Notes
Sunday 3 January 2021 - Saturday 10 January 2021
[Notebook:DN 86: Hilbert / Minkowski]
[page 326]
Sunday 3 January 2021
[page 327]
A Call to Spy A Call to Spy - Wikipedia
It may be that discovery relies more on intuition rather than logic and that once the intuitive ansatz is in place the logic and mathematics refine it until it becomes a [testable] hypothesis. Thinking of Einstein's light beam rider and weightless free fall. I am in the grip of a similar intuition with my desire to make Hilbert space the underlying space of spacetime and the first step toward justification is the comprehensive linearity of applied Hilbert space versus the non-linearity of gravitation although it has a linear core in geodesic [inertial] free fall. Now I go through von Neumann again trying to stretch my understanding to embrace more evidence for my intuitive fantasy. This is my project for 2021 e32_hilbert_to_minkowski, ultimately to become my home made theological PhD thesis, next edition of Scientific Theology [and the identification of theology and physics, finally a use for the domain name physicaltheology.com].
Then I might be able to get a job as a prophet. Jonathan Lee Walton: Ralph Warnock's Georgia Critics don't understand Black churches
von N: page 7: 'In both theories [matrix and wave] a classical mechanical problem is inititally proposed which is characterized by a Hamiltonian function H(qi, pi) (where we have i degrees of freedom). John von Neumann: The Mathematical Foundations of Quantum Mechanics
Ratatouille - it may be good to make theology as exciting as a musical, which is as it has always been really.
Allegri, Miserere Psalm 51. From a quantum mechanical point of view the whole universe is music, the transfinite music of the spheres. Miserere (Allegri) - Wikipedia, Claire College Cambridge Choir: Miserere
[page 328]
Cantor / Fourier series / Hilbert space / transfinite numbers Jourdain in Cantor [Introduction] Georg Cantor: Contributions to the Founding of the Theory of Transfinite Numbers (Translated, with Introduction and Notes by Philip E B Jourdain)
The whole universe is a collection of dynamic transfinite frequencies evolving linearly and mapping onto curved gravitational space by the Hermitian products of complex amplitudes. We build it up from the initial quantum of action with all the data encoded in periodic functions / energy going down through the initial hardware in Hilbert space all marked / ordered by phase. We want to build the layered Fourier structure in software and let it run.
An exciting year's work here and all related to music. Each Hilbert basis vector is a voice, first a pure frequency and then built up to s particular voice (harp, oboe) by superpositions and the superpositions continue right up to the Miserere and from there to the universe starting from very high frequencies and gradually going down to f = 1/age of universe.
Quantum mechanically a forest is a superposition of dynamic trees which are superpositions of atoms. All linear. Veltman gave me ideas of Hilbert space representing children playing, dogs barking etc, and the fact that we can represent any function as a Fourier superposition. Martinus Veltman: Diagrammatica: The Path to the Feynman Rules page 33
To do this we replace the Turing machines in the transfinite computer network with linear hermitian operators (as in quantum communication and computation). And we make things transfinite using tensor products and classical reality emerges as parts of this enormous system interact with one another and 'square their amplitudes'. We need only to take this story to the emergence of spacetime and particles and then finish off by saying "and now all these particles form a gigantic superposition which is us, Earth and the universe.
[page 329]
2021 Universe divine: good
Theology ≡ Physics: work in progress, founded on quantum trinity
We imagine two linear Hermitian operators, one the system and the other the observer, spinning through their eigenvalues and eigenvectors and when they meet and find a common eigenvector they perform the absolute value manoeuvre and we get the observed value. There is no collapse of any wave functions, the system is just like a coin spinning in the air, as is the observer until they meet and complete the circuit on a common eigenfunction and a corresponding value which is related to the probability of [the meeting of] eigenfunction[s], since in the amplitude world the dies are loaded.
We can model the nesting of processes in the transfinite computer network by the nesting of phases in the domain of Hermitian operators, rather as the spinning coin is a nest of spinning atoms and a small subsystem in the processes of as two-up game. Two-up - Wikipedia
Back to Jourdain on Cantor: page 9 'The greatest influence on Cantor [seems to have been] . . . Weierstrass, a contemporary of Riemann's who attacked many of the same problems in the theory of analytic functions of complex variables by very different and more rigorous methods.' Georg Cantor - Wikipedia
page 11: 'We will pass over his early work . . . and examine his immensely important work on the foundations of arithmetic, to which he was led by the needs of a rigorous theory of analytic functions.' Analytic function - Wikipedia
[page 330]
Jourdain page 13: Bolzano-Weierstrass theorem - "point of condensation" Bolzano-Weierstrass theorem - Wikipedia
page 14: ' "The geometrical analogue of this proposition may possibly be claimed to be evident; but if our ideal in the theory of functions . . . is to found this theory on the conception of number alone, this proposition leads to considerations out of which as theory of irrational numbers such as Weierstrass's is built".'
page 15; '. . . before Weierstrass, the introduction of irrational "number" was explicitly or implicitly geometrical. The view that number has s geometrical basis was taken by Newton and most of his successors.'
A stone is a 1, but we know that this is only at a certain level of resolution. At other levels i is indistinguishable from the rest of the universe, etc. Only Peano's axioms give us a solid basis for whole number. The physical basis of unity is the atom of action, Planck's quantum.
page 16: Cauchy defined real numbers by "going to the limit".
page 17: Weierstrass avoided the Cauchy error by assuming that the sum of the infinite series of rational number can only be defined when we have already defined the real numbers.
page 28: Cantor: ' "I believe that the logical error that was first avoided by Weierstrass escaped notice almost universally in earlier times and was not noticed on the ground that it was one of the rare cases in which actual errors can lead to none of the more important mistakes in calculation".'
END: Notebook Science DB85
BEGIN: Notebook Hilbert/Minkowski DB 86
[page 1]
Monday 4 January 2021
Jourdain in Cantor:
Tuesday 5 January 2021
Jourdain page 18: ' With Weierstrass a number was said to be "determined" (represented?) if we know of what elements it is composed and how many of each element occurred in it.'
page 19: Ordering; ' When a and b are not equal there is at least one rational number which is contained in a without being contained in b or vice versa.: in the first case a was said to be greater than b; in the second a was said to be less than b.
