Notes
Sunday 31 May 2020 - Saturday 6 June 2020
[Notebook: DB 84 Pam's Book]
[page 329]
Sunday 31 May 2020
Chapter V I The formulation of the problem: we delete the problem of psycho-physical parallelism by making the whole system psychological and accepting that the universe 'measures' itself [becomes conscious] by the communication of particles and this process increases entropy and is responsible for the creation of the world. This is the fundamental insight that I wish to parlay into a PhD.
Monday 1 June 2020
The question: how does Hilbert space represent a quantized world? Quantization is a constraint on the mappings of Hilbert space onto itself which is represented as a constraint on the permissible set of operators in the space which is realized as a constraint on the applicable set of measurement operators [since we understand that most of the time the universe measures itself in the absence of physicists, this is in effect a constraint on all interactions which reach a result if the two reagents share some code basis, ie eigenfunctions].
Gittins: the world is divine; keep it simple; keep saying it until it sinks in. Ross Gittins: The RBA has just one message for Scott Morrison and Josh Frydenberg
My perennial problem is having ambition above my ability, but there is really nothing I can do about it because what I want to do has to be done. The latest point of contact is spelt out just above, how does Hilbert space represent a quantized world [starting, we presume from the fact that it has an infinity of orthogonal = independent dimensions]. I can state that as a constraint on operators, but what exactly is the constraint which shows as non-commutativity — the transform from A to B minus the transform from B to A is equal to something like the quantum of action. I just have to understand this better so I can explain it to myself and to anyone reading my stuff [and the simplest way would be to start with the 2 dimensional spaces used in quantum computation]. This little
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problem is just another step on the way to conceiving the universe as a mind and one way to get some clues about this is to make a model of the brain in Hilbert space and see what non-commutativity looks like there. Another approach is to put the computer network into Hilbert space and look at non-commutativity from that point of view: something to work on tomorrow.
In the discussions leading to my thesis I had great difficulty explaining to my supervisor the role of layering in the development of the network model at the heart of the thesis. The concept is developed from the OSI layering described by Tanenbaum. In the explanation of my thesis that I am now writing I hope to take advantage of Place's explanation of the consistency of the idea that consciousness is a brain process. OSI model - Wikipedia, Andrew Tanenbaum; Computer Networks, Ullin T. Place: Is Consciousness a Brain Process?
Tuesday 2 June 2020
We have a number of representations of quantum mechanics due to [Planck, Bohr,] Heisenberg, Schrödinger, Dirac, von Neumann and Feynman. It would be nice to dream up a simple network version built around the notion that all interactions involve an integral number of quanta of action and [so] avoid the integration of infinitesimal actions, [an approach] which would seem to be closer to the actual interaction processes in nature which obviously avoid all the problems that come with infinitesimals, differentiation and integration, infinities and renormalization. Feynman's Thesis. Richard Feynman: A New Approach to Quantum Mechanics
Energy the root of excitement and structure. From our logical
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beginning we see energy as a sequence of quanta of action, so the universe is quantized by the not [wave generator] operator from the very beginning. Is this bugs bunny talking? So everything that happens is one or more quanta of action. With a photon absorbed or emitted by an atom the angular momentum of the relevant electron is changed by one quantum of action while the photon has a certain amount of energy which is measured by its frequency, ie the inverse of the time it takes the photon to execute one quantum of action [maybe its spin]. So we are looking for the correlation between these quanta, the change of the angular momentum and the inverse of the quantum frequency [which is a function of the energy difference between two states of an atomic electron]. High energy = short time, ie quantum of action executed quickly just as for high momentum the quantum of action is executed in a short space [and for spin the quantum of action executed a closed circuit].
Wednesday 3 June 2020
The logical / digital approach can only deal with integers, like a computer, where we express rational numbers as binary "decimals" in floating point base 2, 4, 8, 16, etc notation. We find in physics that a lot of the values that we measure for things like c, ℏ, g, not to mention π, e, sin x etc are mathematically treated as real numbers even though practical calculation must treat them as rationals. Now it would seem that an adequately complete model of the universe should yield values of all the fixed constants computed by some natural process. We may say that the most fundamental constants like c, g, ℏ and k may be more or less arbitrary but then we have to come up with a story about how the universe uses these (as physicists use them) to come up with numbers like the frequency of spectral lines etc. The basic idea would seem to be (using the heuristic of simplicity) that we look for a chain of computation leading from simple applications of e, h, c etc leading layer by layer (maybe like a layered Feynman network) to the numbers we get in the laboratory.
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As the hills get steeper we go down through the gears always keeping the donk as close as possible to maximum power to maximize the rate of climb. With infinite reduction and infinite traction we are unstoppable.
Thursday 4 June 2020
If we assume that the energy of the universe is zero we might guess that the fixed points of both the classical and quantum Lagrangians (maxima and minima) are zero, implying that action happens when KE = PE, so KE - PE = 0, and the effect of applying the variational method is to find the zero point. Feynman's path integral method may have this effect, and we can then see this fact as a reflection in all events in the universe of the initial emergence of energy from the pure action of the initial singularity by the creation of equal quantities of potential and kinetic energy which may be understood as positive and negative "charge" which, like electric charge, add up to zero, ie electrical neutrality as in an unionized atom.
Feynman writes:
'The probability that a particle will be found to have a path x(t) lying somewhere within a region of space time is the square of a sum of contributions, one from each path in the region. The contribution from a single path is postulated to be an exponential whose (imaginary) phase is the classical action (in units of ℏ) for the path in question.
