Einstein (1923), Albert, and Einstein, Lorentz, Minkowski, Weyl and Sommerfeld, The Principle of Relativity - A collection of original memoirs on the special and general theory of Relativity. With notes by A. Sommerfeld. Translated by W. Perrett and G. B. Jeffery, Methuen 1923 Minkowski: ' We can determine the ratio of the units of length and time beforehand in such a way that the natural limit of velocity becomes c = 1. If we introduce it = s in place of t the quadratic differential expression dτ² = - x² - y² - z² - s² thus becomes perfectly symmetrical in x, y, z, s; and this symmetry is communicated to any law which does not contradict the world postulate. Thus the essence of this postulate may be clothed in a very pregnant manner in the mystic formula 3.10⁵ = i seconds.' 
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Goddard (1998), Peter , and Stephen Hawking, Abraham Pais, Maurice Jacob, David Olive, and Michael Atiyah, Paul Dirac, The Man and His Work, Cambridge University Press 1998 Jacket: Paul Adrien Maurice Dirac was one of the founders of quantum theory and the aithor of many of its most important subsequent developments. He is numbered alongside Newton, Maxwell, Einstein and Rutherford as one of the greatest physicists of all time. This volume contains four lectures celebrating Dirac's life and work and the text of an address given by Stephen Hawking, which were given on 13 November 1995 on the occasion of the dedication of a plaque to him in Westminster Abbey. In the first lecture, Abraham Pais describes from personal knowledge Dirac's character and his approach to his work. In the second lecture, Maurice Jacob explains not only how and why Dirac was led to introduce the concept of antimatter, but also its central role in modern particle physics and cosmology. In the third lecture, David Olive gives an account of Dirac's work on magnetic monopoles and shows how it has had a profound influence in the development of fundamental physics down to the present day. In the fourth lecture, Sir Michael Atiyah explains the widespread significance of the Dirac equation in mathematics, its roots in algebra and its implications for geometry and topology.' 
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Hartle (2003), James B., Gravity: An Introduction to Einstein's General Relativity, Addison-Wesley 2003 'The aim of this groundbreaking new book is to bring general relativity into the undergraduate curriculum and make this fundamental theory accessible to all physics majors. Using a "physics first" approach to the subject, renowned relativist James B. Hartle provides a fluent and accessible introduction that uses a minimum of new mathematics and is illustrated with a wealth of exciting applications. The emphasis is on the exciting phenomena of gravitational physics and the growing connection between theory and observation. The Global Positioning System, black holes, X-ray sources, pulsars, quasars, gravitational waves, the Big Bang, and the large scale structure of the universe are used to illustrate the widespread role of how general relativity describes a wealth of everyday and exotic phenomena.' 
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Hobson (2006), M. P., and G. P. Efstathiou, A. N. Lasenby, General Relativity: An Introduction for Physicists, Cambridge University Press 2006 'After reviewing the basic concept of general relativity, this introduction discusses its mathematical background, including the necessary tools of tensor calculus and differential geometry. These tools are used to develop the topic of special relativity and to discuss electromagnetism in Minkowski spacetime. Gravitation as spacetime curvature is introduced and the field equations of general relativity derived. After applying the theory to a wide range of physical situations, the book concludes with a brief discussion of classical field theory and the derivation of general relativity from a variational principle.'  
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Khinchin (1960, 1998), Aleksandr Yakovlevich, The Mathematical Foundations of Quantum Statistics, Dover 1998 'In the area of quantum statistics, I show that a rigorous mathematical basis of the computational formulas of statistical physics . . . may be obtained from an elementary application of the well-developed limit theorems of the theory of probability.' 
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Nicholls (2025), Jeffrey, Cognitive Cosmogenesis: A systematic integration of Physics and Theology, ' 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. Three years later I discovered Bernard Lonergan, a Jesuit. Lonergan was a faithful Catholic who had set out to bring the the work of Aquinas into the twentieth century. Lonergan presented me with a new proof for the existence of God. I was not convinced. I read him a few more times and slowly became a heretic. I could no longer believe in the Catholic God. I said so, and after five years the Order let me go. 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. Austin Macauleyd his ideas quite cosmic. Three years later I discovered Bernard Lonergan, a Jesuit. Lonergan was a faithful Catholic who had set out to bring the the work of Aquinas into the twentieth century. Lonergan presented me with a new proof for the existence of God. I was not convinced. I read him a few more times and slowly became a heretic. I could no longer believe in the Catholic God. I said so, and after five years the Order let me go. 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. The third step is to 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. 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.