"sum", "product" This all seems to assume that rational numbers are units without order [or magnitude] and we are talking about what Cantor called cardinal, a count of elements. Ordinal requires distinguishable and orderable elements.
Then a leap to infinity: 'The "sum" of an infinite number of numerical quantities a, b, . . . . was defined to be the aggregate (s) whose elements occur in one (at least) of a, b, . . . . each of these elements e being taken a number of times (n) equal to the number of times it occurs in a.by the number of times it occurs in b and so on. In order that s be finite and determined, it is necessary that each of the elements that occurs in it occurs a finite number of times, and it is necessary and sufficient that we can assign a number N such that the sum of any finite number of the quantities a, b, . . . is less than N.
page 20: '. . . with Weierstrass the new numbers were aggregates of numbers previously defined.' This deals with size but how does it deal with density. ie the "closeness" of rational and real numbers? "Point of condensation" appears
[page 2]
to be used to connect size and density throughout point set theory and the whole thing may be a chimera because this approach to continuity is not "real".
Jourdain page 24: Cantor research on trigonometrical series - problem to establish the uniqueness of trignonometrical development. Trigonometric series - Wikipedia, Alexander S Kechris: Set Theory and Uniqueness for Trigonometric Series
page 25: ' In 1871 Cantor gave a simpler proof of the uniqueness of the representation.'
page 30: Axiom: ' To each numerical magnitude belongs also, reciprocally, a determined point of the straight line whose coordinate is equal to this numerical magnitude [given a 0]. This theorem is called an axiom . . . . It also serves to give to the numerical magnitudes a certain objectivity, of which, however, they are completely independent.'
page 41: The series of positive integers has, as is easy to show, the smallest infinite power, but the class of aggregates with this power is extraordinarily rich and extensive, comprising, for instance, Dedekind's "finite corpora", Cantor's "systems of points of the νth species", all n-ple series and the totality of real (and also complex) algebraic numbers.'
'A continuum of many dimensions has the same power as a continuum of one dimension' [in unbounded fantasyland, ie unrepresented].
The fundamental constraint on physics is Landauer's contention that all information is physical, ie represented, and representations exist as particles in spacetime.
Dynamic vs static superposition: circle group vs list where the group is ordered by phase but the list is simply an unordered set?
pasge 67: Cantor the formalist: ' "mathematics is, in its development, quite
[page 3]
free and only subject to the self evident condition that its conceptions are both free from contradictions in themselves and stand in fixed relations, arranged by definitions, to previously formed and tested conceptions".'
The content of this sentence is a clear and distinct output of a cognitive process that can understand terms like contradiction and definition which must have some physical representation in mind = the world.
We draw a plan and build a house to conform to it. Science has the opposite problem. We have the universe and now we are trying to discern if there is a plan. We have one big clue: from little things big things grow. We all started as a single egg that grew, multiplied and differentiated to become our current selves. The universe also began from a living fertile egg, the initial singularity of absolute simplicity containing no visible plan only the potential to explore the space of possibility to find those consistent self-sustaining systems [which look like groups] which have gradually formed this gigantic and very complex universe.
Cantor's approach to introducing new concepts into mathematics discussed by Jordan on pp 67-73 sounds very much like the description of the creation of the universe above: ' In his judgement, this process is everywhere the same; we posit a thing without properties [the axiomatic method], which is at first nothing else but a name or a sign A, and give it in order different, even infinitely many predicates whose meaning for ideas already present is known and which may not contradict one another. By this the relations of A to the conception already present, and in particular to the allied ones, are determined. When we have completed this, all the condition for the awakening of the conception A, which slumbers within us, are present and it enters completed into "existence" . . ..'
[page 4]
Something like the entrance of amplitudes into the world of real particles.
Cantor began with Fourier series and then got sidetracked into complex analysis, functional analysis, continuity, real numbers and ultimately digitized analysis in the form of transfinite analysis. We need to follow his track back to Fourier and quantum mechanics, looking for clues to make a transfinite network of operators and vectors in Hilbert space.
How do we connect Hilbert spaces together to make a gravitationally closed universe? [We know that the universe grew from a simple Hilbert space] so maybe the key lies in Lie groups that work for fundamental particles [Yang Mills particles] so that we just need to fit [expanding] Hilbert space to an [expanding] differentiable manifold. Lie Group - Wikipedia
Our basic guide to the cognitive universe is neurophysiology. What does it teach us? Time based integration of signals as neuron works to decide when to fire. We would like to apply this idea to quantum states. The idea here is that superposition is not a static thing but a dynamic group cycling through its elements by bringing them into contact with one another. Linear operators form a ring so that they can add, subtract and multiply, their group operations, but not divide.
Sitting here thinking about the cognitive universe using the cognitive microcosm in my central nervous system to do it.
Wednesday 6 January 2021
One wonders if all the abstruse and fancy detail of analytic function theory applies to the dawn of the universe when we might expect Pseudo-Dionysius' heuristic of simplicity to apply. Since, however, the initial poetry is in motion we would expect whatever is going on to involve complex numbers. In a way complex numbers are natural accompaniments to phase and this applies before the emergence of time so the evolution of a complex number [z] is in effect dv/dz.
[page 5]
To create a cognitive cosmology all we need to do is to find the physical events in the world which are equivalent to cognitive events in our minds, and in the most general view what we are looking for is simply an event simpliciter (or per se). The root of intelligence is simply any event, that is any meeting or we might say 'unmeeting' like the decay of a neutron, uranium nucleus or a relationship. Event ≡ change of relationship ≡ communication.
So we begin with the initial singularity and this begins to reproduce but in order for the children to exist they must differentiate first by forming different species and then by creating space so that more or less identical individuals can exist in different places courtesy of the exclusion principle.
We may follow the initial course of differentiation following the cognitive pattern of the trinity. The father and son are kinetic fermions and the potential spirit is the boson or set of bosons holding them together (perhaps to be modelled by quarks and gluons). And then the pattern repeats in new segments of space / love / potential creating the closed curvature of the gravitational space which presents elements of its initial simplicity in its inertial geodesics.
So we start with a simple story and embellish it with gravitation, quantum field theory, low energy relativistic quantum mechanics, field theory, the emegrence of space-time etc etc.
Thursday 7 January 2021
We want to make this work. What have we got? linearity and layering, which is a form of superposition. The task looks impossible, but the linearity and layering point to some possibility. We begin with a single quantum of actin which grows like an embryo and eventually becomes a universe. How would this work?