Richard P. Feynman: Space-Time Approach to Non-Relativistic Quantum Mechanics [in ref above]
Feynman explains the method by noting that the true path x(t) will be the one where the phase does not change [is stationary] in the first
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order as a result of small variations, whereas as we get further from the true path the phases become relatively random and so cancel one another. We might assume from this that the true path is equivalent to one complete cycle of phase (ω = 2π) which is equivalent to precisely one quantum of action. which is what I want to see for every physical event. If this argument is good, we can conclude that the Lagrangiam approach to quantum mechanics always yields a path of integral phase, that is integral action. Now we have to see how this translates into energy, given that the energy transaction in any quantum event of integral phase balances the book at KE - PE = 0, ie a version of double entry bookkeeping. All looks loverly, so now have to write myself an essay on the calculus of variations. Stock trading also going well, looking forward to +5000+ week and better housing.
We may see energy as in effect an analysis of action and see the work of Aristotle as such an analysis, attributing four causes to an act which he names as matter [υλη], form [ειδος, μοφη], agent [κινουν], and end [τελος]. This analysis is not so much physical as metaphysical in that it arises from the contemplation of action by a conscious and perceptive thinker, Aristotle, the first twenty years of whose philosophical career was spent under the tutelage of Plato. Plato, insofar as we can gauge his opinions from his own writing, saw himself as standing between the exemplary world of immaterial forms and a rather imperfect world of material beings. Like the gnostics who followed him centuries later, he seemed to feel that he had special insight into the immaterial world not granted to everybody. This seems to have been a common belief in ancient times, propagated particularly by those who felt that they had special inside knowledge of the working of the world and has been appropriated by many individuals and institutions since, embodied generally in the doctrine of the divine right of kings and popes. Plato - Wikipedia
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Aristotle broke from Plato in attributing reality to the physical observable world and through his doctrine of matter and form explained how the invisible forms of heaven could be represented to human inspection by being represented in matter. Whereas Plato emphasized the eternity of the forms, Aristotle was able to combine this idea with the changing physical world by claiming that things changed by matter, like clay, being imbued with different forms, like the form of cup or the form of saucer. Aristotle added to this idea of matter and form the notion of agent, whose role was to shape matter into different forms, and the end, purpose or final cause which was the purpose that motivated the agent, either to make bronze into drinking vessels or edged weapons. This analysis is simple, straightforward, complete and easily understood by anyone with any experience of making things. It has become central to many religious beliefs which imagine a creator forming clay into human beings whose role and purpose is both to exhibit the power of the creator and to honour, glorify and worship their creator both for bringing them into existence and for its intrinsic magnificence. We see footprint of these ideas in Aristotle's construction of the first unmoved mover, the source of all motion, change and creation in the world. Aristotle - Wikipedia, Andrea Falcon (Stanford Encyclopedia of Philosophy): Aristotle on Causality, Unmoved mover - Wikipedia
The principal objection to this view probably comes from those who would like to deny the existence of a creator and at the same time hold that because the world is not conscious the notion of a final cause leading the world to do things for a purpose has no meaning. This leaves them in a quandary whose solution began to emerge when Darwin explained that the evolution of species is a consequence of variation and selection. Although he does not state it explicitly, we can more of less assume that he understood the process to be driven by the energy of the Sun which thus assumes the role of first mover,
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although not unmoved in the Aristotelian sense. We can now develop Aristotle's paradigm further by explaining in more detail how the universe grew from the pure act of the initial singularity whose nature was examined by Aristotle and Aquinas, through quantum mechanics and relativity, via Darwin to the world we inhabit and are an intimate functioning part of, our divine milieu. The Catholic Church has produced a rather anthropomorphic and mythopoetical vision of this process, much devoted, like the work of Plato, to political considerations, which can now be expressed in much clearer and more scientific language to provide us with a clear evidence based account or our origin and future, something I see as my life's work.
Teilhard de Chardin divides hid account of the Divine Milieu into two sections which he calls the divinisation of activities and the divinisation of passivities which I see as representative of the two features of the emergence of energy from action in the form of kinetic energy and potential energy: the representation of the agent and the possibilities upon which the agent acts, both necessary and obvious features of any action, and, following the heuristic of simplicity, present in the universe from the beginning . . . in ever increasing complexity throughout the creation of the divine milieu. Pierre Teilhard de Chardin; The Divine Milieu
Friday 5 June 2020
This little history sets the scene for the introduction of Feynman's Lagrangian approach to quantum mechanics, which we may see as the theoretical foundation for the application of energy to understand the creation of the world, building on the fundamental role of energy
[page 336]
in relativity and quantum mechanics.
Given that the universe is closed it seems to follow that (at least in sum) action and reaction are equal and opposite. It seems equally clear (that in the absence of expansion, ie in atoms) spatial motion must be circular, ie closed.
Motions are guided by potentials so it seems logical that the potential must be real and observable (eg the pipe) in order to guide the motion of whatever is flowing (the water). The pipe also needs to be leakproof if the flow is to be conserved, and leakproof = complete, as for instance the real numbers, which are free of holes.
It is a mistake to one side of a duality prior to another, whatever one's prejudices. So heads and tails are two sides of the same coin, representatives of a symmetry just like potential and kinetic, capital and consumption are symmetries of action and cashflow respectively.
