vol VII: Notes

2016

Notes

Sunday 28 February 2016 - Saturday 5 March 2016

[Notebook: DB 80: Cosmic plumbing]

Sunday 28 February 2016

[page 36]

Monday 29 February 2016

Muse has gone a bit dry while watching my parents' approaching death, but now time to get back to work.

Einstein had trouble coupling coordinates and space-time metric. Now the task is to couple dynamic logical process and space-time and I feel that the clue lies in the boson/fermion - and/nand coupling via the spin-statistics theorem. Spin-statistics theorem - Wikipedia

Tuesday 1 March 2016

Wednesday 2 March 2016

The notion that the universe is some sort of logical [psychological] machine has been with me ever since my monastic days when I studied Aristotelian psychology and metaphysics and began to see that a universal computer network was complex enough to explain all the phenomena we observed. The big question for me was what is the hardware on which the universe runs? I have rather lost sight of this question over the years as I became more

[page 37]

mathematically formalist in my approach, influenced by physics which sees the universe performing complex infinite dimensional quantum mechanical computations or superpositions without really considering how this can actually happen, or asking how an infinite superposition of distinct state can exist in one region (pixel, 4xel) of spacetime. Where am I now? I have come to the point where the hardware of the universe is the fixed points in the divine dynamics, and the software is in effect the network communications that relate these fixed points to one another.

At the moment (and for some months) I have been thinking that the basic bifurcation in the divine dynamics, akin to the ancient trinity is the distinction between fermions and bosons. The Father and the Son are fermions, distinct persons, and the Spirit is a boson, the message between Father and Son which both unites and differentiates them. The fermions are akin to the logical nand, the bosons to and, and we would like to see how this logical picture is coupled to the spin-statistics theorem.

Thursday 3 March 2016

Friday 4 March 2016

Saturday 5 March 2016

Physical confinement - energy barrier - logical confinement.

Deviating further and further from the standard model. Now guess that the direction of time is not a statistical / thermodynamic phenomenon, but rather that it is determined by irreversible real computation rather than by reversible complex operations.

Von Neumannn used Hilbert space to unify the continuous and discrete approaches to quantum mechanic. The orthogonal basis vectors are discrete, their probabilities are continuous. Here we are trying to

[page 38]

introduce the logical continuum which is a discrete sequence of events linked by logical operators so that we can interpret an eigenvector as a formal ordered representation of the sequence of logically determined states in a Turing machine (computer). von Neumann

Been feeling rather brain dead lately, possibly from stress about the painful fate of my mother whose care in the old people's home has been less than ideal, but I am inspired by the prospect of returning home and getting back to my hopeless / hopeful task of reinventing the world as divine.

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Further reading

Books

Click on the "Amazon" link below each book entry to see details of a book (and possibly buy it!)

Abelard, Peter, and Translated with an introduction by Betty Radice, Letters of Abelard and Heloise, Penguin (USA) 1998 Jacket: The grim tale of Abelard and Heloise has echoed down from the twelfth century as one of the world's great love stories. These staunch Christians, as their letters reveal, found a path through self-pity into acceptance of a changed but lasting relationship. Whilst Heloise attained fame for her learning and administrative genius as an abbess, Abelard became an inspired teacher in Paris and the foremost logician of his day. This new translation includes Abelard's account of his misfortunes (Historia Calamitatum); four of their personal letters; the 'letters of direction', in which he advises her how to adapt for women the rule of Benedict; correspondence between Heloise and Peter the Venerable; and two of Abelard's hymns.'  Amazon   back

Archer, Jeffrey, The Fourth Estate, Harpercollins Uk 1996 Amazon customer review: 'We hear much of how the media of the world is controlled by the hands of a few men. THis fictionalized account of Rupert Murdoch and Robert Maxwells fight over the worlds media empires will help all those interested in how the media operates in the world today(or more precisely in the 1990s). This book is also a superb read, it combines the flair of real life with the fictionlized account of the private affairs of two great men, both of whom a flawed. A great character study. By far it is Archers best work.' Seth J Frantzman  Amazon   back

