Natural Theology

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Notes DB 91: Divine_Gravitation_2024

Sunday 29 December 2024 - Saturday 4 January 2025

[page 315]

Sunday 29 December 2024

Trentmann: Out of Darkness a retrospective look at the Nazi horror. Who/what to blame? What do I think? I put the 'problem of evil' in the dynamics of evolution, something predictable that can be dealt with [by removing all the incentives to human predation upon one another and unnecessary predation on the environment, eg 100% solar energy]. Frank Trentmann (2024): Out of the Darkness: The Germans, 1942-2022

All of my work is part of a search for the holy grail and the heart of the matter is that we live in it, in the heart of God which is the substance of love.

Quantum theory and "timing". Hermitian matrix - Wikipedia

If the world is to grow from an empty set something like the fixed point theorem must be operative so we simply assume that it is.

The beauty of the randomness of waves is that they vary around zero so stationary nodes can be created by superposing equal and opposite directions from zero to get static systems which are wave functions to get a static systems [nodes that do not vary ] which are equivalent to Hermitian operators which are self adjoint meaning

[page 316]

that the diagonal elements are real, ie Hermitian operators are equl to their conjugate transpose, ie the element in the i th row and the j th column aij = the complex conjugate of the element in the j th row and the i th column gji. These matrices have real eigenvalues, ⟨w, Av⟩ = ⟨Aw, v⟩.

Wikipedia: 'Hermitiean matrices are fundamental to quantum mechanics because they describe operaors with necessarily real eigenvalues, a possible measurement outcome which must be real.

Monday 30 December 2024

Can we think of the words in a language as a basis of orthogonal eigenvalues which can be added, using coefficients (eigenvalues) to make sentences which may be seen as higher order words (eigenvectors) which can be added (once again with coefficients) to make paragraphs illustrating the symmetry with respect to complexity of both quantum mechanics and natural language all built around the concept of Hermitian operators.

I might say that I have 'winged it' throughout my life, working (like a normal animal) by feeling rather than logic and the whole of cognitive cosmogenesis is a flight of

[page 317]

feeling which to be practically useful must be brought down to earth by the extraction of real eigenvalues as we [and the world] we do with quantum mechanics. The central mystery of quantum mechanics, physics and theology is at its simplest expression encapsulated in the difference between real and complex numbers expressed in real and complex function space and the difference between Hilbert and Minkowski space which is carried by the difference between fermions and bosons. This is in effect the essence of my 'terrific theorem' wished for on page 314. If wishes were horses beggars would ride and the key to the relationship between physics and theology is to turn theological wishes into physical horses, which is the role of the Sun in evolution. So where does the energy of the Sun come from? Turning H into He, ie energy is a product of union [releasing potential]. Jeffrey Nicholls (2025): Cognitive Cosmogenesis: A systematic integration of Physics and Theology

Yesterday at a party I had a rare attack of love at first sight and possibly offended the person by explaining my dissatisfaction with the Catholic Church leading her to reveal that she is a lover of Jesus. Back home I read an article on female cutting in Gambia in which an Imam was quoted as saying in in effect that it enables us to control women by denying them pleasure by removing their clitorises, and these two events fused the experience of my life, the denial of pleasure leading me to enter a monastery. Now the core of lust for life is revealed to me, the biological heaven of sexuality

[page 318]

and the drive to reproduce which is the answer to death, the source of eternal life. Female genital mutilation - Wikipedia, Rachel Chason (2024_12_28): Female cutting debate in Gambia takes surprising turn: To women’s pleasure

In some way this links to my preoccupation with death and my love affair with my dying Auntie and other family members [who have died] while I have been living in Adelaide working on my revision of theology and physics, the relation between potential and dynamism and the blindness instilled in me by my ignorance of female sexual pleasure. The heart of lust-for-life is the liberation of pleasure - no longer is Earth to be a vale of tears and a testing ground to earn heaven through pain, but heaven itself. The point is to overturn the radical perversion of pain implicit in the crucifixion of the saviour, a perversion embedded in those who feel that inflicting pain is the proper means of control, not the liberation of pleasure. This is the practical conclusion of cognitive cosmogenesis built into quantum mechanics and hermitian operators. All of this is the answer to the perversion suffered in my youth.

Theology and religion must study the moral aspects of our treatment of the planet as well as the physical and biological elements.