The third step is to 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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von Neumann (2018), John, and Nicholas A. Wheeler (editor), Robert T Beyer (translator), The Mathematical Foundations of Quantum Mechanics, Princeton University Press 2018 ' Quantum mechanics was still in its infancy in 1932 when the young John von Neumann, who would go on to become one of the greatest mathematicians of the twentieth century, published Mathematical Foundations of Quantum Mechanics--a revolutionary book that for the first time provided a rigorous mathematical framework for the new science. Robert Beyer's 1955 English translation, which von Neumann reviewed and approved, is cited more frequently today than ever before. But its many treasures and insights were too often obscured by the limitations of the way the text and equations were set on the page. In this new edition of this classic work, mathematical physicist Nicholas Wheeler has completely reset the book in TeX, making the text and equations far easier to read. He has also corrected a handful of typographic errors, revised some sentences for clarity and readability, provided an index for the first time, and added prefatory remarks drawn from the writings of Léon Van Hove and Freeman Dyson. The result brings new life to an essential work in theoretical physics and mathematics.' 
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Wilczek (2008), Frank, The Lightness of Being: Mass, Ether, and the Unification of Forces, Basic Books 2008 ' In this excursion to the outer limits of particle physics, Wilczek explores what quarks and gluons, which compose protons and neutrons, reveal about the manifestation of mass and gravity. A corecipient of the 2004 Nobel Prize in Physics, Wilczek knows what he’s writing about; the question is, will general science readers? Happily, they know what the strong interaction is (the forces that bind the nucleus), and in Wilczek, they have a jovial guide who adheres to trade publishing’s belief that a successful physics title will not include too many equations. Despite this injunction (against which he lightly protests), Wilczek delivers an approachable verbal picture of what quarks and gluons are doing inside a proton that gives rise to mass and, hence, gravity. Casting the light-speed lives of quarks against “the Grid,” Wilczek’s term for the vacuum that theoretically seethes with quantum activity, Wilczek exudes a contagious excitement for discovery. A near-obligatory acquisition for circulating physics collections.' --Gilbert Taylor  
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Alexandra Witze (2024_12_12), Mars rover makes epic climb to explore some of the oldest rocks in the Solar System, 'After a months-long climb up the side of a crater on Mars, NASA’s Perseverance rover has finally emerged on its rim — and now faces a 4-billion-year-old landscape never before explored on the red planet. Flying Mars rocks to Earth could cost an astronomical $11 billion “These are amongst the oldest rocks in the Solar System,” says Kenneth Farley, a geochemist at the California Institute of Technology in Pasadena and the mission’s project scientist. He spoke on 12 December at a meeting of the American Geophysical Union in Washington DC. Researchers hope that the rocks outside of Jezero Crater hold signs of whether Mars might have once sustained extraterrestrial life, when it was warmer and wetter than today. The rover landed in Jezero nearly four years ago and has been exploring the crater’s floor and a fossilized river delta for such signs ever since. Over the course of its 32-kilometre journey, it has drilled rock samples and stored 15 of them in its belly; there are 11 empty tubes remaining that could be filled with additional intriguing rocks from the fresh Martian terrain it now faces. . . . Of the samples already on board Perseverance, Farley said his favourite is one gathered in July, from an area called Cheyava Falls. The rock is astrobiologically intriguing because it is covered in spots, like those of a leopard, with dark rims and lighter interiors. On Earth, rocks that have such patterns can host microbes: chemical reactions causing the dark rims to form serve as an energy source for the microorganisms. With the instruments it has on board, Perseverance determined that the dark rims on the rocks at Cheyava Falls are likely an iron-phosphate material, and the spots rich in organic compounds, which contain carbon. Organic compounds can be made by living organisms or through non-living processes, but researchers are optimistic about this sample hinting at ancient life because of the combination of the spotting pattern, the detection of the organic compounds, and evidence that water flowed through the site. back