Does this hold with probability amplitudes and measured events? Observed things are real to me, and maybe this is a symmetry that holds for all interaction and not just psychological events. The old notion that the whole universe is alive is a symmetry that covers all events.
The Lagrangian formulation applies to completed actions and the completion implies an integral number of quanta, as for instance the action involved in a photon entering or leaving an atom, as Planck discovered. The action is inherently quantized by E=hf, the equation that determines the inertia of the photon.
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Feynman's path integral method is in effect a Feynman diagram pixellated by points in the real continuum spanning the whole of spacetime analogous to the network implicit in the differential manifold of general relativity, with the same cardinality but what looks like a different metric, the metric of gravitation determined by local energy density, the metric of quantum theory computed by the inner product of the Hilbert space in which every point in spacetime is orthogonal to every other — something like this, to be fleshed out by reading more. Path integral formulation - Wikipedia
General relativity is formulated in terms of distances. Quantum theory is formulated in terms of probability amplitudes whose absolute squares give the probability of a particle (state) covering the distance from a to b. The quantum mechanical layer is a stratum under the space-time / gravitational layer and so provides the alphabet from which gravitational messages are constructed and energy serves as the symmetry connecting quantum mechanics to gravitation. So we expect to find within or emerging from quantum mechanics the four orthogonal dimensions of space-time and we see a connection between the use of complex periodic vectors in quantum mechanics and the notion implicit in the Minkowski metric that one or other of space or time is represented by a complex variable. We might see here a footprint of the fundamental theorem of algebra that tells us that all polynomials have complex solutions. Fundamental theorem of algebra - Wikipedia
The use of real numbers in gravitational calculations is very convenient and is unlikely to create errors in our calculations of the large scale structure of spacetime. However, when we come to the local structure of the universe studied by QED and QCD the use of real numbers may be a source of problems with infinity and the cosmological constant which might be solved [if we recognise] that the domain of gravitation and field theories in general is not the real numbers but the integers mapped onto quanta of action, since the quantum of action is atomic, ie indivisible: subjecting it to the indignities of infinitesimal approach to calculus maybe a mistake, since the world is not a continuum
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but has vast, exciting and interesting structure whereas a continuum carries no information at all as we learn from the mathematical theory of communication and Noether's theorems on symmetry (= no-information).
Saturday 6 June 2020
Following Einstein, we build the big picture from little pictures, beginning with a quantum of action [which we might identify with the initial singularity and the traditional god of Aristotle and Aquinas]. Let this bifurcate into an equivalent quantum of potential and kinetic energy which is (?) equivalent to a probability amplitude operating between potential and kinetic energy analogous to a pendulum. We are winging it here. We guess that much f the energy of the universe exists in the form of dark matter and dark energy that does not radiate photons and so can only be 'seen' by gravitational cosmological phenomena such as the expansion of the universe and the dynamics of galaxies We might speculate that these forms of energy are too primordial to have generated the necessary particle and electromagnetic structure to create the photons upon which most of our astronomical observations rely. There is a gap in our understanding between the initial singularity and the first light in the universe, that is, I suspect, the emergence of space-time and photons. Here we have a zone where the current models using QED and QCD do not have much to say as there is need for a philosophical ansatz to set off a new round of speculation about the days when god had not yet learned to speak. Dark matter - Wikipedia, Dark energy - Wikipedia
Good to have a fundamental principle, said before but worth saying again: the universe complexifies by breaking symmetries
[page 339]
and the measure of its complexification is the increase in entropy, conceived more as an information theoretical measure than a thermodynamic measure, although the mathematical expressions are very close. We may think of the different applications of this measure as instances of breaking the mathematical or formal symmetry.
The close connection between the velocity of light and the metric structure of inertial space suggests that the emergence of photons and the emergence of space-time are closely connected. Perhaps the most interesting thing about photons is that they have no rest mass, are always in motion, have energy and momentum closely connected to the quantum of action and, from an observer's point of view, are outside space and time which suggests that they predate it and could be part of its alphabet.
It is hard to imagine photons without electrons, the lightest stable charged particles. What is the origin of electric charge? Is it analogous to mass charge and colour charge? Ie does mass create and absorb gravitons in a way analogous to electrons creating and absorbing photons?
Photons couple time to space so we might think of them as existing in time / energy and cresting space / momentum although remaining outside it, hence their adherence to null geodesics and following the curvature of space-time. Maybe space arises as a broken symmetry of time which explains the close parallel between energy / time and momentum / space which reflects the underlying unbroken symmetry.
All space is imbued with potential (gravitation) which is neutralized by free fall ie PE + KE = 0 to give inertial space, the natural home of all particles of energy. Formally we understand
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gravitation as the curvature of space-time but we must find the source of this formal structure in energy and quantum physics, that is, how do we make curved space-time and inertial space-time out of Hilbert space? Since this structure emerges at the beginning we may guess that although it is constructed from energy, it is symmetrical with respect to energy density [as we expect with a computer network, since processing speed (ie energy) does not change the formal structure of algorithms].
All we have got to do this is the structure of Hilbert space, the inner product metric and operators / functions. We can imagine that at the initial level of simplicity the actual values of metrics and operators is not so important as the structure implicit in them.