What might be the strongest plank in my platform [is] the common belief that quantum computing is more powerful than Turing. Consider Deutsch. David Deutsch (1997): The Fabric of Reality: The Science of Parallel Universes - and its Implications

[page 319]

Tuesday 31 December 2024

One reason for holding that quantum mechanics is more powerful than Turing computation is the belief that the computations in the quantum world use continuous [analogue] variables and solve the eigenvalue equation as a point selected in a continuum whereas Turing computation is digital and rational and proceeds step by step rather than in a single operation.

Quantum searching; quantum Fourier transform. Grover's algorithm - Wikipedia, Quantum Fourier transform - Wikipedia

page xx: '. . . we do not yet understand what exactly it is that makes quantum computers powerful or on what class of problems they can be expected to outperform classical computers.' Nielsen & Chuang (2026): Quantum Computation and Quantum Information

Quantum evolution operates at the interface between the possible and the real, like evolution, randomness exploring spaces in which there is an occasional viable structure that it capable of reproducing itself [and so able to establish a group and become permanent].

Are my intuitions trustworthy?

Wednesday 1 January 2025

Cognitive Cosmology book proofs to check. A sad year with Andrew's death but I am looking forward to the publication of my book and the associated article as my final "coming out" after 60 years of concentrated search for a new universal theology and physics.

[page 320]

But the usual big doubt — can I really believe what I am saying. It all comes down to the interpretation of quantum mechanics and symmetry with respect to complexity. Can I explain it in the last paragraph of the article?

From a quantum mechanical and evolutionary point of view, the world is liberal. This is how dinosaurs turned into birds. As I see it the world starts off with no rules, just an omnipotent empty set analogous to the God of Aquinas, but without omniscience. Theocrats in general, like the Popes, claim to have infallible communication with their omnipotent God who knows what is good for us, tells the theocrats, and they enforce it, usually with violence. This is how we get shocking crimes like female genital mutilation which is very prevalent in many religious doctrinal traditions and is both painful and disastrous for the victims. It is in general another manifestation of the tendency to treat females as subhuman. [This] is implicit in the Papal decrees that women are not [spiritually] fit to serve as priests. [Luke 22:31 (quoted by John Paul II) says nothing about gender: "But I have prayed for you, that your faith should not fail; and when you have returned to Me, strengthen your brethren.”Pope Paul VI (1976_10_15): Inter Insigniores: On the question of admission of women to the ministerial priesthood (15 October 1976), John Paul II (1994_05_22): Ordinatio Sacerdotalis

L4L page 2: The sexual crimes of theocracy [Coming].

Since sex sells I wish to build the marketing of my book around the theocratic abuse if sexuality by religious

[page 321]

organizations across the spectrum, my own experience and what I have learnt about female sexuality from lesbian pornography and the terrible crimes inflicted on women by religious organizations ranging from female genital mutilation to the bogus claims propagated by the Popes of the Roman Catholic Church that women are not humanly capable of being priests.

It is hard to imagine how many more cases of child sexual abuse will be revealed when it becomes possible to investigate this issue in jurisdictions which are seriously limited in the rule of law and personal freedom and whose political structure is very much under the thumb of powerful and murderous theocrats. The Australian Government, under Prime Minister Julia Gillard inaugurated a Royal Commission into Institutional Responses to Child Sexual abuse [but cases are still coming to light and it seems that it will be a very log time before our children are safe from sexual predators]. Parliament of Australia | Monica Biddington: Funding for the Royal Commission into institutional responses to child sexual abuse

Thursday 2 January 2025

Acknowledgements: This work has grown on a meandering trail of a lifetime of small increments for which I alone am responsible. Links to a comprehensive and growing background are available at jeffreynicholls.net

Unitarity is the only constraint on quantum operators (gates, wave equations); AA = 1, adjoint = transpose + complex conjugate. Hermitian = self-adjoint. It would be goId to know what this

[page 322]

really meant. Any meaning is a mapping and any mapping (like marriage) is [prima facie] a constraint. Maybe I was never married. My vice is to be unconstrained, ie random, but even random has a bounded space 0, 1, or i, 0 1.

In effect it is Minkowski space, ie real eigenvalues, that imposes a constraint on Hilbert space, or is it that Hilbert space is unconstrained but linearity forces it to create fermions and bosons? Cognitive Cosmology: page 20: space-time—the cosmic memory and operating system.

Real arithmetic = set theory = beans = particles, linearity. Quadratic = complex, Dirac equation [derived by eliminating quadratic momentum in Schrödinger equation]. What is the electron operator? The photon operator? Complex numbers break out of real consistency. The real boundary in quantum mechanics is the boundary between real and complex numbers spanned by self-adjoint operators. Get this into [my essay] cognitive_cos_dec2024. Dirac equation - Wikipedia

The heuristic of simplicity males the base states of naked gravitation complex — something like this. The key to Hilbert space is that the inner products of vectors with positive length may be zero.