Bertrand Russell: . . .
[page 6]
In the modern world, if communities are unhappy it is often because they have ignorances, habits, beliefs and passions which are dearer to them than happiness or even life. I find many men in our dangerous age who seem to "be in love with" misery and death, and who grow angry when hopes are suggested to them. They think that hope is irrational and that, in sitting down to lazy despair, they are merely facing facts. I cannot agree with these men. To preserve hope in our world makes calls upon our intelligence and our energy. In those who despair it is very frequently the energy that is lacking. Bertrand Russell: Reflections on My Eightieth Birthday, 1952, Bertrand Russell: The Autobiography of Bertrand Russell: The Final Years 1944-1969
Kondo problem Kondo effect - Wikipedia
What has the velocity of light to do with electromagnetic interaction? Something that follows from the fact that light is an electromagnetic phenomenon.
What makes us think electrons interact with themselves? The whole notion that the vacuum is an enormous sea of energy revealed by cosmological constant computations which are off by a factor of 10100 shows how totally stupid this idea is. Casimir effect - Wikipedia
Friday 8 January 2021
The fundamental error in modern physics is that one can have unbounded energy in a zero space-time volume, the definition of the initial singularity [since the existence of time at least is a prerequisite for the existence of energy].
Why am I so reluctant to call out the deficiencies in modern physics when I have my knife deep into the Roman Catholic Church? I know enough to know that the Church is blatantly wrong. My knowledge of modern physics is much more
[page 7]
restricted but on an anecdotal level it seems as far off as the church although from a practical technological view it gets many things right. This may not prove much. The engineers who devised steam engines knew almost no thermodynamics but their intuitive knowledge of water, heat and steam carried them a long way toward overcoming the engineering problems like developing low friction leak proof pistons and cylinders and aerodynamic turbine blades, and thermodynamics, when it became available, provided targets but did little for the engineers trying to meet these targets. Similarly we might say that many quantum mechanical triumphs are the result of engineered trial and error and the theory often follows the engineering rather than leads it. We may therefore place a certain level of trust in socio-political theological engineering in our search for a theory of everything. The pursuit of action rather than energy as a fundamental logical concept may be part of this project.
I am getting the Thomistic feeling that I am dealing with a load of straw such is the vast distance between the world and reality represented by such leaders as Donald Trump, Pope Francis and many of the conventional doctrines of physics which see the universe as a puppet of a Christian god and so are prepared to acknowledge mysteries and unexplained behaviour.
The riots in DC are a final clear and distinct representation of the ±30k instances of lies and misrepresentations issued by the Trump regime in the last 4 years.
What we need to do is to take the digital approach to quantum theory and assume that the universe works like clockwork as implied by the apparently
[page 8]
precise values of Planck's constant, the velocity of light, Boltzmann's constant, the gravitational constant, and the values of thousands of electronic transitions, and assume that the random elements in quantum theory are network interrupts arising from the complex network topology and the random interrupts in network processes arising from the random transmission of messages in the network.
We start with the Dirac equation and the Lamb shift. Dirac equation - Wikipedia, Lamb shift - Wikipedia
Saturday 9 January 2020
Awoke excited. Can't remember any dreams but imagine it has something to do with invisible subconscious processes. Wait and see if anything becomes observable.
Everything I read evokes a judgement, good or bad. What are my criteria? On the whole their tendency toward reinforcing human peace and solidarity and reducing our footprint on Earth, in other words I am trying to tune my opinions to the theological model of a divine universe. My rewritten physical theology website is intended to showcase the political and religious policies that derive from natural theology, and hopefully to motivate some investment in and return from these policies.
I have still got the imposter syndrome. I know I am no imposter when I reject the Catholic History of Salvation, but I am still insecure about the identification of physics and cosmology necessary to complete the transformation of theology from mythology to science. I have listed endless clues, but the case is not yet closed.
[page 9]
I am still lost in space, but confident that I have enough life left to complete the job, or at least leave a compelling enough foundation to encourage others far more perceptive than me to complete the work. I would like 2021 to be my tipping point, to put the finishing touches in 2022 then to enjoy a romantic holiday with my new baby.
My 'apologia' if I ever write it would probably attribute my career as an imposter to the cognitive dissonance induced in me from an early age when I discovered that the pleasure of masturbation was a mortal sin, consigning me to an eternity of agony in hell. The radical answer has been to see first that life is finite, and [second] that heaven on Earth is possible.
One of the key notions in the theory of renormalization is the distinction between 'bare' and 'dressed' particles. Particles are considered to self interact, thus dressing themselves in a cloud of particles which has the effect of changing their properties like charge and mass observed from a distance. As collision processes are taken to higher and higher energies the dressing is more deeply penetrated and the particles involved revert more closely to their bare properties. A serious problem to this picture, common to the whole of quantum field theory, is the representation of the virtual particles responsible for dressing. If they cannot be represented they cannot exist. This suggest that the whole notion of self interaction and virtual particles may need revision. Back in the Trinity, the self interaction of the Father with itself produced a real distinct particle, the Son, and they interact through the Spirit in a cognitively natural way, independent of energy. In the theory of computation, the outcome of logical operations is independent of their speed fand energy. I have said it at last, and maybe killed the cosmological constant problem with the same blow.
[page 10]
The 'uncertainty principle' is in fact the 'certainty principle'. Every action [like a lego construction] is precisely one integral number of quanta of action. We have a difference here, between reality and measurement. Reality is perfectly integral. On the other hand, a tape measure graduated in integers gives rise to uncertainty when used to measure something complex enough to obscure its integral (atomic) constituency.
I am facing an ancient dilemma, reason against instinct. Reason suggests that the enormous progress physics made in understanding how the world works since the 1850s is unassailable. My instinct, nevertheless, is that it requires radical revision. Rather than putting relativity and quantum mechanics on a par and attempting at the cost of some expensive compromises like vacuum fluctuations to reconcile them, I want to make quantum mechanics primary and derive relativity from it, so greatly simplifying and streamlining the quantum theory of particles in spacetime. Is it worth trying? Does it help with my theological program? Yes, because we can interpret quantum mechanics as cognitive science opening the way to understanding the universe as mind rather than matter, but how far do we have to go to make this work? The idea is to make low energy non-relativistic quantum mechanics primary and see the high energy world in spacetime and gravitation as an application of this theory, as suggested by Weinberg in vol 1. Steven Weinberg (1995): The Quantum Theory of Fields Volume I: Foundations
The size of the pixels in spacetime depend on the energy involved so that when we go to higher energy we get not only higher resolution in spacetime, but higher resolution of spacetime.