Veltman and others discuss Lorentz transformations of Hilbert space on the assumption that inertial space is the domain of quantum mechanics, but maybe we have got this backwards and Hilbert space is the domain of inertial / curved space-time. So we might be able to see the symmetries of space-time as consequences of the symmetries of quantum mechanics as described by Dirac. Martinus Veltman: Diagrammatica: The Path to the Feynman Rules, Paul Dirac; The Principles of Quantum Mechanics (4th ed)
Music is the historical antecedent of scholarship. Hopefully one of these sentences in the dark will hit a target.
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Further readingBooks
Clark, Ronald, The Life of Bertrand Russell, Bloomsbury Reader 1973, 2012 Preface: '. . . Russell's letters to Lucy Donelly. to Lady Contance Malleson and above all the Lady Ottoline Morrell wikk, when pubkished in full, reveal the deep emotionak complexities of a man to whm no venture was too dangerous, no exploration too unlikely. It will eventually be possible to describe in greater some aspects of Russell's later life although it now seems conclusive — at least to the oreset writer — that these details will not materially alter the picture it is possible to draw today.' (1974)
Amazon
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Dirac, P A M, The Principles of Quantum Mechanics (4th ed), Oxford UP/Clarendon 1983 Jacket: '[this] is the standard work in the fundamental principles of quantum mechanics, indispensible both to the advanced student and the mature research worker, who will always find it a fresh source of knowledge and stimulation.' (Nature)
Amazon
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Feynman, Richard Phillips, Feynman's Thesis: A New Approach to Quantum Mechanics, World Scientific Publishing Company 2005 Amazon editorial review: 'Editorial Reviews
Review
'The young Feynman revealed here was full of invention, verve, and ambition. His new approach to quantum mechanics, after simmering for decades beneath the surface of theoretical physics, burst into new prominence in the 1970s. Now its influence is pervasive, and still expanding. Feynman's original presentation is not only uniquely clear, but also contains insights and perspectives that are not widely known, and might well provide ammunition for another explosion or two.' Frank Wilczek
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Hallett, Michael, Cantorian Set Theory and Limitation of Size, Oxford UP 1984 Jacket: 'This book will be of use to a wide audience, from beginning students of set theory (who can gain from it a sense of how the subject reached its present form), to mathematical set theorists (who will find an expert guide to the early literature), and for anyone concerned with the philosophy of mathematics (who will be interested by the extensive and perceptive discussion of the set concept).' Daniel Isaacson.
Amazon
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Sproul, Barbara C, Primal Myths: Creating the World, Rider (Hutchinson) 1980 back |
Tapsell, Kieran, Potiphar's Wife: The Vatican's Secret and Child Sexual Abuse, ATF Press 2014 Back cover: 'For 1500 years the Catholic Church accepted that clergy who sexually abused children deserved to be stripped of their status as priests and then imprisoned. . . . That all changed in 1922 when Pope Pius XI issues his decree Crimen Sollicitationis that created a de facto 'privilege of clergy' by imposing the 'secret of the Holy Ofice' on all information obtained through the Church's canonical investigations. If the State did not know about these crimes, then there would be no State trials, and the matter could be treated as a purely canonical crime to be dealt with in secret in the Church courts.'
Amazon
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Teilhard de Chardin, Pierre, The Divine Milieu, Harper Perennial Modern Classics 2001 ' "The volume includes a scholarly and most helpful Foreword by Jesuit scholar Thomas M. King, who outlines the life of Teilhard de Chardin and helps the reader to understand the context in which The Divine Milieu was written. He writes of a Jesuit priest whose work did not sit easily with the Roman Catholic hierarchy of the early twentieth century. He portrays a man in some spiritual turmoil, living through events of great magnitude, who is seeking to make sense of all that is around him and of his own reaction to those events. The Divine Milieu was not written for those who were comfortable in their Catholic faith, but for the doubters and waverers – those for whom classical expressions of religious faith had long lost their meaning. I commend this volume.” —Rev. Adrian Burdon, Religion and Theology'
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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. ...'
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Papers
Goedel, Kurt, "On formally undecidable problems of Principia Mathematica and related systems I", in Solomon Fefferman et al (eds), Kurt Goedel: Collected Works Volume 1 Publications 1929-1936, , New York, OUP, 1986, page 145-195. back |
Links
Adolph Hitler, Goodreads, “If you tell a big enough lie and tell it frequently enough, it will be believed.” back |
Alan Turing, On Computable Numbers, with an application to the Entscheidungsproblem, 'The "computable" numbers may be described briefly as the real numbers whose expressions as a decimal are calculable by some finite means. Although the subject of this paper is ostensibly the computable numbers, it is almost equally easy to define and investigate computable functions of an integral variable of a real or computable variable, computable predicates and so forth. . . . ' back |
Andrea Falcon (Stanford Encyclopedia of Philosophy), Aristotle on Causality, ' Each Aristotelian science consists in the causal investigation of a specific department of reality. If successful, such an investigation results in causal knowledge; that is, knowledge of the relevant or appropriate causes. The emphasis on the concept of cause explains why Aristotle developed a theory of causality which is commonly known as the doctrine of the four causes. For Aristotle, a firm grasp of what a cause is, and how many kinds of causes there are, is essential for a successful investigation of the world around us.
. . . Aristotle is committed to a form of causal pluralism . . . For Aristotle, there are four distinct and irreducible kinds of causes. The focus of this entry is on the systematic interrelations among these four kinds of causes.'
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Anne Davies, Australian bushfires: FOIs shed new light on why morison government was ill-prepared, ' Some who sought to warn the federal government early, such as the former NSW fire chief Greg Mullins, felt they were fobbed off by the federal government. . . .