Friday 3 January 2025

Now I am ready for another go at the acknowledgements.

I owe my happiness to a new vision of God. 80 years ago I was baptized into the service of a mysterious

[page 323]

invisible god in the sky who, it turned out, was so displeased with the humanity that he had created that he conspired at the death of his own Son, Jesus of Nazareth, to gain satisfaction for the evil deeds of the people he created. In the 80 years since then my life in contact with the human world has taught me that this God was false, a genocidal warmonger who encouraged their followers to murder the followers of other gods. This book started as a search for a theory of peace. In the 60s I joined the Catholic Order of Preachers, a medieval order formed to justify the slaughter of heretics. There I learned that I could not preach their doctrine. In the 80s, as I studied the history of war, it became clear to me that it all fitted into the Imperial concept of Lebensraum that inspired the imperial and genocidal wars of the twentieth century that contributed to the psychological damage suffered by my young father in the Bougainville campaign to protect Australia from invasion [by Imperial Japan]. It became very clear to me that the [human] world is full and all those powers using military means to occupy the land of others are agents of evil. But they are not the only ones. The Catholic Church [employing innocent looking nuns] occupied my mind with falsehoods the most perverse of which is the idea that pain and suffering on Earth, epitomized in the death of Jesus of Nazareth, is the sure route to a life of eternal bliss with God in heaven.

[page 324]

The world is fully occupied now and we know that we depend upon it absolutely for our physical existence. We have to share it and look after it. This is a blatantly obvious fact, but the theocracies of the world are still stuck in their old genocidal and exploitative ways. The real requirement for world peace is mental space. I first hit on this idea in the 80s and explored it in a series of lectures in 2BOB public radio in Taree in 1987: A theory of Peace 1987: Lecture 1: Mathemtical Theology

This book began to materialize then as my life slowly turned around from a mysterious god in the sky to a solid god beneath my feet. When I joined the Order I was required to task three solemn vows of Poverty, Chastity and Obedience, thereby sacrificing my natural human agency to the Pope and his agents. In Galileo's day the Holy Inquisition was ultimately forced to accept that it could no longer justify killing people like Galileo who could see that this doctrine denied the evidence. Since then the Catholic Church as clung tenuously to three key beliefs: that their God is the true God; that evolution is not the source of the human spirit; and that women are not spiritually qualifed to become priests in the church.

I owe this book to a slow incremental transition from theocracy to science.

[page 325]

This acknowledgement is part of the marketing plan.

The trickiness of evolution Jeffrey S. Groh et al (2025_01_03): Ancient structural variants control sex-specific flowering time morphs in walnuts and hickories

Acknowledgements, or more properly exonorations, ie a list of people who are not to blame for what I have done. Nobody ever supported ted this project so I am confident that I carry the full responsibility for the ideas in this book. I realize that a century is a short time in theology and science and do I do not expect instant results. On the other hand I feel that I am quite close to the truth so I am looking forward to discussion with anyone who is interested as long as they do not exhibit a tendency to teat me as many other organized religions in the world are inclined to treat those they cannot understand.Fortunately I am not a female and I live in a relatively well managed country so I can express my opinions without fear even though I might attrasct some ridicule from people who are certain of their positions.

Saturday 4 January 2025

Cut the acknowledgements down to Charle Darwin and evolution, the random source of creativity built into the theory of probability by Kolmogorov 1956. Darwin broke the threw pillars of Catholicism, infallibility, sexism and determinism

I feel that I have disappointed a lot of people, including my

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deeply Catholic mother, but I have always tried to be helpful and explain what I am doing. This book is my latest effort in this direction. As my father said in his old age, he just sits there typing on his computer. I am trying to put the fortune they left me after a lifetime of doctoring to good use.

In memory of my brother Andrew, who took a very hard way out, partly, I am sure, because the Catholic Church could not accommodate his true nature.

Darwin's scientific manifesto:

In scientific investigations . . . it is permitted to invent any hypothesis, and if it explains various large and independent classes of facts, it rises to the rank of a well grounded theory. Charles Darwin (1875): The Variation of Animals and Plants Under Domestication

Copyright:

You may copy this material freely provided only that you quote fairly and provide a link (or reference) to your source.