Canon Law Society of America, Holy See, Code of Canon Law: Latin-English Edition, Canon Law Society of America 1984 Pope John Paul XXXIII announced his decision to reform the existing corpus of canonical legislation on 25 January 1959. Pope John Paul II ordered the promulgation of the revised Code of Canon law on the same day in 1983. The latin text is definitive. This English translation has been approved by the Canonical Affairs Committee of the [US] National Conference of Catholic Bishops in October 1983.  Amazon   back

Escher, Maurits Cornelius, and John E. Brigham (translator), The Graphic Work: Introduced and explained by the artist, Taco 1989 Introduction: '. . . then there came a moment when it seemed as though scales fell from my eyes. I discovered that technical mastery was no longer my sole aim, for I became gripped by another desire . . . Ideas came into my mind quite unrelated to graphic art, notions which so fascinated me that I longed to communicate them to other people. . . . The ideas that are basic to [my prints] often bear witness to my amazement and wonder at the laws of nature which operate in the world around us. . . . and here is yet another reason for my astonishment - no matter how objective or how impersonal the majority of my subjects appear to me, so far as I have been able to discover, few, if any, of my fellow-men seem to react in the same way to all that they see around them.' pp 5-6  Amazon   back

Feynman, Richard P, and Robert B Leighton, Matthew Sands, The Feynman Lectures on Physics (volume 3) : Quantum Mechanics, Addison Wesley 1970 Foreword: 'This set of lectures tries to elucidate from the beginning those features of quantum mechanics which are the most basic and the most general. . . . In each instance the ideas are introduced together with a detailed discussion of some specific examples - to try to make the physical ideas as real as possible.' Matthew Sands  Amazon   back

Fleming, Ian, For Your Eyes Only, Thomas & Mercer 2012 'A departure from the full-length James Bond novels, For Your Eyes Only is a stunning collection of five stories that sends 007 to Bermuda, Berlin, and beyond, and places him in the dangerous company of adversaries of all varieties.'  Amazon   back

Griffel, D H, Applied Functional Analysis, Dover Publications 2002 Amazon customer review: '... The main strength of Griffel's book is its readability. It is one of the most accessible advanced math books I have encountered, comparable to Munkres' "Topology". Griffel explains the intuitions underlying the abstract concepts he presents. He is also careful to point out when he makes a simplification or omission to avoid a difficult or subtle point more suitable to a pure math treatment of the subject. Furthermore, Griffel explains the logic behind his notation, something that is rarely done in math texts. Each chapter concludes with a set of problems. The problems are challenging, but test and expand the reader's understanding of the material. Hints are given for many of the problems. Overall, this is an excellent resource for the applied mathematician, engineer, or scientist who wants an accessible introduction to functional analysis. Besides, the price of the Dover Edition makes this book a real bargain. Reviewer:"elddm" (Boston, Ma United States)   Amazon   back

Lonergan, Bernard J F, Insight: A Study of Human Understanding, Harper and Row 1978   Amazon   back

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

Merton, Robert C, Continuous Time Finance, Wiley-Blackwell 1992 Amazon Product Description 'Robert C. Merton's widely used text provides an overview and synthesis of finance theory from the perspective of continuous-time analysis. It covers individual financial choice, corporate finance, financial intermediation, capital markets, and selected topics on the interface between private and public finance. For this revised edition a new section on managing university endowments has been added. The book begins with a foreword by Paul Samuelson.'  Amazon   back

Miles, Jack, God : A Biography, Vintage Books 1996 Jacket: 'Jack Miles's remarkable work examines the hero of the Old Testament . . . from his first appearance as Creator to his last as Ancient of Days. . . . We see God torn by conflicting urges. To his own sorrow, he is by turns destructive and creative, vain and modest, subtle and naive, ruthless and tender, lawful and lawless, powerful yet powerless, omniscient and blind.'  Amazon   back