In the aftermath of the fires, Morrison has said he didn’t need to hear from former chiefs as the government could hear from the current ones. But Mullins has said it was precisely their “ex” status that allowed them to speak freely both about bushfire preparedness and its link to climate change. . . .
Mullins told the Guardian: “It was clear that there was never any intention by the PM to listen to us. We were treated with open contempt by the PM, who said he would deal with the current chiefs.
“The deputy prime minister [Michael McCormack] said we were time-wasters and that those who talked about climate change and bushfires were latte-sipping greenies.” ' back |
Aristotle - Wikipedia, Aristotle - Wikipedia, the free encyclopedia, ' Aristotle Greek: Ἀριστοτέλης Aristotélēs, pronounced [aristotélɛːs]; 384 – 322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. He was the founder of the Lyceum and the Peripatetic school of philosophy and Aristotelian tradition. Along with his teacher Plato, he has been called the "Father of Western Philosophy". His writings cover many subjects – including physics, biology, zoology, metaphysics, logic, ethics, aesthetics, poetry, theatre, music, rhetoric, psychology, linguistics, economics, politics and government.' back |
Ben & Jerry's, We Must Dismantle White Supremacy: Silence Is NOT An Option, ' The murder of George Floyd was the result of inhumane police brutality that is perpetuated by a culture of white supremacy. What happened to George Floyd was not the result of a bad apple; it was the predictable consequence of a racist and prejudiced system and culture that has treated Black bodies as the enemy from the beginning. What happened to George Floyd in Minneapolis is the fruit borne of toxic seeds planted on the shores of our country in Jamestown in 1619, when the first enslaved men and women arrived on this continent.' back |
Blackwill & Wright, The End of World Order and American Foreign policy, ' The world has moved away from a standard of world order in which nations work within the same set of constraints and aspire to meet the same set of rules toward a model in which many countries choose their own paths to order, without much reference to the views of others, both near and far. This heterogeneity is not so much a rush to excellence as the projection of the domestic characteristics of the major powers into the international arena. Thus, the corruption, lack of accountability, and absence of freedom in autocratic countries is their version of order. Unbound from alliances and institutions, the vagaries of American domestic politics manifest themselves in unilateralist approaches to order. An application of Kissinger’s model of world order is nowhere to be seen.' (page 12) back |
Caitlin Oprysko, 'There is somethig different here:' Obama says he's encouraged by mass protests of George Floyd killing, ' Former President Barack Obama said on Wednesday that he’d seen a “change in mindset that’s taking place” in the conversation around systemic racism and police killings of unarmed black Americans over the past week, as protests over the death of George Floyd have mushroomed around the globe.
“We have seen in the last several weeks, the last few months, the kinds of epic changes and events in our country that are as profound as anything I’ve seen in my lifetime,” Obama said at the outset of a virtual roundtable on police violence, nodding to the twin crises of the coronavirus pandemic and mass protests from coast to coast. ' back |
Dark energy - Wikipedia, Dark energy - Wikipedia, the free encyclopedia, 'In physical cosmology and astronomy, dark energy is an unknown form of energy which is hypothesized to permeate all of space, tending to accelerate the expansion of the universe. Dark energy is the most accepted hypothesis to explain the observations since the 1990s indicating that the universe is expanding at an accelerating rate.' back |
Dark matter - Wikipedia, Dark matter - Wikipedia, the free encyclopedia, 'Dark matter is an unidentified type of matter comprising approximately 27% of the mass and energy in the observable universe that is not accounted for by dark energy, baryonic matter (ordinary matter), and neutrinos. The name refers to the fact that it does not emit or interact with electromagnetic radiation, such as light, and is thus invisible to the entire electromagnetic spectrum.' back |
First Vatican Council, Decrees of the [first] Vatican Council, Decrees of the Vatican Council, IV: Concerning the Infallible Teaching of the Roman Pontiff back |
Fundamental theorem of algebra - Wikipedia, Fundamental theorem of algebra - Wikipedia, the free encyclopedia, 'The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with an imaginary part equal to zero.
Equivalently (by definition), the theorem states that the field of complex numbers is algebraically closed.' back |
Gabriel Said Reynolds, What Turkey Did to Its Christians, Review of The Thirty-Year Genocide: Turkey’s Destruction of Its Christian Minorities: Benny Morris and Dror Ze’evi
Harvard University Press, $35, 672 pp.
' A traveler in Ottoman Turkey in the mid-nineteenth century would have discovered a robust and diverse Christian presence of different denominations and ethnicities, including Armenians, Greeks, and Assyrians. There were between 3 and 4 million Christians in what is now Turkey—around 20 percent of the total population. . . . By 1924, through three successive waves of massacre, deportation, abduction, and forced conversion, Christians had been reduced to 2 percent of Turkey, and almost all who remained would depart in the following decades. The Thirty-Year Genocide tells the story of this religious cleansing.