Further reading

Books

Darwin (1875), Charles, and Harriet Ritvo (Introduction), The Variation of Animals and Plants Under Domestication (Foundations of Natural History), Johns Hopkins University Press 1875, 1998 ' "The Variation, with its thousands of hard-won observations of the facts of variation in domesticated species, is a frustrating, but worthwhile read, for it reveals the Darwin we rarely see -- the embattled Darwin, struggling to keep his project on the road. Sometimes he seems on the verge of being overwhelmed by the problems he is dealing with, but then a curious fact of natural history will engage him (the webbing between water gun-dogs' toes, the absurdly short beak of the pouter pigeon) and his determination to make sense of it rekindles. As he disarmingly declares, 'the whole subject of inheritance is wonderful.'. 
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Deutsch (1997), David, The Fabric of Reality: The Science of Parallel Universes - and its Implications, Allen Lane Penguin Press 1997 Jacket: 'Quantum physics, evolution, computation and knowledge - these four strands of scientific theory and philosophy have, until now, remained incomplete explanations of the way the universe works. . . . Oxford scholar DD shows how they are so closely intertwined that we cannot properly understand any one of them without reference to the other three. . . .' 
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Nicholls (2025), Jeffrey, Cognitive Cosmogenesis: A systematic integration of Physics and Theology, ' 2025 ' More than 60 years ago my spiritual advisors (rightly or wrongly) diagnosed in me a divine call to the Roman Catholic priesthood. As soon as I turned 18 I entered the Dominican Order
I quickly fell on love with their leading theologian, Thomas Aquinas (1225 - 1275) and read him voraciously. His Latin is so easy and his ideas quite cosmic.
Aquinas revolutionized theology by harmonizing it with the work of Aristotle, the best science available in the Middle Ages. Since the time of Galileo (1562 - 1642) modern science has travelled far beyond Aristotle. We now have comprehensive knowledge of the Universe. We can now see that it is big enough and beautiful enough to be considered divine. It seems obvious to me that it is time to introduce science to theology once again. Just three steps are required:
First, we must assume that the Universe is divine. This makes God observable, amenable to modern science which is based on observation.
Second, it follows, if this is the case, that physics and theology have the same subject and must therefore be consistent.
Third we need open up a new field of research, repeating Aristotle’s ancient journey from physics to theology. In this book I have tried to trace a quantum theoretical path from the unstoppable omnipotent emptiness of the initial singularity to the exquisite complexity of our world. My only guide is the logical constraint placed on omnipotence by consistency.'  
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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. 
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Trentmann (2024), Frank, Out of the Darkness: The Germans, 1942-2022 , Penguin 2025 ' An impressive account of how Germany built a new identity for itself after the barbaric Nazi years ... terrifically insightful ... This book runs to 838 pages, but barely a word is wasted. Trentmann is a skilful and unflashy storyteller with flickers of gentle irony. Echoing Tolstoy’s theory of history as the “sum of human wills”, he aims to stitch the scraps of everyday experience into a quilt of grand narrative. This results in a good deal of richness, colour and subtlety -- Oliver Moody ― The Times  
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Links

Anora - Wikipedia, Anora - Wikipedia, the free encyclopedia, ' Anora is a 2024 American comedy-drama film written, directed, and edited by Sean Baker. It follows the beleaguered marriage between Anora (Mikey Madison), a young sex worker, and Vanya Zakharov (Mark Eydelshteyn), the son of a Russian oligarch. The supporting cast includes Yura Borisov, Karren Karagulian, Vache Tovmasyan, and Aleksei Serebryakov. Anora premiered on May 21, 2024, at the 77th Cannes Film Festival, where it won the Palme d'Or. It was released theatrically on October 18 by Neon. It was named one of the top 10 films of 2024 by the National Board of Review and the American Film Institute, and received five nominations at the 82nd Golden Globe Awards, including Best Motion Picture – Comedy or Musical, Best Actress and Best Director. It grossed $30.2 million worldwide on a $6 million budget, becoming Baker's highest-grossing film.' back

