natural theology

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Notes

Sunday 19 February 2023 - Saturday 25 February

[Notebook: DB 88 Salvation]

[page 292]

Sunday 19 February 2023

My subconscious seems to take a dim view of my natural religion project so I wake again on a new sunny morning with sinking heart. My midnight walk told the story: 'Nothing is finished until it is complete and this is where I fail. My life is always a work in progress. What do I have to do to finished cognitive cosmology? Maybe the end will be when I identify gravitation and god and this identification will solve the problems of quantum field theory. I can only go on step by step making sure each step is relatively secure. I m happy now with page 19: Fixed points, laws and symmetries and now I have to apply it to cc20_memory.

le Carre p 424: 'What would it be like to really and absolutely believe? Like Zara. Like Mustafa. Like Jay Rourke's chums. To know, really and absolutely know that there is a Divine Being not set in time or space who reads our thoughts better than we

[page 293]

ever did and probably before you even have them? To believe that God sends you to war, God bends the paths of bullets, decides which of his children will die, or have their legs blown off or make a few hundred million on Wall Street, depending on God's Grand Design.' John le Carre (2004): Absolute Friends

I.e. we try to apply fixed point theory to God via Trinity and Hilbert space. CC20_memory, 20.1: Mathematics, physics and theology, Principles, 25.0: Scientific Method. The Minkowski metric is a fixed point in the continuous topological set representing the Universe [described by a differentiable manifold. Minkowski space breaks the symmetry of Hilbert space.] Algorithmic Information Theory. Differentiable manifold - Wikipedia, Algorithmic information theory - Wikipedia

Although I was barely aware of it at the time, my natural theology project may have taken root in my mind during the years when I paced up and down Dominican cloisters in Melbourne, Wahroonga and Canberra trying to understand Thomas Aquinas's efforts to explain the doctrine of the Trinity without breaking the absolute unity of [his] God. It was not easy. The documentation is in Latin and my attempt to understand the Trinity had to overcome the fact that God is simple and absolutely structureless. To a modern mind the doctrine is effectively meaningless, a dogmatic truth to be believed on faith because it is impossible to understand rationally. Nevertheless it has become the starting point for my project, and over the last fifty

[page 294]

years or so I have made a few tweaks to explain how one might explain the emergence of our universe inside the quantum initial singularity which is now my version of the Christian God, identical to the God of Aquinas, eternal. simple, creative, logically consistent and from a mathematical point of view subject to Brouwer's fixed point theorem. Brouwer fixed point theorem - Wikipedia

The Trinity is a structure in God, a static point in a dynamic system. It is no different from all the other points in the dynamic divinity except only that it does not move. The function f which describes the kinematics of God is such that the Trinity, call it x, is represented by f(x) = x. The next step is to explain the situation quantum mechanically, now thinking of the fixed points in the divinity as the axioms of abstract Hilbert space listed by John von Neumann. John von Neumann (2014): Mathematical Foundations of Quantum Mechanics

Monday 20 February 2023

Do I have the courage to follow my nose. And perhaps there is a case for moving gravitation up to the page after fixed points? No. The story of the Trinity, Hilbert and Minkowski naturally come next, introducing the algorithm as the fixed point in the world and unitarity as the basic algorithm of [contact] communication by rotation, linked to the definition of Person and

[page 295]

Source [a source is an entity capable of transmitting and receiving information]. This feels dangerously good, I just have to put it into words. Something is emerging from the mist. The fact that it is rays, rather than specific complex numbers [vectors] that count in quantum theory is a step toward the heuristic of simplicity (Principle 2). Overall, the notion that fixed points are closed orbits seems relevant to both gravitation (compact universe) and quantum mechanics (unitary evolution, cyclic). Aquinas, Summa, I, 29, 1: A person is an individual substance of a rational nature

Every move in a binary memory is a combination of creation and annihilation, a quantum of action, the connection between two states, the root of communication, the essence of be-ing.

Somehow the step from boson to fermion is related to the step from Hilbert to Minkowski and is reflected in the spin / statistics theorem. PCT sits somewhere here too, but cannot come into existence until we have spacetime.

'In fact the Main Problem of quantum field theory turned out to be kill it or cure it: either show that the idealizations involved in the fundamental notions of the theory (relativistic invariance, quantum mechanics, local fields, etc) are incompatible in some physical sense, or to recast the theory in such a form that it provides a practical language for the description of elementary particle dynamics.'