Listen to the world, don't push it with scientific violence - high energy physics.
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Further readingBooks
Cantor, 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
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Carroll, Lewis, Lewis Carroll's Alice in Wonderland Illustrated by Ralph Steadman, Clarkson Potter 1973
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Denzinger, Henricus, and Adolphus Schoenmetzer, Enchiridion Symbolorum, Definitionum et Declarationum de Rebus Fidei et Morum, Herder 1963 Introduction: 'Dubium non est quin praeter s. Scripturam cuique theologo summe desiderandus sit etiam liber manualis quo contineantur edicta Magisterii ecclesiastici eaque saltem maioris momenti, et quo ope variorim indicum quaerenti aperiantur eorum materiae.' (3)
'There is no doubt that in addition to holy Scripture, every theologian also needs a handbook which contains at least the more important edicts of the Magisterium of the Church, indexed in a way which makes them easy to find.' back |
Diamant, Anita, The Red Tent, Picador 1988 Amazon editorial review From Library Journal
'Skillfully interweaving biblical tales with events and characters of her own invention, Diamant's (Living a Jewish Life, HarperCollins, 1991) sweeping first novel re-creates the life of Dinah, daughter of Leah and Jacob, from her birth and happy childhood in Mesopotamia through her years in Canaan and death in Egypt. When Dinah reaches puberty and enters the Red Tent (the place women visit to give birth or have their monthly periods), her mother and Jacob's three other wives initiate her into the religious and sexual practices of the tribe. Diamant sympathetically describes Dinah's doomed relationship with Shalem, son of a ruler of Shechem, and his brutal death at the hands of her brothers. Following the events in Canaan, a pregnant Dinah travels to Egypt, where she becomes a noted midwife. Diamant has written a thoroughly enjoyable and illuminating portrait of a fascinating woman and the life she might have lived. Recommended for all public libraries.'
Nancy Pearl, Washington Ctr. for the Book, Seattle
Copyright 1997 Reed Business Information, Inc.
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Gödel, Kurt, and Solomon Feferman et al (eds), Kurt Gödel: Collected Works Volume 1 Publications 1929-1936, Oxford UP 1986 Jacket: 'Kurt Goedel was the most outstanding logician of the twentieth century, famous for his work on the completeness of logic, the incompleteness of number theory and the consistency of the axiom of choice and the continuum hypotheses. ... The first volume of a comprehensive edition of Goedel's works, this book makes available for the first time in a single source all his publications from 1929 to 1936, including his dissertation. ...'
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Hesse, Hermann, The Glass Bead Game (Magister Ludi), Peter Smith Publishing 1992 Amazon Editorial review: 'Final novel by Hermann Hesse, published in two volumes in 1943 in German as Das Glasperlenspiel, and sometimes translated as Magister Ludi. The book is an intricate bildungsroman about humanity's eternal quest for enlightenment and for synthesis of the intellectual and the participatory life. Set in the 23rd century, the novel purports to be a biography of Josef Knecht ("servant" in German), who has been reared in Castalia, the remote place his society has provided for the intellectual elite to grow and flourish. Since childhood, Knecht has been consumed with mastering the Glass Bead Game, which requires a synthesis of aesthetics and scientific arts, such as mathematics, music, logic, and philosophy. This he achieves in adulthood, becoming a Magister Ludi (Master of the Game).' Merriman-Webster Encyclopaedia of Literature
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Lonergan, Bernard J F, and Michael G Shields (translator), Robert M Doran & H Daniel Monsour (editors), The Triune God: Systematics, University of Toronto Press 2007 Translated from De Deo Trino: Pars systematica (1964) by Michael G Shields. Amazon Product Description
'Buried for more than forty years in a Latin text written for seminarian students at the Gregorian University in Rome, Bernard Lonergan's 1964 masterpiece of systematic-theological writing, De Deo trino: Pars systematica, is only now being published in an edition that includes the original Latin along with an exact and literal translation. De Deo trino, or The Triune God, is the third great installment on one particular strand in trinitarian theology, namely, the tradition that appeals to a psychological analogy for understanding trinitarian processions and relations.
The analogy dates back to St Augustine but was significantly developed by St Thomas Aquinas. Lonergan advances it to a new level of sophistication by rooting it in his own highly nuanced cognitional theory and in his early position on decision and love. Suggestions for a further development of the analogy appear in Lonergan's late work, but these cannot be understood and implemented without working through this volume. This is truly one of the great masterpieces in the history of systematic theology, perhaps even the greatest of all time.'
Amazon
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Monsarrat, Nicholas, The Nylon Pirates, House of Stratus 2009 Amazon Product Description
'Alcestis, a British luxury liner, moored in New York and bound on a cruise to the Caribbean, South America and Africa, awaits her exclusive passengers - businessmen with mid-life crises, large bank balances and unforgiving wives; legacy-laden women looking for love and adventure; and divorcees with settlements to squander. But another group of passengers threatens to upset their opulent trip. These are the twentieth-century pirates - suave, elegant, discreet and utterly unscrupulous, with a singular purpose in mind and a collection of ruthless strategies.'
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Russell, Bertrand, The Autobiography of Bertrand Russell: The Final Years 1944-1969, Routledge 1998 ' Bertrand Russell was born in 1872 and died in 1970. One of the most influential figures of the twentieth century, he transformed philosophy and can lay claim to being one of the greatest philosophers of all time. He was a Nobel Prize winner for Literature and was imprisoned several times as a result of his pacifism. His views on religion, education, sex, politics and many other topics, made him one of the most read and revered writers of the age. This, his autobiography, is one of the most compelling and vivid ever written.'
Amazon
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Veltman, Martinus, Diagrammatica: The Path to the Feynman Rules, Cambridge University Press 1994 Jacket: 'This book provides an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics. The aim is to make clear what the physical foundations of present-day field theory are, to clarify the physical content of Feynman rules, and to outline their domain of applicability. ... The book includes valuable appendices that review some essential mathematics, including complex spaces, matrices, the CBH equation, traces and dimensional regularization. ...'