Brouwer fixed point theorem - Wikipedia, Brouwer fixed point theorem - Wikipedia, the free encyclopedia, 'Among hundreds of fixed-point theorems] Brouwer's is particularly well known, due in part to its use across numerous fields of mathematics. In its original field, this result is one of the key theorems characterizing the topology of Euclidean spaces, along with the Jordan curve theorem, the hairy ball theorem, the invariance of dimension and the Borsuk–Ulam theorem. This gives it a place among the fundamental theorems of topology.' back

Carissa Wong (2024), Cubic millimetre of brain mapped in spectacular detail, ' Researchers have mapped a tiny piece of the human brain in astonishing detail. The resulting cell atlas, which was described today in Science1 and is available online, reveals new patterns of connections between brain cells called neurons, as well as cells that wrap around themselves to form knots, and pairs of neurons that are almost mirror images of each other. The 3D map covers a volume of about one cubic millimetre, one-millionth of a whole brain, and contains roughly 57,000 cells and 150 million synapses — the connections between neurons. It incorporates a colossal 1.4 petabytes of data. “It’s a little bit humbling,” says Viren Jain, a neuroscientist at Google in Mountain View, California, and a co-author of the paper. “How are we ever going to really come to terms with all this complexity?” Slivers of brain The brain fragment was taken from a 45-year-old woman when she underwent surgery to treat her epilepsy. It came from the cortex, a part of the brain involved in learning, problem-solving and processing sensory signals. The sample was immersed in preservatives and stained with heavy metals to make the cells easier to see. Neuroscientist Jeff Lichtman at Harvard University in Cambridge, Massachusetts, and his colleagues then cut the sample into around 5,000 slices — each just 34 nanometres thick — that could be imaged using electron microscopes. back

Charles Torre (2018_06_16), What is a Photon? Foundations of Quantum Field Theory, 'I have always been dismayed by the fact that one can get a PhD in physics yet never be exposed to the theory of the photon. To be sure, we talk about photons all the time and we know some of their salient properties. But how do they arise in the framework of quantum theory? What do they have to do with the more familiar theory of electromagnetism? Of course, most people don’t ever learn what a photon really is because a photon is an entity which arises in quantum field theory, which is not a physics class most people get to take.' back

Christopher Shields (Stanford Encyclopedia of Philosophy b), The Active Mind of De Anima III 5 , ' After characterizingnous the mind (nous) and its activities in De Animaiii 4, Aristotle takes a surprising turn. In De Anima iii 5, he introduces an obscure and hotly disputed subject: the active mind or active intellect (nous poiêtikos). Controversy surrounds almost every aspect of De Anima iii 5, not least because in it Aristotle characterizes the active mind—a topic mentioned nowhere else in his entire corpus—as ‘separate and unaffected and unmixed, being in its essence actuality’ (chôristos kai apathês kai amigês, tê ousia energeia; DA iii 5, 430a17–18) and then also as ‘deathless and everlasting’ (athanaton kai aidion; DA iii 5, 430a23). This comes as no small surprise to readers of De Anima, because Aristotle had earlier in the same work treated the mind (nous) as but one faculty (dunamis) of the soul (psuchê), and he had contended that the soul as a whole is not separable from the body (DA ii 1, 413a3–5). back

Deepa Parent (2024_12_11), Iranian women could face death penalty for defying new morality laws, ' Women in Iran could face the death sentence or up to 15 years in prison if they defy new compulsory morality laws due to come into effect this week. New laws promoting the “culture of chastity and hijab” passed by the Iranian authorities earlier this month impose severe penalties for those caught “promoting nudity, indecency, unveiling or improper dressing”, including fines of up to £12,500, flogging and prison sentences ranging from five to 15 years for repeat offenders. Article 37 of the new law also stipulates that those promoting or propagating indecency, unveiling or “bad dressing” to foreign entities, including international media and civil society organisations, could face a decade in prison and up to £12,500 in fines. Those whose conduct is considered by the authorities to amount to “corruption on Earth” could be sentenced to death under article 296 of Iran’s Islamic penal code. Amnesty International said this legal provision in effect meant that women and girls sending videos of themselves unveiled to media outside Iran or “otherwise engaging in peaceful activism” may be sentenced to death. The human rights group said the law also appeared to provide immunity for anyone who wanted to carry out their “religious duty” and enforce compulsory veiling on women. Anyone intervening or attempting to stop the arrest or harassment of woman and girls defying compulsory veiling could themselves be imprisoned or fined under article 60 of the new law.' back