The book’s authors, Benny Morris and Dror Ze’evi, argue, with meticulous detail, that the “thirty-year genocide” is not a story of Turk-versus-Armenian. It is a story of Muslim-versus-Christian.' back |
George Chauncey, The Deviant's War, Review of THE DEVIANT’S WAR: The Homosexual vs. the United States of America By Eric Cervini
' If the L.G.B.T.Q. movement had saints, a Jewish homosexual atheist scientist named Franklin Kameny would have an exalted place in the pantheon. Most people believe the 1969 Stonewall riots gave birth to militant gay politics. But for almost a decade before Stonewall, Kameny boldly challenged the reigning orthodoxy that homosexuality was a mental illness and led an audacious campaign against the federal government’s ban on employing gay workers. Brilliant, fearless, cantankerous and unstoppable, he was lionized in his old age by a movement that by the Obama era had achieved victories not even he could have anticipated. In Eric Cervini, a young historian of L.G.B.T.Q. politics and the author of the exhaustively researched and vividly written biography “The Deviant’s War,” Kameny has found his hagiographer.' back |
George Santayana (1913), Winds of Doctrine, 'The present age is a critical one and interesting to live in. The civilisation characteristic of Christendom has not disappeared, yet another civilisation has begun to take its place. We still understand the value of religious faith; we still appreciate the pompous arts of our forefathers; we are brought up on academic architecture, sculpture, painting, poetry, and music. We still love monarchy and aristocracy, together with that picturesque and dutiful order which rested on local institutions, class privileges, and the authority of the family. We may even feel an organic need for all these things, cling to them tenaciously, and dream of rejuvenating them. On the other hand the shell of Christendom is broken. The unconquerable mind of the East, the pagan past, the industrial socialistic future confront it with their equal authority. Our whole life and mind is saturated with the slow upward filtration of a new spirit—that of an emancipated, atheistic, international democracy.' back |
Jennifer Szalai, In 'Surviving Autocracy,' Masha Gessen Tells Us to Face the Facts, ' “Most Americans in the age of Trump are not, like the subjects of a totalitarian regime, subjected to state terror,” Gessen writes in the new book. But the last few months have shown what can happen when a president’s contempt for expert knowledge collides with a dire need for it: “We could have imagined, but we could not have predicted, that a pandemic would render his arrogant ignorance lethal.” ' back |
John D. Stoll, Corporate Activism Gets Its Day. Ben & Jerry's Has Been At It for Decades, ' This past week, after George Floyd was killed while in the custody of Minneapolis police, we witnessed a herd of companies committing to do something that is hard to chart on spreadsheets: address America’s structural racism problems. . . . Then there was Ben & Jerry’s.
“The murder of George Floyd was the result of inhumane police brutality that is perpetuated by a culture of white supremacy,” the ice-cream maker said on its website this past week. In a 700-word statement, the company supplied a four-point plan to “dismantle white supremacy in all its forms.” ' back |
John Paul II, Ex Corde Ecclesiae, '27. Every Catholic University, without ceasing to be a University, has a relationship to the Church that is essential to its institutional identity. As such, it participates most directly in the life of the local Church in which it is situated; at the same time, because it is an academic institution and therefore a part of the international community of scholarship and inquiry, each institution participates in and contributes to the life and the mission of the universal Church, assuming consequently a special bond with the Holy See by reason of the service to unity which it is called to render to the whole Church. One consequence of its essential relationship to the Church is that the institutional fidelity of the University to the Christian message includes a recognition of and adherence to the teaching authority of the Church in matters of faith and morals. Catholic members of the university community are also called to a personal fidelity to the Church with all that this implies. Non-Catholic members are required to respect the Catholic character of the University, while the University in turn respects their religious liberty. back |
John Paul II, Ordinatio Sacerdotalis, 22 May 1994, '4. Although the teaching that priestly ordination is to be reserved to men alone has been preserved by the constant and universal Tradition of the Church and firmly taught by the Magisterium in its more recent documents, at the present time in some places it is nonetheless considered still open to debate, or the Church's judgment that women are not to be admitted to ordination is considered to have a merely disciplinary force.
Wherefore, in order that all doubt may be removed regarding a matter of great importance, a matter which pertains to the Church's divine constitution itself, in virtue of my ministry of confirming the brethren (cf. Lk 22:32) I declare that the Church has no authority whatsoever to confer priestly ordination on women and that this judgement is to be definitively held by all the Church's faithful.'
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Karen Attiah, How Western media would cover Minneapolis if it happened in another country, ' In recent years, the international community has sounded the alarm on the deteriorating political and human rights situation in the United States under the regime of Donald Trump. Now, as the country marks 100,000 deaths from the coronavirus pandemic, the former British colony finds itself in a downward spiral of ethnic violence. The fatigue and paralysis of the international community are evident in its silence, America experts say.' back |
Kurt Gödel 1, On formally undecidable propositions of Principia Mathematica and related systems, I, The classic paper, part I. back |
Kurt Gödel I, On formally undecidable propositions of Principia Mathematica and related systems I, '1 Introduction
The development of mathematics towards greater exactness has, as is well-known, lead to formalization of large areas of it such that you can carry out proofs by following a few mechanical rules. The most comprehensive current formal systems are the system of Principia Mathematica (PM) on the one hand, the Zermelo-Fraenkelian axiom-system of set theory on the other hand. These two systems are so far developed that you can formalize in them all proof methods that are currently in use in mathematics, i.e. you can reduce these proof methods to a few axioms and deduction rules. Therefore, the conclusion seems plausible that these deduction rules are sufficient to decide all mathematical questions expressible in those systems. We will show that this is not true, but that there are even relatively easy problem in the theory of ordinary whole numbers that can not be decided from the axioms. This is not due to the nature of these systems, but it is true for a very wide class of formal systems, which in particular includes all those that you get by adding a finite number of axioms to the above mentioned systems, provided the additional axioms don’t make false theorems provable.' back |
Mick Broderick, Sixty years on, two TV programs revisit Australia's nuclear history at Maralings, 'Over successive Sunday nights, the ABC has premiered two important television programs recounting the history of nuclear testing in Australia – the documentary Maralinga Tjuratja and a six-drama series Operation Buffalo. Both explore the ramifications of the Anglo-Australian nuclear venture conducted at Maralinga during the cold war – but in very different ways.' back |
OSI model - Wikipedia, OSI model - Wikipedia, the free encyclopedia, 'The Open Systems Interconnection model (OSI model) is a conceptual model that characterizes and standardizes the communication functions of a telecommunication or computing system without regard to its underlying internal structure and technology. Its goal is the interoperability of diverse communication systems with standard protocols. The model partitions a communication system into abstraction layers. The original version of the model defined seven layers.' 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 |
Paul Krugman, Trump Takes Us to the Brink, ' How did we get here? The core story of U.S. politics over the past four decades is that wealthy elites weaponized white racism to gain political power, which they used to pursue policies that enriched the already wealthy at workers’ expense.