Nin, Anais, Incest: From a Journal of Love: The Unexpurgated Diary of Anais Nin 1932-1934, Houghton Mifflin Harcourt 1992 Amazon editorial review: From Library Journal "This second volume of the unexpurgated version of Nin's diary spans the period from October 1932 to November 1934. It draws upon previously unpublished material from the period covered by the first volume of the diary as published in 1966. Incest follows Henry & June ( LJ 10/1/86), focusing not only on Nin's continued relationship with author Henry Miller but also on her physical and emotional attachments to four other men. Nin offers intimate details of disturbing events such as her intense incestuous affair with her father and her abortion during her sixth month of pregnancy. Her diary offers direct insight into a narcissistic, passionate, analytical, and complex mind, but the brief introduction does disappointingly little to explain the editorial process that created this version of Nin's diary, which differs dramatically in style and content from its expurgated counterpart. Nevertheless, this is an important supplement to the 1966 diary and is recommended for most literature collections.' - Ellen Finnie Duranceau, MIT Lib. Copyright 1992 Reed Business Information, Inc.  Amazon   back

Polanyi, Michael, and Amaryta Sen (foreword), The Tacit Dimension, University Of Chicago Press 2009 Amazon product description: '“I shall reconsider human knowledge by starting from the fact that we can know more than we can tell,” writes Michael Polanyi, whose work paved the way for the likes of Thomas Kuhn and Karl Popper. The Tacit Dimension argues that tacit knowledge—tradition, inherited practices, implied values, and prejudgments—is a crucial part of scientific knowledge. Back in print for a new generation of students and scholars, this volume challenges the assumption that skepticism, rather than established belief, lies at the heart of scientific discovery.'  Amazon   back

von Neumann, John, and Robert T Beyer (translator), Mathematical Foundations of Quantum Mechanics, Princeton University Press 1983 Jacket: '. . . a revolutionary book that caused a sea change in theoretical physics. . . . JvN begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which JvN regards as the definitive form of quantum mechanics. . . . Regarded as a tour de force at the time of its publication, this book is still indispensable for those interested in the fundamental issues of quantum mechanics.'  Amazon   back

Wilmott, Paul, Derivatives: The Theory and Practice of Financial Engineering, John Wiley & Sons 1988 Amazon Product Description 'Derivatives by Paul Wilmott provides the most comprehensive and accessible analysis of the art of science in financial modeling available. Wilmott explains and challenges many of the tried and tested models while at the same time offering the reader many new and previously unpublished ideas and techniques. Paul Wilmott has produced a compelling and essential new work in this field. The basics of the established theories - such as stochastic calculus, Black-Scholes, binomial trees and interest-rate models - are covered in clear and precise detail, but Derivatives goes much further. Complex models - such as path dependency, non-probabilistic models, static hedging and quasi-Monte Carlo methods - are introduced and explained to a highly sophisticated level. But theory in itself is not enough, an understanding of the role the techniques play in the daily world of finance is also examined through the use of spreadsheets, examples and the inclusion of Visual Basic programs.'  Amazon   back

Papers

Friedman, Matt, et al, "100-Million_Year Dynasty of Giant Planktivorous Bony Fish in the Mesozoic Seas", Science, 327, 5968, 19 February 2010, page 990-993. 'Large-bodied suspension feeders (planktivores), which include the most massive animals to have ever lived, are conspicuously absent from Mesozoic marine environments. The only clear representatives of this trophic guild in the Mesozoic have been an enigmatic and apparently short-lived Jurassic group of extinct pachycormid fishes. Here, we report several new examples of these giant bony fishes from Asia, Europe, and North America. These fossils provide the first detailed anatomical information on this poorly understood clade and extend its range from the lower Middle Jurassic to the end of the Cretaceous, showing that this group persisted for more than 100 million years. Modern large-bodied, planktivorous vertebrates diversified after the extinction of pachycormids at the Cretaceous-Paleogene boundary, which is consistent with an opportunistic refilling of vacated ecospace.'. back

