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

Dauben (1990), Joseph Warren, Georg Cantor: His Mathematics and Philosophy of the Infinite, Princeton University Press 1990 Jacket: 'One of the greatest revolutions in mathematics occurred when Georg Cantor (1843-1918) promulgated his theory of transfinite sets. . . . Set theory has been widely adopted in mathematics and philosophy, but the controversy surrounding it at the turn of the century remains of great interest. Cantor's own faith in his theory was partly theological. His religious beliefs led him to expect paradox in any concept of the infinite, and he always retained his belief in the utter veracity of transfinite set theory. Later in his life, he was troubled by attacks of severe depression. Dauben shows that these played an integral part in his understanding and defense of set theory.' 
Amazon   back

Hopkins (2001), Keith, A World Full of Gods: The Strange Triumph of Christianity, Penuin Random House 2001 ' In this provocative, irresistibly entertaining book, Keith Hopkins takes readers back in time to explore the roots of Christianity in ancient Rome. Combining exacting scholarship with dazzling invention, Hopkins challenges our perceptions about religion, the historical Jesus, and the way history is written. He puts us in touch with what he calls “empathetic wonder”—imagining what Romans, pagans, Jews, and Christians thought, felt, experienced, and believed-by employing a series of engaging literary devices. These include a TV drama about the Dead Sea Scrolls; the first-person testimony of a pair of time-travelers to Pompeii; a meditation on Jesus’ apocryphal twin brother; and an unusual letter on God, demons, and angels.' 
Amazon   back

Kolmogorov (1956), Andrey Nikolaevich, and Nathan Morrison (Translator) (With an added bibliography by A T Bharucha-Reid), Foundations of the Theory of Probability, Chelsea 1956 Preface: 'The purpose of this monograph is to give an axiomatic foundation for the theory of probability. . . . This task would have been a rather hopeless one before the introduction of Lebesgue's theories of measure and integration. However, after Lebesgue's publication of his investigations, the analogies between measure of a set and mathematical expectation of a random variable became apparent. These analogies allowed of further extensions; thus, for example, various properties of independent random variables were seen to be in complete analogy with the corresponding properties of orthogonal functions . . .' 
Amazon   back

Teilhard de Chardin (1965), Pierre, The Phenomenon of Man, Collins 1965 Sir Julian Huxley, Introduction: 'We, mankind, contain the possibilities of the earth's immense future, and can realise more and more of them on condition that we increase our knowledge and our love. That, it seems to me, is the distillation of the Phenomenon of Man.'  
Amazon   back

Aquinas, Summa, I, 22, 3, Does God have immediate providence over everything?, ' I answer that, Two things belong to providence—namely, the type of the order of things foreordained towards an end; and the execution of this order, which is called government. As regards the first of these, God has immediate providence over everything, because He has in His intellect the types of everything, even the smallest; and whatsoever causes He assigns to certain effects, He gives them the power to produce those effects. Whence it must be that He has beforehand the type of those effects in His mind. As to the second, there are certain intermediaries of God's providence; for He governs things inferior by superior, not on account of any defect in His power, but by reason of the abundance of His goodness; so that the dignity of causality is imparted even to creatures.' back

BSR, Business for Social Responsibility, ' The period from 2015 has seen several crucially important developments bringing strong momentum to the movement to achieve a more just and sustainable world. The landmark Paris Agreement has sparked previously unimagined climate action. Over the past few years, we have also seen significant increases in ESG investing, the emergence of innovative business models and technologies driven by sustainability imperatives, and rising regulatory and policy initiatives promoting sustainable business. Sustainability is now firmly established as being of fundamental importance to business and the wider world. At the same time, watershed global events including Brexit, political shocks in the United States, COVID-19, the injustice, and inequity symbolized by the murder of George Floyd and the #MeToo movement, Russia’s war on Ukraine, and a politically weaponized backlash against ESG has created a turbulent environment. Combined with the widespread, rapid, and intensifying impact of climate change, and lingering social and economic inequalities underscore the urgency of achieving progress at scale. back