Until Trump’s rise it was possible — barely — for people to deny this reality with a straight face. At this point, however, it requires willful blindness not to see what’s going on.
I still see occasional news reports that describe Trump as a “populist.” But Trump’s economic policies have been the opposite of populist: They have been relentlessly plutocratic, centered largely on a successful effort to ram through huge tax cuts for corporations and the rich, and a so far unsuccessful attempt to take health insurance away from poor and working-class families.' back |
Paul Rosenberg, The Power Worshippers: A look inside the American religious right, ' For 40 years now, the religious right has been a fixture in American politics and for all that time it has befuddled observers who continually misunderstand it, beginning with its support for Ronald Reagan, a divorced Hollywood actor, against Jimmy Carter. Reagan was the first US president to describe himself as a "born-again Christian". . . .
The secret to making sense of them is simply stated in the title of Katherine Stewart's new book: The Power Worshippers: Inside the Dangerous Rise of Religious Nationalism. It draws on more than a decade of first-hand experience and front-line reporting that began when her daughter's public elementary school was targeted to house a fundamentalist Bible club.' back |
Pius IX, The Syllabus of Errors Condemned by Pius IX, 'Venerable Brethren, you see clearly enough how sad and full of perils is the condition of Catholics in the regions of Europe which We have mentioned. . . .. Venerable Brothers, it is surprising that in our time such a great war is being waged against the Catholic Church. But anyone who knows the nature, desires and intentions of the sects, whether they be called masonic or bear another name, and compares them with the nature the systems and the vastness of the obstacles by which the Church has been assailed almost everywhere, cannot doubt that the present misfortune must mainly be imputed to the frauds and machinations of these sects. It is from them that the synagogue of Satan, which gathers its troops against the Church of Christ, takes its strength.' back |
Plato - Wikipedia, Plato - Wikipedia, the free encyclopedia, 'Plato (. . . Greek: . . . Plátōn, "broad" 428/427 BC – 348/347 BC), was a Classical Greek philosopher, mathematician, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the foundations of natural philosophy, science, and Western philosophy. Plato was originally a student of Socrates, and was as much influenced by his thinking as by what he saw as his teacher's unjust death.' back |
Pope Pius X, 24 Thomistic Theses, 'The Twenty-Four Fundamental Theses Of Official Catholic Philosophy
Commentary by P. Lumbreras, O.P., S.T.Lr., Ph.D.
Latin translation of theses by Hugh McDonald
Citations of St. Thomas from CatholicApologetics.info and Fr. Edouard Hugon, O.P.'s Les vingt-quatre theses thomistes
(Double-click any Latin word for its definition in Lewis & Short.)
In our preceding paper we proved by documents of recent Popes that the Church, in exercising her right, has adopted the scholastic philosophy as her official philosophical teaching, that by scholastic philosophy the Church understands not only chiefly but exclusively the philosophy of St. Thomas, and that St. Thomas' philosophy stands for at least the twenty-four theses approved and published by the Sacred Congregation of Studies.
In this paper we will give a translation of these theses with a very brief explanation of each.
Sacred Congregation of Studies
Decree of Approval of some theses contained in the Doctrine of St. Thomas Aquinas and proposed to the Teachers of Philosophy
Sacred Congregation of Studies
Datum Romae, die 27 iulii 1914.
B. Card Lorenzelli, Praefectus
Ascensus Dandini, a Secretis' back |
Richard Ackland, Protecting paedophile priests goes back to canon law, 'In 1922, Pope Pius XI issued Crimen Sollicitationis, which imposed the secret of the holy office. Priests who were meddlesome in the worst ways imaginable were to be kept under wraps.
This was subsequently confirmed in 1962. In 1974 the "secret of the holy office" was rebadged as the "pontifical secret".
It was confirmed again in 2001 by Pope John Paul II. Later Benedict XVI (the German pope) conveniently declared the secrecy provisions extended to allegations of priests having sex with intellectually disabled people.