Amazon
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Weinberg (1995), Steven, The Quantum Theory of Fields Volume I: Foundations, Cambridge University Press 1995 Jacket: 'After a brief historical outline, the book begins anew with the principles about which we are most certain, relativity and quantum mechanics, and then the properties of particles that follow from these principles. Quantum field theory then emerges from this as a natural consequence. The classic calculations of quantum electrodynamics are presented in a thoroughly modern way, showing the use of path integrals and dimensional regularization. The account of renormalization theory reflects the changes in our view of quantum field theory since the advent of effective field theories. The book's scope extends beyond quantum elelctrodynamics to elementary partricle physics and nuclear physics. It contains much original material, and is peppered with examples and insights drawn from the author's experience as a leader of elementary particle research. Problems are included at the end of each chapter. '
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Papers
Mank, Judith E, "Sexual Selection and Darwin's Mystery of Mysteries", Science, 326, 5960, 18 December 2009, page 1639-1640. 'Darwin referred to the origin of species as "that mystery of mysteries", and despite decades of study, evolutionary biologists still cannot agree on the underlying processes that have produced the great diversity of life around us. Most contentious of all has been the question of whether speciation can occur within a population (sympatrically). On page 1704 of this issue, van Doorn et al. suggest that mating preferences can halt the movement of genes within a population. Their work gives credibility to the concept of sympatric speciation, which has long been the ugly duckling of evolutionary biology, and suggests that both local adaptation and sexual selection may play a far more important role in speciation than previously thought.'. back |
van Doorn, G Sander, Pim Edelaar, Franz J Weissing, "The Origin of SDpecies by Sexual and Natural Selection", Science, 326, 5960, 18 December 2009, page 1704-1707. 'Ecological speciation is considered an adaptive response to selection for local adaptation. However, besides suitable ecological conditions, the process requires assortative mating to protect the nascent species from homogenization by gene flow. By means of a simple model, we demonstrate that disruptive ecological selection favors the evolution of sexual preferences for ornaments that signal local adaptation. Such preferences induce assortative mating with respect to ecological characters and enhance the strength of disruptive selection. Natural and sexual selection thus work in concert to achieve local adaptation and reproductive isolation, even in the presence of substantial gene flow. The resulting speciation process ensues without the divergence of mating preferences, avoiding problems that have plagued previous models of speciation by sexual selection.'. back |
Links
A Call to Spy - Wikipedia, A Call to Spy - Wikipedia, the free encyclopedia, ' A Call to Spy (also known as Liberté: A Call to Spy) is a 2019 American historical drama film written and produced by Sarah Megan Thomas and directed by Lydia Dean Pilcher. The title a stylistic variant to a call to arms, the film is inspired by the true stories of three women who worked as spies in Churchill's Secret Army. It stars Sarah Megan Thomas as Virginia Hall, Radhika Apte as Noor Inayat Khan, and Stana Katic as Vera Atkins.' back |
Alex Lo, Forget the rise of China, it's the fall of America you should worry about, ' France under Napoleon III, Britain under Winston Churchill and Soviet Russia under Mikhail Gorbachev didn’t know they had already lost their empire until it was too late. The fate of the United States will be no different from those in the face of the irresistible rise of China. This has less to do with China and everything to do with America’s internal decay.
But with their exceptionalism and profound myopia, Americans think they are exempt from history’s merciless fate. They won’t be. There are four areas in which Americans have reigned supreme from the second half of the last century: the military, the capitalist financial system, medicine and disease control, and democratic institutions.
In every one of them, signs of decay and decline abound..' back |
Alexander S Kechris, Set Theory and Uniqueness for Trigonometric Series, ' This is the problem (which arose through the work of Riemann and Heine) that Heineproposed, in 1869, to the 24 year old Cantor, who had just accepted a position at theuniversity in Halle, where Heine was a senior colleague.In the next few sections we will give Cantor’s solution to theuniqueness problem andsee how his search for extensions, allowing exceptional points, led him to the creation of settheory, including the concepts of ordinal numbers and the method of transfinite induction.' back |
Analytic function - Wikipedia, Analytic function - Wikipedia, the free encyclopedia, ' In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do not hold generally for real analytic functions. A function is analytic if and only if its Taylor series about x0 converges to the function in some neighborhood for every x0 in its domain.' back |
Ann Hornaday, The unbreakable gaze of Steve McQueen: 'I'm asking you, please look', ' The “it” McQueen refers to is the practice of segregating Black students into schools for the “educationally subnormal,” where they were warehoused, neglected and funneled into menial jobs. Although the formal system was largely dismantled by the time McQueen was Kingsley’s age, he remembers being similarly tracked. He attended a school in which some students were shuttled into a program “very much targeted to get children into Oxford and Cambridge.” He and his working-class peers, on the other hand, were “put on the fast lane” to become a manual worker. “My path was mapped out for me,” he recalls ruefully.' back |
Aquinas 264, Whether the angels differ in species?, 'I answer that, Some have said that all spiritual substances, even souls, are of the one species. Others, again, that all the angels are of the one species, but not souls; while others allege that all the angels of one hierarchy, or even of one order, are of the one species.
But this is impossible. For such things as agree in species but differ in number, agree in form, but are distinguished materially. If, therefore, the angels be not composed of matter and form, as was said above (Article 2), it follows that it is impossible for two angels to be of one species; . . . ' back |
Asher Schechter, Meet Judaeo-ISIS: The Inevitable Result of Israel's Presence in the West Bank, 'In the early 1980s, the Israeli philosopher Yeshayahu Leibowitz coined the highly controversial term “Judeo-Nazis” to describe Israel’s conduct during the First Lebanon war and Israel's mounting militarization. But that was then. The footage of extremists now celebrating the cold-blooded murder of an innocent toddler begs a more up-to-date term for this sort of bloodlust, motivated by religious fanaticism – Judeo-ISIS, perhaps.' back |
Bertrand Russell, Reflections on My Eightieth Birthday, 1952, ' On REACHING the age of eighty it is reasonable to suppose that the bulk of one's work is done, and that what remains to do will be of less importance. The serious part of my life ever since boyhood has been devoted to two different objects which for a long time remained separate and have only in recent years united into a single whole. I wanted, on the one hand, to find out whether anything could be known; and, on the other hand, to do whatever might be possible toward creating a happier world.' back |
Billy House & Nick Wadhams , Pelosi Says Military Chief Assured Her on Trump's Nuclear Powers, ' The comments came after Pelosi said in a letter to fellow Democrats that she spoke to General Mark Milley, chairman of the Joint Chiefs of Staff, about “available precautions for preventing an unstable president from initiating military hostilities or accessing the launch codes and ordering a nuclear strike.”
