanzee lineage. This transformation involved the reduction of pelvic canal dimensions to support bipedal locomotion. At the same time, human brain size also expanded significantly, which gave rise to the obstetrical dilemma, a hypothesis that highlights the mismatch between the large brain size of infants and the narrowed female birth canal. Initially proposed in the 1960s, empirical support for this classic hypothesis has been equivocal, largely owing to limitations in sample size and a lack of appropriate types of data.' back |
Marjorie O'Rorke Boyle (1997), Chaff: Thomas Aquinas's Repudiation of His Opera omnia, ' I cannot": Thomas Aquinas replied to an anxious inquiry about
I why he had abruptly ceased writing and dictating his Summa
theologiae. His companion and confessor, Reginald of Piperno,
afraid that overzealous study had induced insanity, insisted that he
continue. "I cannot," repeated Aquinas, "because everything that I have
written seems to me chaffy." . . . Reginald importuned Aquinas to tell him why he refused to write and why he was stunned. After many interrogations Aquinas answered, "I adjure you by the living almighty God, and by the faith you have in our order, and by charity that you strictly promise me you will never reveal in my lifetime what I tell you. Everything that I have written seems to me chaffy in respect to those things that I have seen and have been revealed to me."
Processus canonizationis s. Thomae, Neapoli 79, ed. M.-H. Laurent, fascicule 4 of Fontes vitaes. Thomae Aquinatis, ed. Dominic M. Prummer (Toulouse, n.d.), pp. 376-77 back |
Morwenna Ferrier (2025_05_17), ‘A push towards the conservative’: Cannes tries to ban oversized outfits and naked dressing, ' Not for the first time, organisers of the Cannes film festival, the ritziest and most photographed in the industry’s calendar, have decreed that various outfits will not be allowed on the red carpet this year.
An official statement released earlier this week stated that for “decency reasons” there will be “no naked dressing” – and no oversized outfits either – “in particular those with a large train that hinder the proper flow of traffic of guests and complicate seating in the theatre”.
Encouraged instead are cocktail and black dresses, and – perhaps with US guests in mind – “a dark-coloured pantsuit”. After some back and forth over high-heeled shoes in recent years, anything goes, as long as they are “elegant”. As for the men, it’s simply tuxedos or dark suits. [. . .]
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Ordination of women and the Catholic Church - Wikipedia, Ordination of women and the Catholic Church - Wikipedia, the free encyclopedia, ' The teaching of the Catholic Church on ordination, as expressed in the 1983 Code of Canon Law, the Catechism of the Catholic Church, and the apostolic letter Ordinatio sacerdotalis, is that only a Catholic male validly receives ordination, and "that the Church has no authority whatsoever to confer priestly ordination on women and that this judgement is to be definitively held by all the Church's faithful." In other words, the male priesthood is not considered by the church a matter of policy but an unalterable requirement of God. As with priests and bishops, the church ordains only men as deacons. back |
Peter R. Holland - Wikipedia, Peter R. Holland - Wikipedia, the free encyclopedia, ' In 1993, Holland published his book “The Quantum Theory of Motion’’ in which he presented a comprehensive account of the causal interpretation of quantum mechanics initiated by Louis de Broglie and, in a more complete form, by David Bohm.
Recent work
Drawing upon numerical trajectory-based methods for solving the Schrödinger equation, and upon methods of hydrodynamics, Holland showed in 2004 how the time evolution of the wavefunction could be derived exactly from the dynamical evolution of a congruence of spacetime trajectories. The method achieves the same result as Richard Feynman's path integral formulation (the mapping of the initial wavefunction through time) but, instead of using Feynman's 'all possible paths' between two points, it employs at most one path. back |
Pope Leo XIII, Aeterni Patris: Encyclical on the restoration of Christian philosophy, ' The only-begotten Son of the Eternal Father, who came on earth to bring salvation and the light of divine wisdom to men, conferred a great and wonderful blessing on the world when, about to ascend again into heaven, He commanded the Apostles to go and teach all nations, and left the Church which He had founded to be the common and supreme teacher of the peoples. [. . .]