Cantor's first uncountability proof - Wikipedia, Cantor's first uncountability proof - Wikipedia, the free encyclopedia, 'Georg Cantor's first proof of uncountability demonstrates that the set of all real numbers is uncountably, rather than countably, infinite. This proof differs from the more familiar proof that uses his diagonal argument. . . . In 1891 Cantor published his diagonal argument, which produces an uncountability proof that is generally considered simpler and more elegant than his first proof. Both uncountability proofs contain ideas that can be used elsewhere. The diagonal argument is a general technique that is useful in mathematical logic and theoretical computer science, while Cantor's first uncountability proof can be generalized to any ordered set with the same order properties as the real numbers.' back

Cantor's paradox - Wikipedia, Cantor's paradox - Wikipedia, the free encyclopedia, 'In set theory, Cantor's paradox is derivable from the theorem that there is no greatest cardinal number, so that the collection of "infinite sizes" is itself infinite. The difficulty is handled in axiomatic set theory by declaring that this collection is not a set but a proper class; in von Neumann–Bernays–Gödel set theory it follows from this and the axiom of limitation of size that this proper class must be in bijection with the class of all sets. Thus, not only are there infinitely many infinities, but this infinity is larger than any of the infinities it enumerates.' back

Cantor's theorem - Wikipedia, Cantor's theorem - Wikipedia, the free encyclopedia, ' In mathematical set theory, Cantor's theorem is a fundamental result which states that, for any set A , the set of all subsets of A, the power set of A, has a strictly greater cardinality than A itself. For finite sets, Cantor's theorem can be seen to be true by simple enumeration of the number of subsets. Counting the empty set as a subset, a set with n elements has a total of n 2>sup> subsets, and the theorem holds because n2>sup> > nfor all non-negative integers. Much more significant is Cantor's discovery of an argument that is applicable to any set, and shows that the theorem holds for infinite sets also.' back

Chris Barrie, Australian military must hold hard to its moral compass to restore trust of people, ' It is also extraordinary to me that the trial was allowed to proceed. Though proceedings were initiated in 2018, two years before the delivery of the Australia Defence Force inspector-general’s Afghanistan inquiry report, carried out by Justice Paul Brereton (aka the Brereton report), I think the report should have shaped the risk of continuing with the trial. The findings in that report are that 39 cases of potential war crimes require further investigation with a view headed towards instituting criminal proceedings. In the public version of the report we do not have the more detailed information in the unredacted report. No doubt that people in the Office of the Special Investigator (OSI) set up on 4 January 2021, will be using the unredacted report to establish further proceedings. If there were 39 credible war crimes committed in Afghanistan one wonders what the probability that Roberts-Smith might be involved in at least one of them would be? Maybe, this defamation action was based on risk perceptions encapsulated in the SAS’s motto “who dares wins”.' back

Clonal selection - Wikipedia, Clonal selection - Wikipedia, the free encyclopedia, ' In immunology, clonal selection theory explains the functions of cells of the immune system (lymphocytes) in response to specific antigens invading the body. The concept was introduced by Australian doctor Frank Macfarlane Burnet in 1957, in an attempt to explain the great diversity of antibodies formed during initiation of the immune response. The theory has become the widely accepted model for how the human immune system responds to infection and how certain types of B and T lymphocytes are selected for destruction of specific antigens.' back

Colin Heseltine, China doesn’t want a war – it has better ways to achieve its goals, ' Marles is correct; China doesn’t lend itself to simplistic platitudes. A good way forward would be for the government to present the security environment being shaped by China in realistic rather than hawkish terms. In the current atmosphere of extreme mistrust between the US and China language matters. The government wouldn’t undermine its case for strengthening ADF capabilities, if it ensured a rational and calm discourse rather than in the overwrought and fearful one we often hear. The mooted visit to China by the prime minister this year would provide an opportunity to calibrate the narrative.' back