Cameron Houston (2024_12_31), Nation’s top lawmakers to meet after Catholic Church found not liable for clerical abuse, ' Attorneys-general offices from across Australia will meet next week to consider urgent legislative reforms after a contentious court decision that a Catholic diocese was not liable for the clerical abuse of a five-year-old boy. The High Court ruled in November that the Ballarat diocese, in regional Victoria, could not be held responsible for misconduct by its former priest, Father Bryan Coffey, because he could not be legally considered an employee of the church. The landmark decision has upended thousands of legal cases against religious orders nationwide, including more than 1800 civil claims currently before courts in Victoria. The Ballarat diocese and its current bishop, Paul Bird, were initially sued in the Supreme Court of Victoria by a man who said he was sexually assaulted by Coffey at his parents’ home in Port Fairy, in south-west Victoria, in 1971. The man, known in court documents as DP, has spoken for the first time and called for urgent intervention by state and territory legislatures. . . . The Victorian courts had extended that principle to the church, ruling that Coffey was still a “servant of the diocese” and through his pastoral role had the “power and intimacy” to abuse children during visits to parishioners’ homes. However, the nation’s highest court ruled the lower courts had overreached. The High Court said it had repeatedly refused previous attempts to extend the boundaries of vicarious liability to include independent contractors. “Expanding the doctrine to accommodate relationships that are ‘akin to employment’ would produce uncertainty and indeterminacy,” the judgment summary read. However, the High Court conceded in its judgment that “reformulation of the law of vicarious liability is properly the province of the legislature”.' back

Cavan W. Concannon (2924_12_24), New Year’s Eve celebrates St. Silvester – the 4th-century pope whose legend shaped ideas of church and state, ' On Dec. 31, while many people are preparing for their New Years Eve parties, some Roman Catholic Christians will also mark the feast day for St. Silvester. Little is known for certain about Silvester’s life, but he lived during a transformational period in the history of Christianity. From 314-335 C.E., Silvester was the bishop of Rome: what we now call the pope, although the role was not so powerful at the time. “Pope” comes from the Greek word for “father,” and was widely used by bishops until the fifth century, when the bishop of Rome began to monopolize the title. Silvester’s era was one of both turmoil and transition for Christians living in the Roman Empire, as some Christian communities emerged from persecution into a powerful alliance with the Roman state. His story is deeply intertwined with this alliance, which would fundamentally change the trajectory of the movement initiated by the figure of Jesus of Nazareth three centuries earlier. Christianity would now become the faith of kings, states and empires. . . . Legends about Silvester only grew with time – and even include a battle with a demonic dragon. But perhaps the most infamous legacy of Silvester is connected to the so-called “Donation of Constantine.” This forged document was first drafted in the eighth century C.E. The Donation states that Emperor Constantine had bequeathed to the Roman bishop – at the time Silvester – control of the city of Rome, the western Roman Empire, huge tracts of land under imperial control, and authority over churches in the other centers of the Christian world, Constantinople. For centuries, this document would undergird papal claims to both ecclesial and civil power. In the 15th century, German cardinal Nicholas of Cusa and the Italian scholar Lorenzo Valla showed the Donation to be a forgery, but by that point popes had already amassed the authority and wealth now associated with the office.' back

Clint Jasper (2025_01_02), Mandatory climate reporting begins this year, marking generational change for corporate Australia, ' Australia has introduced new mandatory climate reporting rules that require business owners to estimate their company's emissions and outline plans to tackle future risks. The legislation, passed in 2024, is the most significant change to reporting requirements and director responsibilities in a generation, according to the Australian Institute of Company Directors (AICD). It will require companies to disclose their greenhouse gas emissions and explain how a range of future climate scenarios could impact their business, in a sustainability report filed alongside their financial data. Initially, the legislation will apply only to Australia's largest companies but by 2027, thousands of corporate and not-for-profit organisations will be included — something AICD managing director and CEO Mark Rigotti said would be a significant change in the way companies approach their mandatory disclosures. "It's actually quite a fundamental step change in reporting and there probably hasn't been as significant a change since 2003, when we moved from sort of domestic financial standards to international financial reporting standards," Mr Rigotti said. What's changing? The law requires companies to publish an annual "climate statement" that outlines any material climate risks they may face, and their scope one, two and three greenhouse gas emissions.' back

Darius von Guttner Sporzynski (2025_01_02), Isidore of Seville: the patron saint of the internet who shaped knowledge for generations, ' In a world where information flows freely, it’s easy to forget that, for centuries, knowledge was much harder to come by. Imagine living in a time when the internet didn’t exist, books were scarce, libraries were few, and most people couldn’t even read. This was the world of Isidore of Seville, a man dedicated to gathering and sharing knowledge to be passed down for generations. Thanks to his work, he was named the patron saint of the internet in 1997 by Pope John Paul II, recognising his impact on knowledge and communication. . . . Isidore was a bishop and scholar who lived in Seville in what is now Spain during a time we often call the “Dark Ages”, roughly 500–1000 AD. After the fall of the Roman Empire, much of Europe was in chaos – as if the lights had been turned ofd. . . . He saw preserving and sharing information as essential to keeping civilisation alive and thriving. To do this, he wrote his most famous work, Etymologiae, which became a go-to book for centuries. . . . Isidore wasn’t just a writer. As a senior leader in the Christian Church, he played an important role in both religion and education. He set up “cathedral schools” for training future priests. These schools would later inspire the first European universities, where students could study a wide range of subjects.' back