Differentiable manifold - Wikipedia, Differentiable manifold - Wikipedia, the free encyclopedia, ' In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a vector space to allow one to apply calculus. Any manifold can be described by a collection of charts (atlas). One may then apply ideas from calculus while working within the individual charts, since each chart lies within a vector space to which the usual rules of calculus apply. If the charts are suitably compatible (namely, the transition from one chart to another is differentiable), then computations done in one chart are valid in any other differentiable chart. ' back

Gabriel Garcia Ochoa (2024_12_08), The book that sparked a revolution: One Hundred Years of Solitude, the literary masterpiece now adapted for TV, ' First published in 1967, One Hundred Years of Solitude takes place in Macondo, an imaginary town in Colombia based on Aracataca, García Márquez’s hometown. . . . One Hundred Years of Solitude is funny, tragic, sensual and political. The novel explores cyclical time, meta-fiction, social taboos, the history of Latin America and more specifically, Colombia. The Buendías are constantly entangled in passionate and unhealthy love affairs, driven by their obsessions, haunted by their secrets. Members of each generation repeat, or respond to, the destructive choices of the last, the patterns of behaviour they are raised with and locked into. . . . The term “magical realism” was coined in 1925 by the art critic Franz Roh, who used it to describe a style of painting that we would now classify as post-expressionism. The 1940s and 1950s saw the rise of two pylons of Latin American literature: the Argentine author Jorge Luis Borges, and Alejo Carpentier from Cuba. Borges and Carpentier lay the foundations for what we now call magical realist literature, and for the famous literary movement of the 1960s, the “Latin American Boom”, during which authors like Carlos Fuentes (Mexico), Mario Vargas Llosa (Peru), and Julio Cortázar (Argentina) were widely read and praised the world over. The “detonator” of “the boom” was Márquez’s One Hundred Years of Solitude. . . . The term “magical realism” was coined in 1925 by the art critic Franz Roh, who used it to describe a style of painting that we would now classify as post-expressionism. The 1940s and 1950s saw the rise of two pylons of Latin American literature: the Argentine author Jorge Luis Borges, and Alejo Carpentier from Cuba. Borges and Carpentier lay the foundations for what we now call magical realist literature, and for the famous literary movement of the 1960s, the “Latin American Boom”, during which authors like Carlos Fuentes (Mexico), Mario Vargas Llosa (Peru), and Julio Cortázar (Argentina) were widely read and praised the world over. The “detonator” of “the boom” was Márquez’s One Hundred Years of Solitude. . . . In The Fragrance of Guava, a series of interviews between García Márquez and Colombian journalist Plinio Apuleyo Mendoza, he explains: “there is not a single line in my novels which is not based on reality”. Reality, he says, “isn’t limited to the price of tomatoes and eggs; everyday life in Latin America proves that reality is full of the most extraordinary things”. According to García Márquez, reality is much more magical than we give it credit for, and realism is not always the right vehicle to do it justice; sometimes it falls short. The depth, complexity, and wondrous nature of the everyday may require other means. And so, the magical realist style of One Hundred Years of Solitude raises another question, which is not unique to Latin America, but applicable to all of us: if magic can be commonplace, can the commonplace be magical too? That is the tacit, hopeful underside to García Márquez’s novel, that what is magical can be a matter of perception. We can find it in a seed, the smell of chocolate, or in the miracle of our existence as primates made of stardust, briefly held together by self-awareness, and if we’re fortunate enough, by love, which according to García Márquez, is the antithesis of solitude.' back