“The situation of this unhinged President could not be more dangerous, and we must do everything that we can to protect the American people from his unbalanced assault on our country and our democracy,” Pelosi said in the letter. back |
Bolzano-Weierstrass theorem - Wikipedia, Bolzano-Weierstrass theorem - Wikipedia, the free encyclopedia, 'In mathematics, specifically in real analysis, real analysis, the Bolzano–Weierstrass theorem, named after Bernard Bolzano and Karl Weierstrass, is a fundamental result about convergence in a finite-dimensional Euclidean space Rn. The theorem states that each bounded sequence in Rn has a convergent subsequence. An equivalent formulation is that a subset of Rn is sequentially compact if and only if it is closed and bounded.' back |
Casimir effect - Wikipedia, Casimir effect - Wikipedia, the free encyclopedia, 'In physics, the Casimir effect or Casimir-Polder force is a physical force arising from a quantized field. The typical example is of two uncharged metallic plates in a vacuum, placed a few micrometers apart, without any external electromagnetic field. In a classical description, the lack of an external field also means that there is no field between the plates, and no force would be measured between them. When this field is instead studied using quantum mechanics, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force—either an attraction or a repulsion depending on the specific arrangement of the two plates. This force has been measured, and is a striking example of an effect purely due to second quantization.' back |
Christian Eschatology - Wikipedia, Christian Eschatology - Wikipedia, the free encyclopedia, ' Broadly speaking, Christian eschatology is the study concerned with the ultimate destiny of the individual soul and the entire created order, based primarily upon biblical texts within the Old and New Testament.
Christian eschatology looks to study and discuss matters such as death and the afterlife, Heaven and Hell, the second coming Jesus, the resurrection of the dead, the rapture, the tribulation, millennialism, the end of the world, the Last Judgment, and the New Heaven and New Earth in the world to come. ' back |
Claire College Cambridge Choir, Miserere, ' Miserere mei, Deus: secundum magnam misericordiam tuam.
Et secundum multitudinem miserationum tuarum, dele iniquitatem meam.
Amplius lava me ab iniquitate mea: et a peccato meo munda me. . . ..
Have mercy upon me, O God: after Thy great goodness.
According to the multitude of Thy mercies, do away mine offences.
Wash me thoroughly from my wickedness: and cleanse me from my sin. . . .. '
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David Von Drehle, How do liberty and human rights survive the age of the Internet?, ' A century ago, Justice Oliver Wendell Holmes Jr. foretold our dilemma in one of his most famous opinions. Freedom of expression, he wrote, can’t coexist with reckless misuse of that freedom. “The most stringent protection of free speech would not protect a man in falsely shouting fire in a theatre,” Holmes wrote. We can, and do, argue over where the freedom ends and the misuse begins, but unless a line is drawn somewhere, the freedom cannot endure.' back |
David, Urwin, Delannoy, Russell & Mullett, Magic, culture and stalactites: how Aboriginal perspectives are transforming archaeological histories, ' New collaborative work at an Aboriginal cave in eastern Victoria, published today, shows the stark difference between contemporary archaeological research and that conducted in the 1970s. . . . A new picture of Cloggs Cave now emerges. The cave was not just a refuge from a cold environment, but a theatre of culturally rich, social and magical activities dating back millenia. It was avoided by people for day-to-day living, and probably used by GunaiKurnai mulla-mullung. . . .
What was located during the 2019 research had been there all along, but was not noticed by previous researchers.
This is partly because new techniques give us a better window into the past activities of Aboriginal people at the cave. These new ways of seeing are matched with new ways of listening and researching — transforming how we tell archaeological histories.' back |
Dirac equation - Wikipedia, Dirac equation - Wikipedia, the free encyclopedia, 'In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1⁄2 massive particles such as electrons and quarks, for which parity is a symmetry, and is consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to account fully for special relativity in the context of quantum mechanics. It accounted for the fine details of the hydrogen spectrum in a completely rigorous way.' back |
Ernst W Mayr - Wikipedia, Ernst W Mayr - Wikipedia, the free encyclopedia, 'Ernst Walter Mayr (July 5, 1904, Kempten, Germany – February 3, 2005, Bedford, Massachusetts U.S.), was one of the 20th century's leading evolutionary biologists. He was also a renowned taxonomist, tropical explorer, ornithologist, historian of science, and naturalist. His work contributed to the conceptual revolution that led to the modern evolutionary synthesis of Mendelian genetics, systematics, and Darwinian evolution, and to the development of the biological species concept.' back |
fqxi.org, FQXi: Foundational Questions in Physics & Cosmology, 'Mission: to catalyze, support, and disseminate research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality but unlikely to be supported by conventional funding sources' back |
From Little Things Big Things Grow - Wikipedia, From Little Things Big Things Grow - Wikipedia, the free encyclopedia, '"From Little Things Big Things Grow" is a rock protest song recorded by Australian artists Paul Kelly & The Messengers on their 1991 album Comedy, and by Kev Carmody (with Kelly) on his 1993 album Bloodlines. It was released as a CD single by Carmody and Kelly in 1993 but failed to chart. The song was co-written by Kelly and Carmody,[1] and is based on the story of The Gurindji Strike and Vincent Lingiari as part of the Indigenous Australian struggle for land rights and reconciliation. back |
Georg Cantor - Wikipedia, Georg Cantor - Wikipedia, the free encyclopedia, Georg Ferdinand Ludwig Philipp Cantor (March 3 [O.S. February 19] 1845 – January 6, 1918) was a German mathematician, born in Russia. He is best known as the creator of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between sets, defined infinite and well-ordered sets, and proved that the real numbers are "more numerous" than the natural numbers. In fact, Cantor's theorem implies the existence of an "infinity of infinities". He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact of which he was well aware of.' back |
Jack L. Rozdilsky, Pro-Trump rioters storm U.S. Capitol as his election tantrum leads to vilence, ' . . . peace and conflict researcher Kristine Höglund has studied the factors that encouraged violence at elections.