A description of elementary particle dynamics

[page 296]

is a literary fixed point, the thing that Parmenides was looking for when he met the Goddess. Streater & Wightman (2000): PCT, Spin, Statistics and All That, John Palmer: Parmenides

So:

1. The initial singularity = god has fixed points: continuous, convex, compact.

2. According to the heuristic of simplicity and the conservation of entropy, the first fixed point will carry the same information as the entropy of the space in which it exists, ie 0 (since God is absolutely simple). What is it? If Aristotle and his team are right, a circle, an unspecified complex number [or ray] of absolute value 1, e, a quantum of action. Quantum state - Wikipedia

3. The union of this fixed point and the divinity defines Hilbert space?

All this has nothing to do with the classical Euclidean space which is at best an approximation to the reality described by Minkowski space.

. . .

States of physical systems are represented by rays: Ray is set φ of vectors ei αφ where α varies over all the real numbers and φ is normalized to 1.

[page 297]

From my point of view the heuristic of simplicity rules out all the complicated detail described in Streater and Wightman and I will continue to seek an understanding that enables us to construct the universe from first principles with very little in the way of fancy mathematics. I take the same attitude to the enormously complex mathematical creations that are devised to explain the simplest and most universal of structures, gravitation. In other words it is time to take the heuristic of simplicity seriously and see if it leads me anywhere. I am way out on a limb here, but if the universe did start as a singularity without an omniscient and omnipotent creators in sight it must have built itself up step by step and the only traditional starting point is that the god of pure action begets further distinct gods of pure action [according to the doctrine of the Trinity] best modelled ss vectors in a Hilbert space. Michio Kaku (1998): Introduction to Superstrings and M-Theory

Knowledge = information + order, maybe an operator modelled by a matrix.

Monastic memories of life just like this trying to recast Christian doctrine into acceptable terms. There I was concerned with establishing that the neural network in my head was capable of the knowledge that the Church reserved for spiritual beings. Early glimpses of cognitive cosmology and the suggestion that I give up Streater and turn to Nielsen

[page 298]

and quantum network computation already outlines in cc16-18. Nielsen & Chuang (2016): Quantum Computation and Quantum Information

My course is not political but scientific and it would be nice to be an Einstein but I am not, but I am persistent. I have felt sorry for Einstein because he was locked into continuous mathematics and general covariance and these beliefs blocked him out of quantum mechanics and made his search for a theory of everything rather sterile. I am quite pleased really that I am still on the trajectory to want a possible theology and my daily harvest of ideas and potential sentences is sufficient to keep me motivated through moments of despair. I am full of hope for a radical revision of theology which is already in a well documented embryonic stage even though readers are few and commentators entirely absent. One day some search engine will find my magic words snd I will become a thing, maybe. Always lost but ploughing ahead.

Every communication is one to one, the communication atom: source—channel—source, made and broken like a phone call.

When the system is fully put together it may look like Feynman diagrams path integrals, etc.

Tuesday 21 February 2023

1. Science is always the study of fixed events

[page 299]

in the past. There is no science without memory so we cannot look back in the Universe beyond the limits of memory.

2. Fixed points are parts of a kinetic system that map onto themselves and so are elements of memory. I live because I map myself onto myself and I guess that this is true for any stable system (particle, source, person) as long as it survives - sur - vive.

3, Fixed points are inevitable when there is no room for change. Change needs creativity, that is randomness enabled by a deficit in control. If the initial singularity can create entropy greater than its own entropy, it cannot control the outcome, opening the way for variation and selection.

4. We may see fixed points as deterministic algorithms which put a computation into a loop, group or particle. Aristotle thought the idea eternal motion must be circular. The modern version of this is the quantum ray, eψ.

5. A ray is a symmetry. Once this symmetry is broken, creation begins, manifested in the Trinity and exploited to create quantum mechanics on page 10: The emergence of quantum mechanics.

Bogged! Why? Something is missing, but its probably in my head

[page 300]

somewhere.

Wednesday 22 February 2023

What is missing? Motivation. Why try to prove that the Universe is divine? What is the value of establishing rapport between physics and theology? Perhaps it is a search for truth, equivalence of mind and reality [to replace all the theological fiction I absorbed in my childhood] and a tribute to Aristotle and Aquinas. Aristotle represented thirteenth century physics imported almost unchanged from Ancient Greece. Aquinas represented thirteenth century Catholic theology. Until his time it was predominantly Platonic, with its head in the heavens. Aquinas used Aristotle to bring theology down to earth and that is exactly what I would like to be doing, uniting Aquinas and quantum computation and communication. We live in the Minkowski world and all our technology is in a sense classical technology, but quantum theory explains the classics, predominanty the low energy solid state physics of computers, solar cells and our own bodies. Perhaps the radical task is to heal the ancient Platonic ruling class chasm between the mysterious invisible heavens snd the physical Earth: In a nutshell, God is a [gorgeous] Body [prone to exciting behaviour]. The claim that God is absolutely simple and untouchably spiritual is false, and I want cosmic cosmology to be a clear road from spirit to matter as neurophysiology is a clear road from creative inspiration to the living wetware in my head.