Godfray, H Charles J, et al, "Food Security: The Challenge of Feeding 9 Billion People", Science, 327, 5967, 12 February 2010, page 812-818. 'Continuing population and consumption growth will mean that the global demand for food will increase for at least another 40 years. Growing competition for land, water, and energy, in addition to the overexploitation of fisheries, will affect our ability to produce food, as will the urgent requirement to reduce the impact of the food system on the environment. The effects of climate change are a further threat. But the world can produce more food and can ensure that it is used more efficiently and equitably. A multifaceted and linked global strategy is needed to ensure sustainable and equitable food security, different components of which are explored here.'. back

Newman, Dianne K, "Feasting on Minerals", Science, 327, 5967, 12 February 2010, page 793-794. 'Far up in the Chilean Andes, in remote arid regions seemingly inhospitable to life, intrepid microorganisms thrive on a diet of rocks and air. Unfazed by long periods of desiccation or high ultraviolet energy flux, they grow in baths of sulfuric acid replete with toxic metals. The microbes fix carbon dioxide into biomass by exploiting the energy to be gained by "eating" (oxidizing) minerals that contain reduced forms of iron and sulfur, such as chalcopyrite (CuFeS2). Through their metabolism, these microbes mobilize precious metals from ore deposits into solution, making them powerful catalysts for biomining. Recent research has begun to elucidate how they achieve this remarkable feat.. back

Normile, Dennis, "Holding Back the Torrent of Rats", Science, 327, 5967, 12 February 2010, page 806-807. 'A "rat flood." That's what the tribes in Bangladesh's Chittagong Hill Tracts call it. Every 48 years, the bamboo forests that dominate the uplands of Bangladesh, Northeast India, and Myanmar (formerly known as Burma) simultaneously produce a feast of pear-sized fruit that allows rat populations to explode. After consuming the fruit, the rodents attack nearby fields, devouring 50% to 100% of the rice crop. Rat floods caused famine in 1863, 1911, and 1959, when the misery touched off a rebellion in what is now India's Mizoram State.'. back

Science editorial, , "What it Takes to Make that Meal", Science, 327, 5967, 12 February 2010, page 809. 'Researchers have been taking a close look at just how much energy it takes to produce even seemingly similar foods. The conclusion: Food choices can have a significant impact on energy use in agriculture.'. back

Stokstad, Erik, "Could Less Meat Mean More Food", Science, 327, 5967, 12 February 2010, page 810-811. 'If people in the developed world ate less meat, it would free up a lot of plants to feed billions of hungry people and gain a lot of good farmland. Some food-security researchers, however, are skeptical; they say the complexities of global markets and human food traditions could also produce some counterintuitive—and possibly counterproductive—results.'. back

Links

Angela Mollard, All men need intimacy. Even priests, 'Denying intimacy and insisting on celibacy as a prerequisite for ministry is not a sacred act but a dark tunnel to a life of secrets, torment and hypocrisy. You only have to look at pictures of Pope Jean Paul II and Anna-Teresa camping and on a ski holiday to understand that human love nourishes.' back

Antiparticle - Wikipedia, Antiparticle - Wikipedia, the free ecyclopdia, 'Feynman–Stueckelberg interpretation By considering the propagation of the negative energy modes of the electron field backward in time, Ernst Stueckelberg reached a pictorial understanding of the fact that the particle and antiparticle have equal mass m and spin J but opposite charges q. This allowed him to rewrite perturbation theory precisely in the form of diagrams. Richard Feynman later gave an independent systematic derivation of these diagrams from a particle formalism, and they are now called Feynman diagrams. Each line of a diagram represents a particle propagating either backward or forward in time. This technique is the most widespread method of computing amplitudes in quantum field theory today. Since this picture was first developed by Ernst Stueckelberg, and acquired its modern form in Feynman's work, it is called the Feynman-Stueckelberg interpretation of antiparticles to honor both scientists.' back