Dirac equation - Wikipedia, Dirac equation - Wikipedia, the free encyclopedia, 'In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1⁄2 massive particles such as electrons and quarks, for which parity is a symmetry, and is consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to account fully for special relativity in the context of quantum mechanics. It accounted for the fine details of the hydrogen spectrum in a completely rigorous way.' back

Female genital mutilation - Wikipedia, Female genital mutilation - Wikipedia, the free ecyclopedia, 'Female genital mutilation (FGM) (also known as female genital cutting, female genital mutilation/cutting (FGM/C) and female circumcision[a]) is the cutting or removal of some or all of the vulva for non-medical reasons. FGM prevalence varies worldwide, but is majorly present in some countries of Africa, Asia and Middle East, and within their diasporas. As of 2024, UNICEF estimates that worldwide 230 million girls and women (144 million in Africa, 80 million in Asia, 6 million in Middle East, and 1-2 million in other parts of the world) had been subjected to one or more types of FGM.' back

Grover's algorithm - Wikipedia, Grover's algorithm - Wikipedia , the free encyclopedia, ' In quantum computing, Grover's algorithm, also known as the quantum search algorithm, is a quantum algorithm for unstructured search that finds with high probability the unique input to a black box function that produces a particular output value, using just O(&sqrt;N) evaluations of the function, where N is the size of the function's domain. It was devised by Lov Grover in 1996.' back

Hermitian adjoint - Wikipedia, Hermitian adjoint - Wikipedia, the free encyclopedia, ' Hermitian operators: A bounded operator A : H → H is called Hermitian or self-adjoint if
A = A*
which is equivalent to
⟨ A x , y ⟩ = ⟨ x, A y ⟩ for all x , y ∈ H.
In some sense, these operators play the role of the real numbers (being equal to their own "complex conjugate") and form a real vector space. They serve as the model of real-valued observables in quantum mechanics. See the article on self-adjoint operators for a full treatment.' back

Hermitian matrix - Wikipedia, Hermitian matrix - Wikipedia, the free encyclopedia, ' In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in the i-th row and j-th column is equal to the complex conjugate of the element in the j-th row and i-th column, for all indices i and j . . .. Hermitian matrices can be understood as the complex extension of real symmetric matrices. . .. Hermitian matrices are named after Charles Hermite, who demonstrated in 1855 that matrices of this form share a property with real symmetric matrices of always having real eigenvalues. Other, equivalent notations in common use are A = AH = A = A although in quantum mechanics Atypically means the complex conjugate only, and not the conjugate transpose.' back

Jeffrey S. Groh et al (2025_01_03), Ancient structural variants control sex-specific flowering time morphs in walnuts and hickories, ' INTRODUCTION: Despite the capacity of many hermaphroditic plants to self-fertilize, the genetic costs of inbreeding have repeatedly driven the evolution of outcrossing strategies such as dioecy. Dioecy and other discrete mating type systems are maintained by rare mating type advantage and are often controlled by sets of tightly linked epistatic alleles (i.e., supergenes). We investigate the genetic underpinnings and evolution of a dimorphic mating system that exploits the temporal dimension - heterodichogamy. In species of hermaphroditic walnuts (Juglans) and hickories (e.g., pecans, Carya), two morphs alternate staminate and pistillate (i.e. male and female) flowering phases across the season, promoting disassortative mating that maintains a stable equilibrium. The genetic underpinnings and evolution of this mating system have remained elusive.' back