[page 301]

The basic structures in the universe are the [fundamental particles] and the basic question is how did they come to be? This question does not seem to be of such great interest to modern physics as how the set of 60 or so particles we have got behave. The Particle Adventure. In cc20_memory I would like to speculate about their origin as dynamic fixed points established by call circular computations, Turing machines that go round in circles never getting anywhere [a common fault in computers, solved by a restart], to be distinguished from [computable] Turing machines that stop with results. In the network model the sources (fundamental fermions) have two aspects to their personalities. On the one hand, like unobserved quantum systems, they just sit there maintaining their existence. On the other, they observe one another, sending messages that str the foundations of structures like atoms and molecules built from fundamental particles. Like network computers, they send a lot of time keeping their won houses, occasionally being interrupted to respond to another machine. Alan Turing (1936): On Computable Numbers, with an application to the Entscheidungsproblem, Particle Data Group. Lawrence Berkeley National Laboratory: The Particle Adventure

Nielsen and Chuang: A song is a vector fed into a mind for processing to create a feeling. Song - Wikipedia

In the beginning, randomness is complete and control is zero. Perfect symmetry, as in a fair die. Layer control grows as structure builds up and [uncontrolled variation] decreases [in proportion].

[page 302]

When we come to human evolution, a significant proportion of matings lead to conception and most of the babies are born living and carefully nurtured even though they may have disabilities. In the entrepreneurial world the success rate may not be so high, but management technology is well developed so a significant proportion of investments are successful. In general systems mature, variation decreases and memory increases. At the limit of mathematical calculation and computation error rates are very small and there is no significant evolution at this level of execution The innovation is all to be found in software engineering. In the art world, we see more variety and less determinism.

Quantum computing: Problem = input vector; answer = output vector. Process = operator or sequence of operations.

The life of a particles is like unobserved Schrödinger equation, a closed unitary loop of varying complexity from photon to baryons and massive bosons. Typical process: The Wu experiment. Wu Experiment - Wikipedia, C.S. Wu et. al.: Experimental Test of Parity Conservation in Beta Decay

Quantum computations are completed in one or a few moves, unlike a classical computer. The picture developed on page page 18: Transfinite Minkowski space how the two [classical and quantum computation] fit together. Each classical move directs a move in the associated Hilbert space which yields the classical outcome. The idea [is] to be developed on page 20: Space-time—the cosmic memory and operating system

[page 303]

where we discuss spacetime as [the] memory and operating system [of the world].

Le Carre page 214: 'According to our anarchist writers world conflict should lead to creative chaos. If such chaos is intelligently exploited a free society will emerge. But hen I looked about me, I was forced to accept that the preconditions of creative chaos did not exist; neither did the intelligent exploiters.' John le Carre (2004); Absolute Friends

Thursday 23 February 2023

Despair is the feeling (Aquinas calls it a passion) arising when faced with an impossible problem, ie no way forward. It is resolved by creation, that is by finding a way forward which may be an insight or a technology. Aquinas, Summa I, II, 40, 4: Is despair contrary to hope?

On page 12 page 12: The quantum creation of Minkowski space we exploited the principle that communication requires contact to explain the quantum creation of Minkowski space and the peculiar metric of this space. Why did this happen? The answer has three point: first, the development is possible and he random variations implicit in a Universe of uncontrolled action are bound to explore this possibility; second, the continued existence of this space is enabled by a closed computational process that we understand to be determinate, consistent and computable; and third, it contributes to a radical increase in the entropy of the Universe and we conceive of increasing entropy as an attractor to the emergence of increasingly complex structure, ie entropy,

[page 304]