Aquinas 20, Summa I, 3, 7: Whether God is altogether simple? , 'I answer that, The absolute simplicity of God may be shown in many ways. First, from the previous articles of this question. For there is neither composition of quantitative parts in God, since He is not a body; nor composition of matter and form; nor does His nature differ from His "suppositum"; nor His essence from His existence; neither is there in Him composition of genus and difference, nor of subject and accident. Therefore, it is clear that God is nowise composite, but is altogether simple. . . . ' back

Barney Zwarz, The tragic legacy of George Pell, 'The penitential prayer with which Catholics begin their Mass, and which Cardinal George Pell would have recited thousands of times, asks God's forgiveness for what they have done and for what they have failed to do. Few people could have failed to do what they should have done more devastatingly than the cardinal. That is perhaps the most shocking, and damaging, revelation of his four days of testimony to the Royal Commission into Institutional Responses to Child Sexual Abuse, given by video link from Rome this week.' back

Christian Thiemann and Daniel Grady, Follow the Money: Human Mobility and Effective Communities, 'Ever wonder where your dollar bills travel after you plop them down for a cup of coffee? The Web site Where's George? allows you to do just that: Record your bill's serial number and then track its journeys as other people spend it across the country. But it's more than just a game. Because every time a dollar is spent in a new place, it means someone moved it there. Christian Thiemann and Daniel Grady of Northwestern University in Evanston, Illinois, have been using the Web site's data to study how people move within the United States.' Science, vol 327 page 951. back

David Brooks, The Governing Cancer of Our Time, 'Politics is an activity in which you recognize the simultaneous existence of different groups, interests and opinions. You try to find some way to balance or reconcile or compromise those interests, or at least a majority of them. You follow a set of rules, enshrined in a constitution or in custom, to help you reach these compromises in a way everybody considers legitimate. The downside of politics is that people never really get everything they want. It’s messy, limited and no issue is ever really settled. Politics is a muddled activity in which people have to recognize restraints and settle for less than they want. Disappointment is normal.' back

Entropy (arrow of time) - Wikipedia, Entropy (arrow of time) - Wikipedia, the fre encyclopedia, 'Entropy is the only quantity in the physical sciences that "picks" a particular direction for time, sometimes called an arrow of time. As one goes "forward" in time, the second law of thermodynamics says, the entropy of an isolated system will increase when no extra energy is consumed.' back

Feynman diagram - Wikipedia, Feynman diagram - Wikipedia, the free encyclopedia, 'In quantum field theory a Feynman diagram is an intuitive graphical representation of a contribution to the transition amplitude or correlation function of a quantum mechanical or statistical field theory' back

Gospel of Luke, Luke 12:22-31: NIV, ' 22 Then Jesus said to his disciples: "Therefore I tell you, do not worry about your life, what you will eat; or about your body, what you will wear. 23 Life is more than food, and the body more than clothes. 24 Consider the ravens: They do not sow or reap, they have no storeroom or barn; yet God feeds them. And how much more valuable you are than birds! 25 Who of you by worrying can add a single hour to his life[? 26 Since you cannot do this very little thing, why do you worry about the rest?' back

Gospel of Luke, Luke 18:22-26: NIV, ' 22 When Jesus heard this, he said to him, "You still lack one thing. Sell everything you have and give to the poor, and you will have treasure in heaven. Then come, follow me." 23 When he heard this, he became very sad, because he was a man of great wealth. 24 Jesus looked at him and said, "How hard it is for the rich to enter the kingdom of God! 25 Indeed, it is easier for a camel to go through the eye of a needle than for a rich man to enter the kingdom of God." 26 Those who heard this asked, "Who then can be saved?" back

Jenna McLaughin, Eight Memorable Passages From Apple's Fiery Response fo the FBI, back

John D Norton, Einstein for Everyone: Spacetime, 'We build a spacetime by taking instantaneous snapshots of space at successive instants of time and stacking them up. It is easiest to imagine this if we start with a two dimensional space. The snapshots taken at different times are then stacked up to give us a three dimensional spacetime.' back