John F. Sopko (2025-01_02), America, Afghanistan and the Price of Self-Delusion, ' The collapse of the U.S.-backed government in Afghanistan on Aug. 15, 2021, revealed what little American lives and money had purchased over 20 years there. It also laid bare a gaping disconnect between reality and what senior U.S. officials had been telling Americans for decades: that success was just around the corner. As the special inspector general for Afghanistan reconstruction since 2012, my staff and I have audited and investigated U.S. programs and spending to rebuild Afghanistan — a mission that, it was hoped, would turn the theocratic, tribal-based “Graveyard of Empires” into a modern liberal democracy. In hundreds of reports over the last 12 years, we have detailed a long list of systemic problems: The U.S. government struggled to carry out a coherent strategy, fostered overly ambitious expectations, started unsustainable projects and did not understand the country or its people. American agencies measured success not by what they accomplished, but by dollars spent or checklists of completed tasks. As our own agency winds down and we prepare to release our final report this year, we raise a fundamental and too rarely asked question: Why did so many senior officials tell Congress and the public, year after year, that success was on the horizon when they knew otherwise? For two decades, officials publicly asserted that continuing the mission in Afghanistan was essential to national interests, until, eventually, two presidents — Donald Trump and Joe Biden — concluded it was not. . . . But a perverse incentive drove our system. To win promotions and bigger salaries, military and civilian leaders felt they had to sell their tours of duty, deployments, programs and projects as successes — even when they were not. Leaders tended to report and highlight favorable information while obscuring that which pointed to failure. After all, failures do not lead to an ambassadorship or an elevation to general. . . . Self-serving delusion was America’s most formidable foe. . . . Ultimately, however, if we do not address the incentives in our government that impede truth-telling, we will keep pursuing projects both at home and overseas that do not work, rewarding those who rationalize failure while reporting success, and burning untold billions of dollars. American taxpayers deserve better.' back

John Paul II, Ordinatio sacerdotalis: On reserving priestly ordination to men alone, '. . . 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 judgment is to be definitively held by all the Church's faithful.' back

John Paul II (1994_05_22), Ordinatio Sacerdotalis, 22 May 1994, '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.' back

Melissa Davey (2017_ 12_11), Why Australia's royal commission on child sexual abuse had to happen – explainer, ' The royal commission delivers its final report to the Australian governor general, Sir Peter Cosgrove, on 15 December, after five years’ work. In 2012 the then prime minister, Julia Gillard, announced a royal commission into institutional responses into child sexual abuse, something survivors and their advocates had been seeking for years after allegations in Australia and in other countries, notably the US and Ireland. “There has been a systemic failure to respond to it,” Gillard said. “The allegations that have come to light recently about child sexual abuse have been heartbreaking. These are insidious, evil acts to which no child should be subject. There have been too many revelations of adults who have averted their eyes from this evil." While successive prime ministers said a royal commission was not needed because state inquiries and investigations had been held, Gillard ordered the commission after explosive allegations made by Peter Fox, a detective chief inspector within New South Wales police. In a letter to the Newcastle Herald, he wrote that victims of historical abuse were coming forward in increasing numbers. “Often the church knows but does nothing other than protect the pedophile and its own reputation,” Fox wrote. “I can testify from my own experience that the church covers up, silences victims, hinders police investigations, alerts offenders, destroys evidence and moves priests to protect the good name of the church.” . . . On Friday it will hand down its final report after 8,000 private sessions and 444 days of public hearings. The commission heard from more than 1,200 witnesses during the public hearings, examined more than 1.2 million documents and generated more than 45,400 pages of transcripts. Although the its final report is due on Friday 15 December it has been incrementally releasing findings from more than 100 pieces of research it commissioned, as well as findings from investigations into various institutions. It has also made recommendations about how a national redress scheme for abuse survivors should work. The overall budget for the commission was $372m. The commission expects to run under budget by the time it concludes. Staffing levels peaked at 325 in October 2016.' back

Parliament of Australia | Monica Biddington, Funding for the Royal Commission into institutional responses to child sexual abuse, ' In November 2012, the Prime Minister, Julia Gillard, announced the establishment of a Royal Commission into institutional responses to instances of child sexual abuse. This followed allegations from a senior police officer in New South Wales that the Catholic Church covered up evidence involving paedophile priests.[1] On 11 January 2013, the Governor-General appointed a six-member Royal Commission to investigate Institutional Responses to Child Sexual Abuse (Royal Commission). The Royal Commission will inquire into how institutions with responsibility for children have managed and responded to allegations and instances of child sexual abuse. It will investigate where systems have failed to protect children, and make recommendations on how to improve laws, policies and practices to prevent and better respond to child sexual abuse in institutions. The Royal Commission commenced its operations in April 2013. The number of hearings and the level of complaints and allegations are not yet clearly established and these factors will have an impact on the budget for administering the Royal Commission. In future, the Government will need to review the need for changes to the funding in consultation with the Royal Commission. The Government will provide $434.1 million over four years (including $66.8 million in 2012‑13 and $43.2 million in capital funding) to fund the Royal Commission.' back

Pope Paul VI (1976_10_15), Inter Insigniores: On the question of admission of women to the ministerial priesthood (15 October 1976), '. . . 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