Among the Scholastic Doctors, the chief and master of all towers Thomas Aquinas, who, as Cajetan observes, because "he most venerated the ancient doctors of the Church, in a certain way seems to have inherited the intellect of all." The doctrines of those illustrious men, like the scattered members of a body, Thomas collected together and cemented, distributed in wonderful order, and so increased with important additions that he is rightly and deservedly esteemed the special bulwark and glory of the Catholic faith.' back |
Pope Paul VI (1976_10_15), Inter Insigniores: On the question of admission of women to the ministerial priesthood , '. . . in execution of a mandate received from the Holy Father and echoing the declaration which he himself made in his letter of 30 November 1975, the Sacred Congregation for the Doctrine of the Faith judges it necessary to recall that the Church, in fidelity to the example of the Lord, does not consider herself authorized to admit women to priestly ordination.' back |
Richard Healey (Stanford Encyclopedia of Philosophy), Quantum-Bayesian and Pragmatist Views of Quantum Theory, ' Quantum theory is fundamental to contemporary physics. It is natural to view a fundamental physical theory as describing or representing the physical world. But many physicists and some philosophers have questioned or rejected this view of quantum theory. They have viewed the theory as concerned with our observation and description of, knowledge or beliefs about, or interactions with the world. Views of this kind have been expressed since the 1920s when quantum theory emerged in close to its present form. This entry is concerned with more recent developments of this tradition by physicists and philosophers, much of it described as quantum-Bayesian or pragmatist. This entry discusses the form of quantum-Bayesianism known as QBism in section 1, addressing common objections in section 2. After section 3 briefly notes pragmatist influences on QBism section 4 sketches a variety of self-described pragmatist approaches to quantum theory, while section 5 mentions some related views.' back |
Rigged Hilbert space - Wikipedia, Rigged Hilbert space - Wikipedia, the free encyclopedia, ' In mathematics, a rigged Hilbert space (Gelfand triple, nested Hilbert space, equipped Hilbert space) is a construction designed to link the distribution and square-integrable aspects of functional analysis. Such spaces were introduced to study spectral theory. They bring together the 'bound state' (eigenvector) and 'continuous spectrum', in one place.
Using this notion, a version of the spectral theorem for unbounded operators on Hilbert space can be formulated. "Rigged Hilbert spaces are well known as the structure which provides a proper mathematical meaning to the Dirac formulation of quantum mechanics".' back |
Robert Pasnau (Stanford Encyclopedia of Philosophy), Thomas Aquinas, ' Between antiquity and modernity stands Thomas Aquinas (ca. 1225–1274). The greatest figure of thirteenth-century Europe in the two preeminent sciences of the era, philosophy and theology, he epitomizes the scholastic method of the newly founded universities. Like Dante or Michelangelo, Aquinas takes inspiration from antiquity, especially Aristotle, and builds something entirely new. Viewed through a theological lens, Aquinas has often been seen as the summit of the Christian tradition that runs back to Augustine and the early Church. Viewed as a philosopher, he is a foundational figure of modern thought. His efforts at a systematic reworking of Aristotelianism reshaped Western philosophy and provoked countless elaborations and disputations among later medieval and modern philosophers.' back |
Rolf Landauer (1999), Information is a Physical Entity, 'Abstract: This paper, associated with a broader conference talk on the fundamental physical limits of information handling, emphasizes the aspects still least appreciated. Information is not an abstract entity but exists only through a physical representation, thus tying it to all the restrictions and possibilities of our real physical universe. The mathematician's vision of an unlimited sequence of totally reliable operations is unlikely to be implementable in this real universe. Speculative remarks about the possible impact of that on the ultimate nature of the laws of physics are included.' back |
Sheldon Goldstein (Stanford Encyclopedia of Philosophy), Bohmian Mechanics, ' Bohmian mechanics inherits and makes explicit the nonlocality implicit in the notion, common to just about all formulations and interpretations of quantum theory, of a wave function on the configuration space of a many-particle system. It accounts for all of the phenomena governed by nonrelativistic quantum mechanics, from spectral lines and scattering theory to superconductivity, the quantum Hall effect and quantum computing. In particular, the usual measurement postulates of quantum theory, including collapse of the wave function and probabilities given by the absolute square of probability amplitudes, emerge from an analysis of the two equations of motion: Schrödinger’s equation and the guiding equation. No invocation of a special, and somewhat obscure, status for observation is required.' back |
Thomas Aquinas, Summa Contra Gentiles, Commentrium in Boetium de Triniate, Postillae Super Isaiam , back |
Thomas Aquinas, Opusculum: De Aeternitate Mundi, back |
Von Neumann algebra - Wikipedia, Von Neumann algebra - Wikipedia, the free encyclopedia, ' In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. It is a special type of C*-algebra.
Von Neumann algebras were originally introduced by John von Neumann, motivated by his study of single operators, group representations, ergodic theory and quantum mechanics. . . . Von Neumann algebras were first studied by von Neumann (1930) in 1929; he and Francis Murray developed the basic theory, under the original name of rings of operators, in a series of papers written in the 1930s and 1940s (F.J. Murray & J. von Neumann 1936, 1937, 1943; J. von Neumann 1938, 1940, 1943, 1949), reprinted in the collected works of von Neumann (1961).' back |
William of Ockham - Wikipedia, William of Ockham - Wikipedia, the free ecyclopedia, c. 1287 – 9/10 April 1347) was an English Franciscan friar, scholastic philosopher, apologist, and theologian, who was born in Ockham, a small village in Surrey. He is considered to be one of the major figures of medieval thought and was at the centre of the major intellectual and political controversies of the 14th century. He is commonly known for Occam's razor, the methodological principle that bears his name, and also produced significant works on logic, physics and theology. William is remembered in the Church of England with a commemoration corresponding to the commonly ascribed date of his death on 10 April. back |
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