Gideon Levi (2024_12_11), Opinion | Syria's Fragile Hope Is Being Battered by Israel's Predatory Campaign of Destruction, ' Predatory birds are now circling around in Syria's skies, smelling the stench of the corpses lying around and descending to get their share. Israel's air force is bombing and destroying the Syrian army, with Israel's land army seizing chunks of its territory. Like water seeking the lowest place, Israel has found another opportunity in the multitude of options appearing on its path lately, destroying Syria's army and taking territory as this beaten and bruised country awakens from the nightmare of the previous regime, facing an unknown future. Ostensibly, there is some logic to Israel's move. The circumstances are favorable for destroying the military capabilities of another enemy. No one can at present stand in its way in the post-traumatic Syria which has just undergone a coup. But one should not ignore the fateful damage which this ugly pillage could entail in the long run. The prophet Isaiah was instructed to give one of his sons a name depicting rapid pillage. Then too, this was a reference to the imminent destruction of Damascus (and the Israelite capital of Shomron). Rapid pillage seems to also be Israel's operational plan 3,000 years later. . . . While Syria is groping its way in the dark, Israel has come in aggressively and forcefully, as is its wont, bombing and taking territory, a real hero against the weak and bleeding. It may benefit from its actions, but it's possible that Syria will recover and not forget who attacked it in its difficult hour, without pretext, without legitimacy. An opponent in a time of weakness is ostensibly an opportunity for attacking, but it could also be an opportunity for extending a hand. This may turn out to be futile, possibly rejected with disgust. But when events unfold so quickly and dramatically, no one can tell what lies in store.' back

Hamilton's principle - Wikipedia, Hamilton's principle - Wikipedia, the free encyclopedia, ' In physics, Hamilton's principle is William Rowan Hamilton's formulation of the principle of stationary action . . . It states that the dynamics of a physical system is determined by a variational problem for a functional based on a single function, the Lagrangian, which contains all physical information concerning the system and the forces acting on it. The variational problem is equivalent to and allows for the derivation of the differential equations of motion of the physical system. Although formulated originally for classical mechanics, Hamilton's principle also applies to classical fields such as the electromagnetic and gravitational fields, and plays an important role in quantum mechanics, quantum field theory and criticality theories.' back

Jeff Sparrow (2024_12_06), Friday essay: ‘A future of dust’ – Jeff Sparrow on Gaza and why, in evil times, writers have a responsibility to take sides, ' "We must ask for no references to Gaza/Palestine/Israel as it’s a very sensitive topic in our area. If these topics are included it drastically changes our risk management plans for events. Thus for safety and harmony we kindly ask the guest speakers avoid these topics and any questions about it that come up." Sam Wallman and I received this message from our publicist, one day before an event at a suburban library about our coauthored book. “Did they even read the damn thing?” Sam joked, as we strategised our response. Twelve Rules for Strife discusses grassroots social change. It celebrates the creativity of the people historian Studs Terkel described as the world’s “etceteras”. It contrasts the power of collective solidarity with what we dub “smug politics”: a liberalism that treats the masses as irredeemably backward, and so requiring careful management by the clever few on whom progress supposedly depends. We had been invited to discuss the political agency of ordinary people – and then told our audience couldn’t hear about the world’s most significant crisis. But Gaza is all I think about. In January, six-year-old Hind Rajab fled the fighting in Gaza City alongside her extended family. An Israeli tank targeted their car, killing almost everyone inside. Amid the wreckage and the blood, Hind’s 15-year-old cousin, Layan Hamadeh, phoned the Palestinian Red Crescent, crying and pleading for help. “They are shooting at us,” she said. “The tank is right next to me.” The dispatchers heard Layan scream as a machine gun again raked the vehicle. When they rang back, Hind, the only person now alive, answered. “I’m so scared. Please come. Come take me. Please, will you come?” She stayed on the phone for three hours, while the Red Crescent transmitted her location to the Israeli army and dispatched an ambulance – and then the line dropped out again. Twelve days later, Hind’s surviving relatives found the wreckage of a van with two dead paramedics sprawled inside. Nearby, they located the car in which Layan, Hind and their family lay. An investigation by the US-based Forensic Architecture team established that 355 bullets had hit the vehicle. The researchers concluded that the shooters must have realised the vehicle contained civilians. “They were small,” writes W.H. Auden in The Shield of Achilles, And could not hope for help and no help came: What their foes liked to do was done.' . . . Writers – and everyone else – must take sides, irrespective of the sensitivities they offend. We have no choice. Gaza is not safe, and neither is the world that allows Gaza to happen.' back