John Markoff, Cryptography Pioneers Win Turing Award, 'SAN FRANCISCO — In 1970, a Stanford artificial intelligence researcher named John McCarthy returned from a conference in Bordeaux, France, where he had presented a paper on the possibility of a “Home Information Terminal.” . . . Whitfield Diffie, then a young programmer at the Stanford Artificial Intelligence Laboratory, read Mr. McCarthy’s paper and began to think about the question of what would take the place of an individual signature in a paperless world. Mr. Diffie would spend the next several years pursuing that challenge and in 1976, with Martin E. Hellman, an electrical engineer at Stanford, invented “public-key cryptography,” a technique that would two decades later make possible the commercial World Wide Web. back

Kimberley Stephens & Joanne Ruthsatz, What Prodigies Could Teach Us About Autism, 'No link has yet been proved between autism and prodigy. Prodigies aren’t typically autistic (unlike savants, in whom extraordinary abilities and autism often coincide), and they don’t have the social or communication challenges that characterize autism. But some aspects of prodigy and autism do overlap. Prodigies, like many autistic people, have a nearly insatiable passion for their area of interest. Lauren Voiers, an art prodigy from the Cleveland area, painted well into the night as a teenager; sometimes she didn’t sleep at all before school began. That sounds a lot like the “highly restricted, fixated interests” that are part of autism’s diagnostic criteria.' back

Laura Secor, How Iran's Reformists Found Their Center, 'FOR decades, Iran’s politics have centered on a contest of visions that pitted democratic reformists against hard-line theocrats. Under President Hassan Rouhani, that binary has begun to give way. Last week’s elections showcased a coordinated movement toward the center of Iran’s political spectrum. This reflects not only the ascendancy of Mr. Rouhani’s centrist faction, whose priorities are not civic empowerment or human rights so much as diplomatic and economic re-engagement with the world. It also reflects a transformation within the reformist camp. Today’s reformists are the left wing of a muted coalition. They navigate a world of lowered expectations and play by rules that demand ingenuity and patience.' back

Light cone - Wikipedia, Light cone - Wikipedia, the free encyclopedia, 'A Light cone is the path that a flash of light, emanating from a single event E (localized to a single point in space and a single moment in time) and traveling in all directions, would take through spacetime. Imagine the light confined to a two-dimensional plane, the light from the flash spreads out in a circle after the event E occurs—and when graphed the growing circle with the vertical axis of the graph representing time, the result is a cone, known as the future light cone (some animated diagrams depicting this concept can be seen here.) ' back

Michael West, The cat is out of the bag on corporate tax avoidance, back

Michelle Boorstein and Julie Zauzmer, 'Payout chart' for molestation: Secret archive held chilling details of clergy abuse, 'A Catholic diocese in Pennsylvania announced Thursday that it will post the names online of priests credibly accused of sexually abusing children, a decision that came two days after a dramatic grand jury report alleged a decades-long cover-up. . . . The report relied on a secret archive at the Altoona-Johnstown diocese, which dates back to the 1950s and was opened up this summer when authorities obtained a search warrant. The grand jury interviewed surviving priests and their alleged victims, and compiled a 147-page account detailing accusations against more than 50 religious leaders including priests and teachers. back

Miguel Vatter, Have faith: civil religion can counter the lure of eternal ife for jihadists, 'Machiavelli’s solution was a new interpretation of the figure of the prophet. The prophet’s role was not to found a new church or empire, but to bring to his people a constitution that guarantees that power shall remain in the hands of the people, not their spiritual or worldly representatives. Hence, a civil religion is a philosophical idea of religion that allows us to interpret prophetic religions in a way that is supportive of republican constitutions. The first person to have this idea may have been Al-Farabi, a 10th-century Muslim philosopher. His fundamental thought was that the prophet was both a legislator and a philosopher, rather than a theologian or a political leader.' back

Minkowski space - Wikipedia, Minkowski space - Wikipedia, the free encyclopedia, 'In mathematical physics, Minkowski space or Minkowski spacetime is a combination of Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Although initially developed by mathematician Hermann Minkowski for Maxwell's equations of electromagnetism, the mathematical structure of Minkowski spacetime was shown to be an immediate consequence of the postulates of special relativity.' back