Quantum Fourier transform - Wikipedia, Quantum Fourier transform - Wikipedia, the free encyclopedia, ' In quantum computing, the quantum Fourier transform (QFT) is a linear transformation on quantum bits, and is the quantum analogue of the discrete Fourier transform. .. . The quantum Fourier transform was discovered by Don Coppersmith. With small modifications to the QFT, it can also be used for performing fast integer arithmetic operations such as addition and multiplication. . . . The quantum Fourier transform acts on a quantum state vector (a quantum register), and the classical Discrete Fourier transform acts on a vector. Both types of vectors can be written as lists of complex numbers. In the classical case, the vector can be represented with e.g. an array of floating point numbers, and in the quantum case it is a sequence of probability amplitudes for all the possible outcomes upon measurement (the outcomes are the basis states, or eigenstates). Because measurement collapses the quantum state to a single basis state, not every task that uses the classical Fourier transform can take advantage of the quantum Fourier transform's exponential speedup.' back

Rachel Chason (2024_12_28), Female cutting debate in Gambia takes surprising turn: To women’s pleasure, ' SERREKUNDA, Gambia — When Gambian lawmakers and religious leaders pushed this year to overturn a ban on female genital cutting, they sparked fears globally that this tiny West African nation might be at the forefront of a regression in the region on women’s rights. The effort was unsuccessful, and the ban remains in place. But within conservative Gambia, the debate also had an unexpected consequence: A new focus on women’s pleasure. Women are buying sex toys for the first time. Men are learning about the importance of foreplay. Couples are starting to talk about what’s been missing in the bedroom — and working toward fixing it. “It’s always been about pleasing men and what they like,” said Fatoumata Sanneh, a Gambian women’s rights activist. “Before, there was no conversation about women other than about controlling them. But that with this dialogue, that is changing — we are growing as a country, we are going forward.” Throughout Gambia, a nation of 2.5 million carved out of Senegal during British colonial rule, about 75 percent of women and girls ages 15 to 49 have been subject to female genital cutting, according to the United Nations. The practice — which is widely known as female genital mutilation (FGM) — can involve removing part of the clitoris and labia minora and, in the most extreme cases, sealing the vaginal opening. Proponents of FGM, including a prominent imam who launched the effort to change the law, have said it’s about preserving culture, respecting religion and controlling women’s sexuality. Opponents say it has a range of harms, including risk of death from a botched procedure, recurrent infections, pain and infertility. Even in the “least severe” form, part of the clitoris — a small organ which has thousands of nerve endings and is usually capable of producing the most sexual pleasure for women — is removed. So survivors say that among the most common, but usually least discussed, effects of FGM is a deeply personal one: the loss of feeling.' back

Steven Overly (2024_12_31), Australia Banned Kids From Social Media. Now It Has Advice for the US. , ' As countries around the world race to counter the tech industry’s ever-expanding influence, one issue in particular has become a major rallying cry: protecting children online. And Australia just put itself out front. In late November, Australia became the first country in the world to ban minors under age 16 from social media. Oddly enough, it’s an American who will help enforce the unprecedented legislation: Julie Inman Grant, who has served as Australia’s eSafety Commissioner since 2017. . . . The POLITICO Tech podcast recently interviewed Inman Grant about how she plans to implement the first-of-its-kind law — and what advice she has for the United States.“For too long, the burden for safety has fallen on the parents themselves or the children, rather than the platforms,” she said. “So the way that the government designed this is to put the burden on platforms.” . . . Q: Anyone who has been around teens knows they can find a workaround to a lot of rules, right? And so, how do you verify age? How do you actually make sure this works? A: Well, I’ve been working on age verification in one way, shape or form since 2008. I think you probably remember that the Harvard Berkman Center had an Internet Safety Technical Task Force where they looked at this. And I distinctly remember a quote from Richard Blumenthal, the senator today, who was the [Connecticut] attorney general then — well, if we can put a man on the moon, we can certainly verify the age of a child, right? And on one hand, that made me chuckle. On the other hand, I’m like, he’s right — except it’s not just a technological issue, it’s an ecosystem issue. And what we’ve seen over the past decade and a half is that ecosystem and that industry around safety tech and age assurance really maturing. So there are a range of different tools out there. Obviously biometrics can be used. Some form of government ID or digital ID. Although for this particular bill, digital ID or government ID can’t be the sole way of looking at this. So what I mean by the ecosystem is we need to make sure that we’re balancing the imperatives of safety in terms of preventing children from accessing social media sites, particularly where there are addictive features like endless scroll, where there are opaque algorithms sending people down rabbit holes, where there is no visibility or explanation as to why they’re being served particularly harmful content, for instance. There are a range of other things that need to be considered, but we need to balance the privacy with the safety.' back

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