David Hilbert (1925), On the Infinite, ' We encounter a completely different and quite unique conception of the notion of infinity in the important and fruitful method of ideal elements. The method of ideal elements is used even in elementary plane geometry. The points and straight lines of the plane originally are real, actually existent objects. One of the axioms that hold for them is the axiom of connection: one and only one straight line passes through two points. It follows from this axiom that two straight lines intersect at most at one point. There is no theorem that two straight lines always intersect at some point, however, for the two straight lines might well be parallel. Still we know that by introducing ideal elements, viz., infinitely long lines and points at infinity, we can make the theorem that two straight lines always intersect at one and only one point come out universally true. These ideal "infinite" elements have the advantage of making the system of connection laws as simple and perspicuous as possible. Another example of the use of ideal elements are the familiar complex-imaginary magnitudes of algebra which serve to simplify theorems about the existence and number of the roots of an equation..' back

Eugene Wigner (1960), The Unreasonable Effectiveness of Mathematics in the Natural Sciences, 'The first point is that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it. Second, it is just this uncanny usefulness of mathematical concepts that raises the question of the uniqueness of our physical theories.' back

Eva Weber, Merkel, ' Eva Weber’s documentary Merkel is the astonishing story of how a triple political outsider – a woman, a scientist, and an East German – became one of the most powerful politicians in the world. For years Angela Merkel, the first female Chancellor of Germany, was Western Europe’s most influential leader. Yet despite her historic 16-year Chancellorship of Germany, she remains something of an enigma. Clear-eyed, cool-headed, diligent, and methodical, she put her policies first, keeping her personal life private. From Merkel’s upbringing in East Germany, and studies in quantum chemistry, to her surprising start in politics and fast ascent, this fascinating documentary creates a rich portrait using a vast array of archival material and revealing interviews from friends and colleagues, including journalists, political allies, and critics.' back

Farhad Manjoo, It’s the End of Computer Programming as We Know It. (And I Feel Fine.), ' Though I did find it fascinating to learn to think the way computers do, there seemed to be something fundamentally backward about programming a computer that I just couldn’t get over: Wasn’t it odd that the machines needed us humans to learn their maddeningly precise secret languages to get the most out of them? If they’re so smart, shouldn’t they try to understand what we’re saying, rather than us learning how to talk to them? . . . .. Now that may finally be happening. In a kind of poetic irony, software engineering is looking like one of the fields that could be most thoroughly altered by the rise of artificial intelligence. . . . .. But A.I. coders are quickly getting smart enough to rival human coders. Last year, DeepMind reported in the journal Science that when AlphaCode’s programs were evaluated against answers submitted by human participants in coding competitions, its performance “approximately corresponds to a novice programmer with a few months to a year of training".' back

Flinders University, Virtual Australian Museum of Paleaontology, 'VAMP is the online home of Australian fossils in 3-D. Here you can explore 3-D scans of some of Australia’s most important fossil specimens as never before – in one location, and in exquisite detail. The scans on this site are available for researchers, educators and members of the public to view, rotate, zoom and download. Step into our virtual museum to explore rare and important fossils from sites all around Australia, celebrating more than 600 million years of evolution from the Ediacaran to the Holocene. Learn more about the evolution, anatomy, and discovery of remarkable Australian fossils. We’re uploading new scans all the time, so keep an eye out for exciting additions to the museum! ' back

James Pang & Alex Fornito, Have we got the brain all wrong? A new study shows its shape is more important than its wiring, ' An alternative view, embodied by an approach to modelling brain activity called neural field theory, eschews this division of the brain into discrete areas. This view focuses on how waves of cellular excitation move continuously through brain tissue, like the ripples formed by raindrops falling into a pond. Just as the shape of the pond constrains the possible patterns formed by the ripples, wavelike patterns of activity are influenced by the three-dimensional shape of the brain. . . . .. We used computer simulations to confirm that the close link between brain shape and function is driven by wavelike activity propagating throughout the brain. The simulations relied on a simple wave model that is widely used to study other physical phenomena, such as earthquakes and ocean currents. The model only uses the shape of the brain to constrain how the waves evolve through time and space. ' back

Jeffrey Nicholls (1987), A theory of Peace, ' The argument: I began to think about peace in a very practical way during the Viet Nam war. I was the right age to be called up. I was exempted because I was a clergyman, but despite the terrors that war held for me, I think I might have gone. It was my first whiff of the force of patriotism. To my amazement, it was strong enough to make even me face death.
In the Church, I became embroiled in a deeper war. Not a war between goodies and baddies, but the war between good and evil that lies at the heart of all human consciousness. Existence is a struggle. We need all the help we can get. Religion is part of that help and theology is the scientific foundation of religion.' back