By 2010, the scandals of paedophile priests were well and truly on the front page. The heat was on, so the Vatican got busy and came up with a harmless amendment to the established code. A restricted form of reporting to the civil authorities was permitted, but only where the civil law required it.' back |
Richard P. Feynman, Space-Time Approach to Non-Relativistic Quantum Mechanics, ' Abstract: Non-relativistic quantum mechanics is formulated here in a different way. It is, however, mathematically equivalent to the familiar formulation. In quantum mechanics the probability of an event which can happen in several different ways is the absolute square of a sum of complex contributions, one from each alternative way. The probability that a particle will be found to have a path x(t) lying somewhere within a region of space time is the square of a sum of contributions, one from each path in the region. The contribution from a single path is postulated to be an exponential whose (imaginary) phase is the classical action (in units of ℏ) for the path in question. The total contribution from all paths reaching x,t from the past is the wave function ψ(x,t).This is shown to satisfy Schroedinger’s equation.' back |
Ross Gittins, The RBA has just one message for Scott Morrison and Josh Frydenberg, ' It’s possible Reserve Bank governor Dr Philip Lowe has been reading a book about speechmaking – the one that says: keep the message simple and keep saying it until it sinks in. . . .
Lowe said that when the JobKeeper wage subsidy scheme was due to end in late September was "a critical point for the economy". This was also when the banks’ six-month deferral of mortgage and other payments would come to an end.
"It will be important to review the parameters of that [JobKeeper] scheme. It may be that, in four months’ time, we bounce back well, and the economy does reasonably well, and these schemes, which were temporary in nature, can be withdrawn without problems," he said.' back |
Steven Weinberg, The Cosmological Constant Problems [Talk given at Dark Matter 2000, Marina del Rey, CA, February 2000], 'Abstract. The old cosmological constant problem is to understand why the vacuum energy is so small; the new problem is to understand why it is comparable to the present mass density. Several approaches to these problems are reviewed. Quintessence does not help with either; anthropic considerations offer a possibility of solving both. In theories with a scalar field that takes random initial values, the anthropic principle may apply to the cosmological constant, but probably to nothing else.' back |
Supremae Sacrae Conregationis Sancti Officii Instructio, De Modi Procedendi in Causis Sollicitationis, 'Instructio De modo procedendi in causis de crimine sollicitationis. SERVANDA DILLIGENTER IN ARCHIVO SECRETO CURIAE PRO NORMA INTERNA NON PUBICANDA NEC ULLIS COMMENTARIIS AGENDA' back |
The Guardian, Deaths Inside: Indigenous Australian deaths in custody 2020, ' More than 400 Aboriginal and Torres Strait Islander people have died in custody since the end of the royal commission into Aboriginal deaths in custody in 1991.
The royal commission emphasised the importance of monitoring and maintaining accurate data about deaths in custody. Despite public reporting and tracking through the Australian Institute of Criminology’s national program, detailed, up-to-date information is hard to find.
In 2018, Guardian Australia’s reporting team collected and analysed all available coronial data and other sources to build this searchable database.
One year on, we have updated “Deaths inside”, which tracks every known Indigenous death in custody in every jurisdiction from 2008 - 2020.' back |
Thomas L. Friedman, How We Broke the World, ' If recent weeks have shown us anything, it’s that the world is not just flat. It’s fragile.
And we’re the ones who made it that way with our own hands. Just look around. Over the past 20 years, we’ve been steadily removing man-made and natural buffers, redundancies, regulations and norms that provide resilience and protection when big systems — be they ecological, geopolitical or financial — get stressed. We’ve been recklessly removing these buffers out of an obsession with short-term efficiency and growth, or without thinking at all.' back |
Tiger Webb, Changing the ABC's pronunciation guidance on Indigenous words, ' . . . A more serious issue is that the modified spelling key does not accurately reflect many sounds common to Aboriginal and Torres Strait Islander languages.
Given the ABC has made serious, strong commitments to highlight the use of Indigenous place and nation names in its content, as well as our participation in wider community initiatives like Walking Together and the UN International Year of Indigenous Languages, this seems a critical oversight. ' back |
Ullin T. Place, Is Consciousness a Brain Process?, The thesis that consciousness is a process in brain is put forward as a reasonable scientific hypothesis, not to be dismissed on logical grounds alone. conditions under which two sets of observations are treated as observations of same process, rather than as observations of two independent correlated processes, are discussed. It is suggested that we can identify consciousness with a given pattern of brain activity, if we can explain subject's introspective observations by reference to brain processes with which they are correlated. It is argued that problem of providing a physiological explanation of introspective observations is made to seem more difficult than it really is by ‘phenomenological fallacy’, mistaken idea that descriptions of appearances of things are descriptions of actual state of affairs in a mysterious internal environment. back |
Unmoved mover - Wikipedia, Unmoved mover - Wikipedia, the free encyclopedia, ' The unmoved mover (Ancient Greek: ὃ οὐ κινούμενον κινεῖ, romanized: ho ou kinoúmenon kineî, lit. 'that which moves without being moved'] or prime mover (Latin: primum movens) is a concept advanced by Aristotle as a primary cause (or first uncaused cause) or "mover" of all the motion in the universe. As is implicit in the name, the unmoved mover moves other things, but is not itself moved by any prior action. In Book 12 (Greek: Λ) of his Metaphysics, Aristotle describes the unmoved mover as being perfectly beautiful, indivisible, and contemplating only the perfect contemplation: self-contemplation. He equates this concept also with the active intellect. This Aristotelian concept had its roots in cosmological speculations of the earliest Greek pre-Socratic philosophers and became highly influential and widely drawn upon in medieval philosophy and theology. St. Thomas Aquinas, for example, elaborated on the unmoved mover in the Quinque viae. ' back |
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