In general physicists are inclined to interpret the increase in entropy as 'time's arrow', but we may also see that the emergence of Minkowski space gives an inevitable direction to causality, a reality made obvious by the shaoe of the relativistic light cone. One feature of this is that it makes no sense to speak of time going backwards, so the alleged symmetry in the direction of time to which come attribute the existence of antimatter fails to make logical sense and Wu's discovery of symmetry breaking in parity (ie the spatial mirror symmetry is broken) is connected this through (I think) the CPT theorem, insofar as the fracture of P parity is compensated by the broken reversibility of time, and the permanent existence of positive and negative charge saves the theorem. All this may turn out to make the independence of Hilbert space necessary to maintain a consistent Universe, Thus, it slowly emerges, may be the real task for page 20_memory. Light cone - Wikipedia

The trouble in quantum field theory may have started with Dirac's delta which was initially thought to be a bit outre by the mathematical community but then found its way in through the doctrine of distributions which shows us how to smear points so that quantum field theory will work. Dirac delta function - Wikipedia, Distribution (mathematics) - Wikipedia

Von Neumann: ' It should be emphasized that the correct structure need not consist in a

[page 305]

mathematical refinement and explanation of the Dirac method, but rather that it requires a procedure differing from the very beginning, namely the reliance on the Hilbert theory of operators. John von Neumann (2014): Mathematical Foundations of Quantum Mechanics, Introduction page 2.

It seems patently obvious that al the difficulties of quantum field theory str self inflicted wounds. Aristotle was right when he said something like infinitum non datur (probably because everything we observe is finite, Descartes 'clear and distinct idea').

The plague of infinities that has arisen from the use of real numbers and infinitesimal points in field theory has been tamed with the mathematical technologies of renormalization and distributions to correct these artificially introduced difficulties. Renormalization - Wikipedia

Friday 24 February 2023

Another point: If the world was created by an omniscient and omnipotent god capable of fashioning all the molecular machinery of the human body out of dust the initial state of creation may have been very complex at the beginning and carefully designed as the anthropic principle people and many physicists seem to think, but if on the other hand it started from a structureless initial singularity we would expect to find the initial states very simple and this is the position I am trying to explore. The photon, for instance, in some way realized

[page 306]

as a real, eternal and invisible physical particle following, and in some sense creating, the null geodesic which is built into the metric of Minkowski space by the requirement that communication requires contact. Massless bosons are one of the principal means of communication and contact in some way complimentary to the massive bosons of electroweak theory. Electroweak interaction - Wikipedia

Saturday 25 January 2023

Still stuck on cc20_memory. The first incarnation of memory is to be found in photons carrying information from their source to their destination with the only change being made to them by their frequency / energy varied by passage through gravitational potential This is the first coupling, we might guess, in the interplay between quantum mechanics and gravitation which derives from the zero energy bifurcation between gravitation (God I: the creator) and quantum mechanics (God II: energy, mass, particles) [god I ≡ potential]. We imagine that potential and kinetic are the first two forms of action to emerge from the initial singularity, closely related to the emergence of spacetime, null geodesics and the metric of Minkowski space. Keep at it, it is coming, beginning with photons.

[page 307]

Photon is not the cause of Minkowski space but it is consistent with it. In other words, they both came into existence by zero sum bifurcation and this same cause-free evolutionary process may explain all the other developments in the Universe by variation and selection. Causal processes, insofar as they are deterministic, may not be creative, but duplicative.

Next thing perhaps massive bosons emerge in the same event as the emergence of 3D space and the exclusion principle, another example of zero sum bifurcation (ZSB?). Communication and causality thus enter the universal process.

We think of sources as personalities with a spectrum of behaviours / traits / eigenvectors. Energy levels are established by [rates of] communication as in atoms. All communications involve one quantum of action, but the energy involved depends on the potential environment / gradient [here we are getting close to Einstein's idea that he could unite gravitation and electromagnetism].

We draw inspiration for all this using the principle of symmetry with respect to complexity in the context of human behaviour, either free humans or those bound by corporations which, like atoms, put constraints on interactions. Marriage is a corporation. Corporate constraint, as in an army, is workable if it boosts the power of the cooperating group above the sum of their individual powers, eg my body and its cells.