Noel Debien, Five points to help you understand Pell's testimony, back

PBS, Online NewsHour: The Mass Suicide near San Diego -- March 27 1997, 'Recent news reports have been filled with the troubling story of a mass suicide involving a computer-related cult. At a mansion outside San Diego, police found 39 bodies dressed in black and covered in purple shrouds. The members apparently killed themselves to prepare for the arrival of a alien spaceship they say is hiding behind the Hale-Bopp comet. After a background report by Charles Krause, Jim Lehrer leads a discussion of the suicides with a panel of cult experts.' back

Robyn Blewer, To believe or not to believe: child witnesses and the sex abuse royal commissiomn, 'Truth-telling is a base premise of Catholic religious instruction. Therefore, child witnesses who emerged from these institutions – through fear alone of the fiery depths of hell – had another dimension of witness reliability. In the right circumstances, with adult police and adult judges and adult juries ready to believe them, the impediments to these children being heard were significantly reduced. That children from religious institutions were not listened to or protected, in circumstances where the law may well have done so, speaks volumes about the Catholic Church. While Pell claims these “muck-ups” were due to the personal failings of a few members of the church, the history of children in Australian courts suggests otherwise. All the structures were in place, bolstered by Catholic dogma, to hear the testimonies of these children within the courts. That they were not heard points to an organisational structure that consistently and repugnantly failed the most vulnerable of its members.' back

Spin-statistics theorem - Wikipedia, Spin-statistics theorem - Wikipedia, the free encyclopedia, 'In quantum mechanics, the spin–statistics theorem relates the spin of a particle to the particle statistics it obeys. The spin of a particle is its intrinsic angular momentum (that is, the contribution to the total angular momentum that is not due to the orbital motion of the particle). All particles have either integer spin or half-integer spin (in units of the reduced Planck constant ħ. The theorem states that: The wave function of a system of identical integer-spin particles has the same value when the positions of any two particles are swapped. Particles with wave functions symmetric under exchange are called bosons. The wave function of a system of identical half-integer spin particles changes sign when two particles are swapped. Particles with wave functions antisymmetric under exchange are called fermions.' back

The Book of Joshua, Joshua 18:10-14, '10 Joshua then cast lots for them in Shiloh in the presence of the LORD, and there he distributed the land to the Israelites according to their tribal divisions. 11 The lot came up for the tribe of Benjamin, clan by clan. Their allotted territory lay between the tribes of Judah and Joseph:' back

Timothy W Jones, For whom the Pell tolls: what did we learn from George Pell's royal commission appearance?, 'It is evident that Archbishop Frank Little and Bishop Ronald Mulkearns neglected their responsibilities and even contravened canon law in their dealings with sexually offending clergy. But Pell’s claims to have fulfilled his moral responsibility in the face of this dysfunction ring hollow. Pell chose to keep knowledge of his fellow priests' offending at bay and allowed his superiors' neglect and malpractice to continue. After the exposure of this legal dysfunction and moral cowardice, we can expect the royal commission’s recommendations will include changes to Roman Catholic governance and canon law.' back

United States District Court, Central District of California, Eastern Division, In the matter of the search of an Apple iphone seized during the execution of a search warranton a black Lexus IS300, California license plate 35KGD203, Spple Inc's mtion to vacate order compelling Apple Inc to assist agents in search, and opposition to Governmnet's motion to compel assistance back

Waren Buffet, Berkshire HsthawayInc, Shareholder Letters, back

Zipf-Mandelbrot law - Wikipedia, Zipf-Mandelbrot law - Wikipedia, the free encyclopedia, 'In probability theory and statistics, the Zipf–Mandelbrot law is a discrete probability distribution. Also known as the Pareto-Zipf law, it is a power-law distribution on ranked data, named after the linguist George Kingsley Zipf who suggested a simpler distribution called Zipf's law, and the mathematician Benoît Mandelbrot, who subsequently generalized it.' back