Jennan Ismael (Standord Encyclopedia of Philosophy), Quantum Mechanics, ' Quantum mechanics is, at least at first glance and at least in part, a mathematical machine for predicting the behaviours of microscopic particles — or, at least, of the measuring instruments we use to explore those behaviours — and in that capacity, it is spectacularly successful: in terms of power and precision, head and shoulders above any theory we have ever had. Mathematically, the theory is well understood; we know what its parts are, how they are put together, and why, in the mechanical sense (i.e., in a sense that can be answered by describing the internal grinding of gear against gear), the whole thing performs the way it does, how the information that gets fed in at one end is converted into what comes out the other.' back

Julian Borger (2024_12_12), Death feels imminent for 96% of children in Gaza, study finds, ' A new study of children living through the war in Gaza has found that 96% of them feel that their death is imminent and almost half want to die as a result of the trauma they have been through. A needs assessment, carried out by a Gaza-based NGO sponsored by the War Child Alliance charity, also found that 92% of the children in the survey were “not accepting of reality”, 79% suffer from nightmares and 73% exhibit symptoms of aggression. “This report lays bare that Gaza is one of the most horrifying places in the world to be a child,” Helen Pattinson, chief executive of War Child UK, said. “Alongside the levelling of hospitals, schools and homes, a trail of psychological destruction has caused wounds unseen but no less destructive on children who hold no responsibility for this war.” The survey questioned parents or caregivers of 504 children from families where at least one child is disabled, injured or unaccompanied. The sample was split between southern and northern Gaza and was complemented by more in-depth interviews. The survey was carried out in June this year, so is likely to understate the accumulated psychological impact of Gaza’s children now, after more than 14 months of Israel’s assault on the territory. Dr Yasser Abu Jamei, a leading Palestinian psychiatrist dealing with mental health in Gaza ‘We can’t give up on 1 million children’: the charity bringing psychological first aid to Gazans Read more The estimated death toll in Gaza is more than 44,000 and a recent assessment by the UN Human Rights Office found that 44% of the fatalities it was able to verify were children. . . . About 1.9 million Palestinians in Gaza, approximately 90% of the territory’s total population, have been displaced, many several times. Half of that number are children who have lost their home and been forced to flee their neighbourhoods. More than 60% of the surveyed children reported having experienced traumatic events during the war and some had been exposed to multiple traumatic events. An estimated 17,000 children in Gaza are unaccompanied, separated from their parents, although the study notes the real number may be much higher. back

Kakutani fixed-point theorem - Wikipedia, Kakutani fixed-point theorem - Wikipedia, the free encyclopedia, 'In mathematical analysis, the Kakutani fixed-point theorem is a fixed-point theorem for set-valued functions. It provides sufficient conditions for a set-valued function defined on a convex, compact subset of a Euclidean space to have a fixed point, i.e. a point which is mapped to a set containing it. The Kakutani fixed point theorem is a generalization of Brouwer fixed point theorem. The Brouwer fixed point theorem is a fundamental result in topology which proves the existence of fixed points for continuous functions defined on compact, convex subsets of Euclidean spaces. Kakutani's theorem extends this to set-valued functions.' back

Mary Sirridge (1999), Quam videndo intus dicimus: Seeing and Saying in De Trinitate XV, ' What is being asserted is that thought has the same form as seeing or speaking respectively, i.e., that it works essentially like seeing or speaking, that thought is a formal and functional isomorph of seeing or speaking.' back

Path integral formulation - Wikipedia, Path integral formulation - Wikipedia, the free encyclopedia, 'The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique trajectory for a system with a sum, or functional integral, over an infinity of possible trajectories to compute a quantum amplitude. . . . This formulation has proved crucial to the subsequent development of theoretical physics, since it provided the basis for the grand synthesis of the 1970s which unified quantum field theory with statistical mechanics. . . . ' back