[page 308]

When a good idea comes it is so clear and pristine that I am not surprised that Descartes thought clarity and distincness are guarantees of truth rather than possibly well formed delusion, The contrasting state, the murk of unknowing is boring and painful but in the mental areas it does not last too long. In the space of biological evolution bright new ideas may take thousands of years to appear and become consolidated so we can be pleased at the rate of scientific evolution, which appears to produce a new species every century or so. I have high hopes for natural theology after 60 years of development, but have been stuck for about ten days since I finished cc19_fixed-points and started cc20_memory. I know I just have to be patient and take a holiday, but it would be lovely to fly again. Meanwhile read a lot. Manley, D. B., & Taylor, C. S. (1996): Descartes Meditations - Trilingual Edition

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Further reading

Books

Kaku (1998), Michio, Introduction to Superstrings and M-Theory (Graduate Texts in Contemporary Physics), Springer 1998 ' Called by some "the theory of everything," superstrings may solve a problem which has eluded physicists for the past 50 years -- the final unification of the two great theories of the twentieth century, general relativity and quantum field theory. This is a course-tested comprehensive introductory graduate text on superstrings which stresses the most current areas of interest, not covered in other presentation, including: string field theory, multi loops, Teichmueller spaces, conformal field theory, and four-dimensional strings. The book begins with a simple discussion of point particle theory, and uses the Feynman path integral technique to unify the presentation of superstrings. Prerequisites are an aquaintance with quantum mechanics and relativity. This second edition has been revised and updated throughout.' 
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le Carre (2004), John, Absolute Friends, Back Bay Books 2004 Jacket: 'An absolutly triumphant bestseller—everywhere hailed as the masterpiece toward which le Carre has been building since the fall of communism. This thrilling tale of loyalty, betrayal and international espionage spans the lives of two friends from the riot-torn West Berlin of the 1960s to the grimy looking glass of Cold War Europe to the present day of terrorism and uncertain new alliances—alliances that aren't always what they seem to be.' 
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Nielsen (2016), Michael A, and Isaac L Chuang, Quantum Computation and Quantum Information, Cambridge University Press 2016 Review: A rigorous, comprehensive text on quantum information is timely. The study of quantum information and computation represents a particularly direct route to understanding quantum mechanics. Unlike the traditional route to quantum mechanics via Schroedinger's equation and the hydrogen atom, the study of quantum information requires no calculus, merely a knowledge of complex numbers and matrix multiplication. In addition, quantum information processing gives direct access to the traditionally advanced topics of measurement of quantum systems and decoherence.' Seth Lloyd, Department of Quantum Mechanical Engineering, MIT, Nature 6876: vol 416 page 19, 7 March 2002. 
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Streater (2000), Raymond F, and Arthur S Wightman, PCT, Spin, Statistics and All That, Princeton University Press 2000 Amazon product description: 'PCT, Spin and Statistics, and All That is the classic summary of and introduction to the achievements of Axiomatic Quantum Field Theory. This theory gives precise mathematical responses to questions like: What is a quantized field? What are the physically indispensable attributes of a quantized field? Furthermore, Axiomatic Field Theory shows that a number of physically important predictions of quantum field theory are mathematical consequences of the axioms. Here Raymond Streater and Arthur Wightman treat only results that can be rigorously proved, and these are presented in an elegant style that makes them available to a broad range of physics and theoretical mathematics.' 
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Links

Alan Turing (1936), 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

Alex Lo, Forgotten Washington-inspired genocide is back in the headlines, ' At the height of the Cold War, the overthrow of then Indonesian president Sukarno, with full US backing, brought an obscure general called Suharto to power, who then went on to launch a bloodbath to wipe out the highly popular and non-violent PKI, the Communist Party of Indonesia, then the world’s largest outside China and the Soviet Union. . . . The 1994 Rwandan genocide, which claimed about 800,000 victims over a four-month period, has been rightly categorised as such. However, except for a few historical scholars, the slaughters in Indonesia, which took place over six months, were rarely described as such. . . . . It’s often assumed that the Cold War was won because liberal democracy and free-market capitalism were superior to communism. That may be so, but the victory was soaked in blood.' back

Algorithmic information theory - Wikipedia, Algorithmic information theory - Wikipedia, the free encyclopedia, 'Algorithmic information theory is a subfield of information theory and computer science that concerns itself with the relationship between computation and information. According to Gregory Chaitin, it is "the result of putting Shannon's information theory and Turing's computability theory into a cocktail shaker and shaking vigorously".' back

Aquinas, Summa I, II, 40, 4, Is despair contrary to hope?, ' Now the object of hope, which is the arduous good, has the character of a principle of attraction, if it be considered in the light of something attainable; and thus hope tends thereto, for it denotes a kind of approach. But in so far as it is considered as unobtainable, it has the character of a principle of repulsion, because, as stated in Ethic. iii, 3, [1112b24] "when men come to an impossibility they disperse." And this is how despair stands in regard to this object, wherefore it implies a movement of withdrawal: and consequently it is contrary to hope, as withdrawal is to approach. back