Jeffrey Nicholls (1992a), An essay on value, ' Killing
1 We must kill to live. The question before is is whether or not to kill some fraction of the old growth forest (OGF) in the Wingham management area (WMA) in order to keep the sawmilling operation at Mt George alive.
Religion
2 Although the Environmental Impact Statement (EIS), as we have it, is a document based largely on resource, commercial and employment considerations, I believe the Commission is facing a religious issue, and will have no peace until it realizes that fact. 3 Matters of life and death are questions of religion. For those who have power over life and death, deciding what to kill is a question of value. The value system of any organism is determined by the history of its survival. 4 If the decision is good, the benefit from killing will exceed the value of what is destroyed, yielding a profit and enhanced probability of survival. A wrong judgement of value leads to the opposite result.' back

Manley & Taylor (1996), Descartes Meditations, A Trilingual HTML Edition edited by David B. Manley and Charles S. Taylor: 'The publication of this English-Latin-French HTML edition of DesCartes' Meditations on First Philosophy is quite simply an experiment in electronic scholarship. We decided to make this edition available and to encourage its free distribution for scholarly purposes. The idea behind the experiment is to see how others involved in electronic scholarship might put these texts to use. We have no pre-determined ideas of what such use may be when transformed from this origin. The texts have no hypertext annotations except for those used for navigation. We invite others to download this edition and to create their own hypertext annotated editions and then to publish those additions on their own Web servers for everyone to use.' back

PGLE, The Partnership for Global LGBTIQ+ Equality., ' “The increase in representation and visibility of the LGBTIQ+ community among the business world, and at landmark global events such as the World Economic Forum, is remarkable,” said Aron Cramer, President and CEO of BSR, the parent organization of PGLE. “It’s a vibrant symbol of the growing consensus among companies that the creation of inclusive, respectful, and safe work environments is good for business, and good for society. The events addressing LGBTIQ+ inclusivity at Davos provide us with an important opportunity, and a prominent platform, to reflect on the progress we’ve made while also acknowledging that true success demands we reach people in all corners of the globe, and particularly those most vulnerable". ' back

Sanam Maher, The activists confronting period taboos in Pakistan, ' The debate around providing women with period products during the floods was only the latest iteration of an issue that has existed for too long, Sana believes. “Most people want to confine women,” she says. “You don’t want to educate women about things like menstruation, and as a result, they are not able to perform to the best of their abilities. The woman stays indoors, stays preoccupied with how to manage something like blood flow. She will drop out of school. Isn’t that what we want? It could be a conversation about breastfeeding or pregnancy and we will still be angry about it. We don’t like the idea of women occupying public space and being present – that’s the real problem".' back

Solemn vow - Wikipedia, Solemn vow - Wikipedia, the free encyclopedia, 'In Roman Catholic canon law, a solemn vow is a vow ("a deliberate and free promise made to God about a possible and better good") that the Church has recognized as such.

Any other vow, public or private, individual or collective, concerned with an action or with abstaining from an action, is a simple vow.

In canon law a vow is public (concerning the Church itself directly) only if a legitimate superior accepts it in the name of the Church; all other vows, no matter how much publicity is given to them, are classified as private vows (concerning directly only those who make them). The vow taken at profession as a member of any religious institute is a public vow, but in recent centuries can be either solemn or simple.' back

Yujia Li et al, Competition-level code generation with AlphaCode, ' Programming is a powerful and ubiquitous problem-solving tool. Systems that can assist programmers or even generate programs themselves could make programming more productive and accessible. Recent transformer-based neural network models show impressive code generation abilities yet still perform poorly on more complex tasks requiring problem-solving skills, such as competitive programming problems. Here, we introduce AlphaCode, a system for code generation that achieved an average ranking in the top 54.3% in simulated evaluations on recent programming competitions on the Codeforces platform. AlphaCode solves problems by generating millions of diverse programs using specially trained transformer-based networks and then filtering and clustering those programs to a maximum of just 10 submissions. This result marks the first time an artificial intelligence system has performed competitively in programming competitions.' back