Sarah Harmouch (2024_12_10), Abu Mohammed al-Golani may become the face of post-Assad Syria – but who is he and why does he have $10M US bounty on his head?, ' xThe fall of President Bashar al-Assad has left a critical question: After a half-century of brutal dynastic rule has come to an end, who speaks for Syrians now? One group staking a major claim for that role is Hayat Tahrir al-Sham, which, under the leadership of Abu Mohammad al-Golani, spearheaded the opposition advance that toppled Assad. But what does the group stand for? And who is al-Golani? The Conversation turned to Sara Harmouch, an expert on Islamist militant groups, for answers. . . . . The U.S. has long listed al-Golani as a Specially Designated Global Terrorist and the Nusra Front as a Foreign Terrorist Organization. In May 2018, the U.S. State Department expanded this designation to include Hayat Tahrir al-Sham. As a result of these designations, the group and its members face legal restrictions, travel bans, asset freezes and banking restrictions. Additionally, the State Department’s Rewards for Justice program is offering up to US$10 million for information on al-Golani. However, news has been circulating that the U.S. is considering removing the $10 million bounty on the Hayat Tahrir al-Sham leader, while the United Kingdom is thinking of removing the group from its terror list. What happens if al-Golani emerges as a post-Assad leader? First, we should note that these are very early days, and it remains unclear what Syria will look like post-Assad. But based on my years researching Islamic history and Hayat Tahrir al-Sham, I’m willing to venture a few educated guesses. Historically, Islamic empires have used distinct governance frameworks to drive their expansion and administration, which might inform Hayat Tahrir al-Sham’s approach to mirroring these successful strategies. First, I think al-Golani is likely to strive for authentic religious leadership, positioning himself as a leader whose personal piety and adherence to Islamic principles align with the religious sentiments of the population at large. This could be complemented by Hayat Tahrir al-Sham emphasizing the role of Sunni Islam in Syria’s state functions and integrating religious legal practices into the nation’s laws. Just as it has established on a localized scale, effective administration might become a cornerstone of Hayat Tahrir al-Sham governance. In Idlib, for example, the group established systems for taxation and community engagement. This is essential for building trust, especially among previously marginalized groups. Additionally, by allowing some autonomy for regions within Syria, Hayat Tahrir al-Sham could mitigate the risk of unrest, balancing strict Islamic law enforcement with Syria’s cultural and ethnic diversity. Overall, should Hayat Tahrir al-Sham under al-Golani try to steer the formation of Syria’s new government, we might expect a governance approach that aims for a blend of traditional Islamic governance and modern statecraft, striving to stabilize and unify the diverse and war-torn country. back

Square-integrable function - Wikipedia, Square-integrable function - Wikipedia, the free encyclopedia, ' In mathematics, a square-integrable function, also called a quadratically integrable function or L ² function or square-summable function, is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite. Thus, square-integrability on the real line (-∞ - +∞) is defined as follows. f : R → C square integrable ⟺ ∫ _∞^∞ |f (x)| ² dx < ∞ An equivalent definition is to say that the square of the function itself (rather than of its absolute value) is Lebesgue integrable. For this to be true, the integrals of the positive and negative portions of the real part must both be finite, as well as those for the imaginary part.' back

Whitehead and Russell (1910), Principia Mathematica, Jacket: 'Principia Mathematica was first published in 1910-1913; this is the fifth impression of the second edition of 1925-7. The Principia has long been recognized as one of the intellectual landmarks of the century. It was the first book to show clearly the close relationship between mathematics and formal logic. Starting with a minimal number of axioms, Whitehead and Russell display the structure of both kinds of thought. No other book has had such an influence on the subsequent history of mathematical philosophy .' back

Wojciech Hubert Zurek (2008), Quantum origin of quantum jumps: breaking of unitary symmetry induced by information transfer and the transition from quantum to classical, 'Submitted on 17 Mar 2007 (v1), last revised 18 Mar 2008 (this version, v3)) Measurements transfer information about a system to the apparatus, and then further on – to observers and (often inadvertently) to the environment. I show that even imperfect copying essential in such situations restricts possible unperturbed outcomes to an orthogonal subset of all possible states of the system, thus breaking the unitary symmetry of its Hilbert space implied by the quantum superposition principle. Preferred outcome states emerge as a result. They provide framework for the “wavepacket collapse”, designating terminal points of quantum jumps, and defining the measured observable by specifying its eigenstates.' back