Aquinas, Summa, I, 29, 1, A person is an individual substance of a rational nature, ' I answer that, Although the universal and particular exist in every genus, nevertheless, in a certain special way, the individual belongs to the genus of substance. . . . . And so it is reasonable that the individuals of the genus substance should have a special name of their own; for they are called "hypostases," or first substances. Further still, in a more special and perfect way, the particular and the individual are found in the rational substances which have dominion over their own actions; and which are not only made to act, like others; but which can act of themselves; for actions belong to singulars. Therefore also the individuals of the rational nature have a special name even among other substances; and this name is "person." Thus the term "individual substance" is placed in the definition of person, as signifying the singular in the genus of substance; and the term "rational nature" is added, as signifying the singular in rational substances.' back

Banerjee, Taranto & Kelsey-Sugg, The partition of India in 1947 came suddenly, creating chaos, bloodshed and mass migration, ' Colonial rule in India, Britain's largest colony for nearly 200 years, ended on August 15, 1947. At the same time, the British empire partitioned the country into two: Hindu-majority India and Muslim-majority Pakistan. Why? Some describe a "myth" of irreconcilable differences between those of different religions, others point to the collapse under British rule of "old communities and the simplification of complex identities", and others still argue that the Brits considered a divided Pakistan "would be a better strategic ally".' back

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

C.S. Wu et. al., Experimental Test of Parity Conservation in Beta Decay, 'I n a recent paper' on the question of parity in weak ~ - interactions, Lee and Yang critically surveyed the experimental information concerning this question and reached the conclusion that there is no existing evidence either to support or to refute parity conservation in weak interactions. They proposed a number of experiments on beta decays and hyperon and meson decays which would provide the necessary evidence for parity conservation or nonconservation. In beta decay, one could measure the angular distribution of the electrons coming from beta decays of polarized nuclei. If an asymmetry in the distribution between 8 and 180' —8 (where 8 is the angle between the orientation of the parent nuclei and the momentum of the electrons) is observed, it provides unequivocal proof that parity is not conserved in beta decay. This asymmetry effect has been observed in the case of oriented Co.' back

CERN Antimatter, CERN Antimatter, ' In 1928, British physicist Paul Dirac wrote down an equation that combined quantum theory and special relativity to describe the behaviour of an electron moving at a relativistic speed. The equation – which won Dirac the Nobel Prize in 1933 – posed a problem: just as the equation x2 = 4 can have two possible solutions (x = 2 or x = −2), so Dirac's equation could have two solutions, one for an electron with positive energy, and one for an electron with negative energy. But classical physics (and common sense) dictated that the energy of a particle must always be a positive number. back

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

Dirac delta function - Wikipedia, Dirac delta function - Wikipedia, the free encyclopedia, 'The Dirac delta or Dirac's delta is a mathematical construct introduced by theoretical physicist Paul Dirac. Informally, it is a function representing an infinitely sharp peak bounding unit area: a function f(x) that has the value zero everywhere except at x = 0 where its value is infinitely large in such a way that its total integral is 1. In the context of signal processing it is often referred to as the unit impulse function. Note that the Dirac delta is not strictly a function. While for many purposes it can be manipulated as such, formally it can be defined as a distribution that is also a measure.' back

Distribution (mathematics) - Wikipedia, Distribution (mathematics) - Wikipedia, the free encyclopedia, ' Distributions, also known as Schwartz distributions or generalized functions, are objects that generalize the classical notion of functions in mathematical analysis. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative. Distributions are widely used in the theory of partial differential equations, where it may be easier to establish the existence of distributional solutions than classical solutions, or where appropriate classical solutions may not exist. Distributions are also important in physics and engineering where many problems naturally lead to differential equations whose solutions or initial conditions are singular, such as the Dirac delta function.' back

Electroweak interaction - Wikipedia, Electroweak interaction - Wikipedia, the free encyclopedia, ' In particle physics, the electroweak interaction or electroweak force is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force. Above the unification energy, on the order of 246 GeV,[a] they would merge into a single force.' back

Garton Ash, Krastev & Leonard, United West, divided from the rest: Global public opinion one year into Russia’s war on Ukraine, ' Summary A new poll suggests that Russia’s war on Ukraine has consolidated ‘the West;’ European and American citizens hold many views in common about major global questions. Europeans and Americans agree they should help Ukraine to win, that Russia is their avowed adversary, and that the coming global order will most likely be defined by two blocs led respectively by the US and China. In contrast, citizens in China, India, and Turkiye prefer a quick end to the war even if Ukraine has to concede territory. People in these non-Western countries, and in Russia, also consider the emergence of a multipolar world order to be more probable than a bipolar arrangement. Western decision-makers should take into account that the consolidation of the West is taking place in an increasingly divided post-Western world; and that emerging powers such as India and Turkiye will act on their own terms and resist being caught in a battle between America and China.' back