Höglund found that conditions that enabled the use of electoral violence include situations where violence is viewed as a legitimate political tool, and agitators have access to arms. Other factors that trigger electoral violence are false interpretations of close elections, misuse of political rights and militant mobilization.
Those conditions currently exist in America — and were on full display during the attack on the U.S. Capitol.' back |
John F. Harris, Trump's America Becomes One of Those 'Shithole Countries', ' It seemed like an attempt at artful difference-splitting, aimed at separating themselves from Trump’s maneuvers without alienating his supporters. But these are not congenial times for difference-splitters.
Which side are you on is indeed the question of the age, but the sides aren’t Republicans and Democrats. The choice is democracy and rule of law on one side, and a brand of politics unhinged from principle or self-restraint on the other.' back |
John von Neumann, The Mathematical Foundations of Quantum Mechanics, ' Mathematical Foundations of Quantum Mechanics by John von Neumann translated from the German by Robert T. Beyer (New Edition) edited by Nicholas A. Wheeler. Princeton UP Princeton & Oxford.
Preface: ' This book is the realization of my long-held intention to someday use the resources of TEX to produce a more easily read version of Robert T. Beyer’s authorized English translation (Princeton University Press, 1955) of John von Neumann’s classic Mathematische Grundlagen der Quantenmechanik (Springer, 1932).'This content downloaded from 129.127.145.240 on Sat, 30 May 2020 22:38:31 UTC
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Jonathan Lee Walton, Ralph Warnock's Georgia Critics don't understand Black churhes, ' The Bible is replete with the scathing indictments of those who wept over oppression. Recall Jeremiah: “Woe to him who builds his palace by unrighteousness, his upper rooms by injustice, making his own people work for nothing, not paying them for their labor” (Jeremiah 22:13); and Amos, decrying those who “trample on the heads of the poor as on the dust of the ground and deny justice to the oppressed” (Amos 2:7). The biblical prophets enunciated their divine call to be voices of the voiceless and defenders of the defenseless. They did not try to soothe or assuage listeners with euphemistic phrases. Their rhetoric was often blunt, unyielding and contentious.' back |
June Carter Cash, June Carter Cash - Keep on the Sunny Side Lyrics, back |
Kate Conolly, Cologne police chief fired as witness says NYE violence was coordinated, 'Cologne’s police chief has been removed from his post amid criticism of his force’s handling of a string of sexual assaults and robberies carried out by groups of men in the German city on New Year’s Eve.
His enforced departure came as a witness to the violence told the Guardian the events appeared to have been coordinated. Lieli Shabani, 35, said she saw three Arabic speaking males who were “clearly giving instructions and directing a lot of the males”.' back |
Lamb shift - Wikipedia, Lamb shift - Wikipedia, the free encyclopedia, 'In physics, the Lamb shift, named after Willis Lamb (1913–2008), is a difference in energy between two energy levels 2S½ and 2P½ (in term symbol notation) of the hydrogen atom which was not predicted by the Dirac equation, according to which these states should have the same energy.
Interaction between vacuum energy fluctuations and the hydrogen electron in these different orbitals is the cause of the Lamb Shift, as was shown subsequent to its discovery.' back |
Lie Group - Wikipedia, Lie Group - Wikipedia, the free encyclopedia, 'In mathematics, a Lie group . . . is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups are named after Norwegian mathematician Sophus Lie, who laid the foundations of the theory of continuous transformation groups.
Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. . . . One of the key ideas in the theory of Lie groups is to replace the global object, the group, with its local or linearized version, which Lie himself called its "infinitesimal group" and which has since become known as its Lie algebra.' back |
Liz Zhen, China's experiment in quantum commnication brings Beijing closer to creating a hack-proof network, ' China’s hack-proof quantum communication technology is “primarily ready” for practical use after a 4,600km (2,858 mile) network was put through two years of experimental service, researchers announced.
Since early 2019, the integrated space-to-ground quantum communication network has proved its “practical security”, and “maintained long-term reliability and stability” through ground fibres and achieved an adequately fast link with a satellite, according to a paper by the researchers published in the science journal Nature on Wednesday.' back |
Max Hastings, How Delusions About World War II Fed Brexit Mania, ' I wrote two years ago that if Johnson achieved his ambition to become prime minister, Britain would forsake any claim to be regarded as a serious country. I do not retract those words. My own vanquished faction can only stand by in sorrow, as the victors in our tragic debate over Europe enfold themselves in the tired old Union flag. back |
Miserere (Allegri) - Wikipedia, Miserere (Allegri) - Wikipedia, the free encyclopedia, 'Miserere (full title: Miserere mei, Deus, Latin for "Have mercy on me, O God") is a setting of Psalm 51 (50) by Italian composer Gregorio Allegri. It was composed during the reign of Pope Urban VIII, probably during the 1630s, for use in the Sistine Chapel during matins, as part of the exclusive Tenebrae service on Holy Wednesday and Good Friday of Holy Week.' back |
National Archives and Records Administration, A Point in Time: The Corona Story, ' A Point in Time: The Corona Story - National Archives and Records Administration - ARC Identifier 1678526 / Local Identifier 263.3213 - National Security Council. Central Intelligence Agency. (09/18/1947 - 12/04/1981). This film concerns the Corona program that produced the world's first photo-reconnaissance (spy) satellites. The film was produced by the Central Intelligence Agency (CIA) and premiered at the "Piercing the Curtain" conference in May of 1995. The film provides an in-depth examination about how and why the Corona program was created, as well as a detailed technological account of how the satellite was built, and its specific operations and capabilities. The film includes footage of Richard Helms, who was the director of the CIA from 1966-1973, as he addressed a press conference about the Corona mission. back |
New York Times Editorial Board, Two Ways of Dealing With Guns, 'This is a big day for Texans yearning to flaunt their handguns in belt and shoulder holsters. A new “open carry” law enacted by the Republican Legislature goes into effect on Friday, posing a challenge for law enforcement, businesses and other institutions that are understandably wary of how social interchange will be affected.' back |
Niha Masih, In the battle over India's history, Hindu nationalists square off against a respected historian, ' NEW DELHI — Romila Thapar is the preeminent historian of ancient India, an octogenarian feted the world over for her scholarship excavating answers to questions at the heart of the country's past. . . . At the age of 89, Thapar is the subject of attacks by supporters of India’s ruling Bharatiya Janata Party, or BJP, who view her as an opponent to be discredited. . . . For Hindu nationalists, India’s past consists of a glorious Hindu civilization followed by centuries of Muslim rule that Modi has described as a thousand years of “slavery.”