Gur Megiddo & Omer Benjakob, The people who kill the truth, ' The investigative report being published here is the fruit of nine months of international cooperation, with dozens of journalists toiling to verify as much as possible the details that Jorge revealed in the series of recorded meetings. Journalists from The Guardian, Der Spiegel, Die Zeit, Le Monde, the international organization of investigative journalists OCCRP, Radio France, Haaretz, TheMarker and other media outlets worked in France, Kenya, Israel, the United States, Indonesia, Germany, Tanzania and Spain to examine the veracity of Jorge’s claims about his worldwide deeds. Shockingly, many of the allegations were corroborated. The proprietors of this toxic international chaos machine, as uncovered in the course of the investigation, are two Israeli brothers, Tal and Zohar Hanan, who live and work in the Israeli commuter city of Modi’in.' back

Jessica Pisano, Why Volodymyr Zelenskyy Is a More Complex Leader Than Most People Know , ' Some Ukrainians have wondered publicly about what will happen after victory, when a common enemy no longer galvanizes societal unity. Yet the vision of politics Zelenskyy promoted for decades from the stage is now present throughout Ukrainian society, and Ukrainians in the south and east of the country who once might have felt sympathy for Russia and have borne the brunt of its violence have now turned irrevocably toward Kyiv. Since Russia’s invasion one year ago, Ukrainians’ shared experience of war has forged a nation whose social fabric, woven of many different threads, has proven far more flexible and resilient, and more resistant to damage, than an undifferentiated weft.' back

Jo McGowan, When Literature Stood on Its Own: The Letters of John Steinbeck, ' His commitment to farmworkers in particular and to the poor in general is a theme running throughout his fiction and journalism. For him, it was a fundamental function of the artist: “I am a very dangerous revolutionary,” he said. “Herein is my revolt: I will fight for the right of the individual to function as an individual without pressure from any direction. I am unalterably opposed to any interference with the creative mind. It may be wrong, but out of it come the only rights we know. I place myself at the service of this revolutionary cause. The minds and spirits of men can and will be free".' back

John Palmer (Stanford Encyclopedia of Philosophy), Parmenides, ' Immediately after welcoming Parmenides to her abode, the goddess describes as follows the content of the revelation he is about to receive:
You must needs learn all things,/ both the unshaken heart of well-rounded reality/ and the notions of mortals, in which there is no genuine trustworthiness./ Nonetheless these things too will you learn, how what they resolved/ had actually to be, all through all pervading. (Fr. 1.28b-32) ' back

John von Neumann (2014), 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 back

Kate Pattison, The huge fandoms of stars like Harry Styles are underestimated – but these highly creative communities can teach young people useful skills, ' This week, Harry Styles finally kicked off the Australian leg of his much anticipated tour. Fans have been preparing for months, creating handmade outfits and learning the “boot scoot” – a dance associated on tour with Styles’ song Treat People With Kindness. As one of the world’s biggest pop stars, the ex-One Direction singer has amassed millions of fans, referred to as “Harries”. You’d be hard pressed to find an article about Styles that doesn’t mention his fans. They’ve sold out shows in minutes, taken over TikTok trends and camped outside venues. They’re also a highly creative bunch of young people, using their fandom to learn new skills that will carry them forward in many aspects of their lives.' back

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

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

Oksana Zabuzhko, The Problem With Russia Is Russia, ' With a sigh, I recall that’s how Chernobyl was discussed in 1986, as a nuclear catastrophe in Russia. Thanks, but no. Never again, please; the age of imperialism is over. If there could be any positive result found in the 12 months of this horrific war — in tens of thousands of people murdered, raped and mutilated, in millions of lives ruined, in the best black soil on earth littered with mines, in innumerable treasures of cultural heritage turned to debris — it would be that we Ukrainians have all together, in a united effort of resistance, proved that non-Russian lives matter. It is good news, for that was not the case before, certainly not in the past century. It gives all those who speak human, with no quotation marks, hope for the future. back

Particle Data Group. Lawrence Berkeley National Laboratory, The Particle Adventure, The Particle Data Group of Lawrence Berkeley National Laboratory presents an award winning interactive tour of quarks, neutrinos, antimatter, extra dimensions, dark matter, accelerators and particle detectors. back

Peter Beinart, You Can’t Save Democracy in a Jewish State, ' The principle that Mr. Netanyahu’s liberal Zionist critics say he threatens — a Jewish and democratic state — is in reality a contradiction. Democracy means government by the people. Jewish statehood means government by Jews. In a country where Jews comprise only half of the people between the Jordan River and the Mediterranean Sea, the second imperative devours the first.' back

Quantum state - Wikipedia, Quantum state - Wikipedia, the free encyclopedia, 'In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in time exhausts all that can be predicted about the system's behavior. A mixture of quantum states is again a quantum state. Quantum states that cannot be written as a mixture of other states are called pure quantum states, while all other states are called mixed quantum states. A pure quantum state can be represented by a ray in a Hilbert space over the complex numbers, while mixed states are represented by density matrices, which are positive semidefinite operators that act on Hilbert spaces.' back

Renormalization - Wikipedia, Renormalization - Wikipedia, the free encyclopedia, ' Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering values of quantities to compensate for effects of their self-interactions. But even if it were the case that no infinities arose in loop diagrams in quantum field theory, it could be shown that renormalization of mass and fields appearing in the original Lagrangian is necessary.' back

Robert Stansfield, Discovered in the deep: a ‘night-time migration’ of marine life – in pictures , ' Seascape: the state of our oceans: These images were taken by underwater photographer Robert Stansfield, from Southampton, UK, on a blackwater dive in the open ocean surround the island of Cozumel, Mexico. ‘The blackwater dives never fail to amaze me with the crazy alien-like life forms that drift past out in the open ocean, well away from a reef,’ says Robert. ‘The idea is to see the largest biomass migration on the planet. Every night a huge volume of life migrates up from the mesopelagic zone up to the epipelagic. This night-time migration gives us the opportunity to see life at the surface that normally lives well beyond recreational diving depths.’ back

Song - Wikipedia, Song - Wikipedia, he free encyclopedia, ' A song is a musical composition intended to be performed by the human voice. This is often done at distinct and fixed pitches (melodies) using patterns of sound and silence. Songs contain various forms, such as those including the repetition and variation of sections.' back

Tim Adams, Bernie Sanders: ‘Oligarchs run Russia. But guess what? They run the US as well’, ' For a generation of millennials raised on digital noise, Sanders became, in 2016, the political equivalent of a rare vinyl record: tangible, authentic, a reliable source of timeless indy riffs. For all but the most self-righteous of those fans – a strident few believed him a sellout for eventually endorsing the “centrist” Biden – he retains that appeal (strange to think that the progressive hero of the land-of-the-next-new-thing is an octogenarian – stranger that both of his most visible political rivals are, too). Sanders has written a new book partly aimed at that millennial generation – its Day-Glo title is It’s OK to Be Angry About Capitalism – reminding the young of their age-old rights and responsibilities. back

Tom Verde, Remapping Jerusalem, Review of Matthew Teller None Quarters of Jerusalem: ' If there is one disappointment in Teller’s otherwise entertaining and informative account, it is the book’s ambiguous title. How Teller arrived at nine quarters is never really explained, though perhaps it is hinted at. If there aren’t really four quarters in Jerusalem, there may as well be nine, or any other number for that matter. The answer is multilayered and complex. Jerusalem’s true quarters can’t be found on any map and remain elusive, until, like Teller, you seek them out and actually encounter the people who live there.' back

William J Broad, A Doodle Reveals da Vinci’s Early Deconstruction of Gravity, ' Now, scientists have discovered that Leonardo did detailed experiments that sought to illuminate the nature of gravity a century before Galileo and some two centuries ahead of Newton’s making its investigation an exact science. The scientists’ study of his gravitational ideas and experimentation was published earlier this month in the journal “Leonardo.” “Nothing could stop him,” Morteza Gharib, an author of the paper and a professor of aeronautics at California Institute of Technology, said in an interview. “He was far ahead in his thinking. It could not wait for the future".' back

Wu Experiment - Wikipedia, Wu Experiment - Wikipedia, the free encyclopedia, ' The experiment established that conservation of parity was violated (P-violation) by the weak interaction, providing a way to operationally define left and right without reference to the human body. This result was not expected by the physics community, which had previously regarded parity as a conserved quantity. . . . As stated by We et al: If an asymmetry in the distribution between θ and 180° − θ (where θ is the angle between the orientation of the parent nuclei and the momentum of the electrons) is observed, it provides unequivocal proof that parity is not conserved in beta decay.' back

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