Thapar considers such assertions both simplistic and incorrect.' back |
Noam Gidron & Peter A. Hall, Populism erupted when people feel disconnected and disrespected, ' Understanding populism’s roots is essential for addressing its rise and threat to democracy. We believe seeing populism as the product not of economic or cultural problems, but as a result of people feeling disconnected, disrespected and denied membership in the mainstream of society, will lead to more useful answers about how to stem populism’s rise and strengthen democracy.' back |
Norimitsu Onishi & Constant Meheut, A Year of Scandals and Self-Questioning for France's Top Publishers, ' It was Mr. Nora himself who drew scrutiny by — no surprise — publishing a book: “Consent,” the account of Vanessa Springora who, at the age of 14, became involved with Mr. Matzneff, the openly pedophile writer who was protected for decades by France’s literary, media and political elite. Its publication last January — and subsequent revelations about Mr. Matzneff, his supporters and his other victims — set off a #MeToo moment in France, a reckoning over sexism, age and consent, and brawls among politicians and feminists in the capital.' back |
Numinous - Wikipedia, Numinous - Wikipedia, the free encyclopedia, 'Numinous . . . (from the Classical Latin numen) is an English adjective describing the power or presence of a divinity. The word was popularised in the early twentieth century by the German theologian Rudolf Otto in his influential book Das Heilige (1917; translated into English as The Idea of the Holy, 1923). According to Otto the numinous experience has two aspects: mysterium tremendum, which is the tendency to invoke fear and trembling; and mysterium fascinans, the tendency to attract, fascinate and compel. The numinous experience also has a personal quality to it, in that the person feels to be in communion with a wholly other. The numinous experience can lead in different cases to belief in deities, the supernatural, the sacred, the holy, and the transcendent.'
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Pseudo-Dionysius the Areopagite - Wikipedia, Pseudo-Dionysius the Areopagite - Wikipedia, the free encyclopedia, 'Pseudo-Dionysius the Areopagite (Greek: Διονύσιος ὁ Ἀρεοπαγίτης), also known as Pseudo-Denys, was a Christian theologian and philosopher of the late 5th to early 6th century (writing before 532), probably Syrian, the author of the set of works commonly referred to as the Corpus Areopagiticum or Corpus Dionysiacum. The author pseudonymously identifies himself in the corpus as "Dionysios", portraying himself as the figure of Dionysius the Areopagite, the Athenian convert of St. Paul mentioned in Acts 17:34 This false attribution resulted in the work being given great authority in subsequent theological writing in both East and West, with its influence only decreasing in the West with the fifteenth century demonstration of its later dating.' back |
Theodosius Dobzhansky - Wikipedia, Theodosius Dobzhansky - Wikipedia, the free encyclopedia, 'Theodosius Grygorovych Dobzhansky, also known as T. G. Dobzhansky, and sometimes Anglicized to Theodore Dobzhansky (Ukrainian — Теодосій Григорович Добжанський; January 24, 1900 - December 18, 1975) was a prominent geneticist and evolutionary biologist, and a central figure in the field of evolutionary biology for his work in shaping the unifying modern evolutionary synthesis. Dobzhansky was born in Ukraine (then part of Imperial Russia) and emigrated to the United States in 1927. back |
Thomas Williams, Saint Anselm (Stanford Encyclopedia of Philosophy), 'Saint Anselm of Canterbury (1033-1109) was the outstanding Christian philosopher and theologian of the eleventh century. He is best known for the celebrated “ontological argument” for the existence of God in chapter two of the Proslogion, but his contributions to philosophical theology (and indeed to philosophy more generally) go well beyond the ontological argument. In what follows I examine Anselm's theistic proofs, his conception of the divine nature, and his account of human freedom, sin, and redemption. . . . Anselm's motto is “faith seeking understanding” (fides quaerens intellectum).' back |
Trigonometric series - Wikipedia, Trigonometric series - Wikipedia, the free encyclopedia, ' In mathematics, a trigonometric series is a series of the form [of an infinite sum of cosines and sines]. It is called as Fourier series [ if it is expressed as integrable functions of sines and cosines iin the range 0 to 2π].
The uniqueness and the zeros of trigonometric series was an active area of research in 19th century Europe. First, Georg Cantor proved that if a trigonometric series is convergent to a function f(x) on the interval [0, 2π], which is identically zero, or more generally, is nonzero on at most finitely many points, then the coefficients of the series are all zero.
Later Cantor proved that even if the set S on which f is nonzero is infinite, but the derived set S' of S is finite, then the coefficients are all zero. In fact, he proved a more general result. Let S0 = S and let Sk+1 be the derived set of Sk. If there is a finite number n for which Sn is finite, then all the coefficients are zero. Later, Lebesgue proved that if there is a countably infinite ordinal α such that Sα is finite, then the coefficients of the series are all zero. Cantor's work on the uniqueness problem famously led him to invent transfinite ordinal numbers, which appeared as the subscripts α in Sα. back |
Two-up - Wikipedia, Two-up - Wikipedia, the free encuclopedia, ' Two-up is a traditional Australian gambling game, involving a designated "spinner" throwing two coins or pennies into the air. Players bet on whether the coins will fall with both heads (obverse) up, both tails (reverse) up, or with one coin a head and one a tail (known as "Ewan"). It is traditionally played on Anzac Day in pubs and clubs throughout Australia, in part to mark a shared experience with Diggers through the ages.' back |
Usman W. Chohan, Martin Shkeli and the outrage of inequality, 'First, Shkreli’s actions exemplify the limitations of a singular devotion to the profit motive, and draw a troublesome distinction between what is legal and what is moral. Martin Shkreli came to notoriety after his company acquired Daraprim, a drug recognised as an essential medicine by the World Health Organization because it is important for AIDS and malarial patients (toxoplasmosis), and raised its price by 5500%, from US$13.50 to US$750.00.' back |
Yehudis Fletcher, Why My Haredi Comunity Can't, and Won't, Deal With Sex Abusers, 'Forget the secular justice system: we’re ‘handling’ sexual abuse in-house, with crimes turned into sins and punishment into repentance. No wonder ultra-Orthodox rabbis have become sex abusers’ most devout defenders.' back |
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