Notes
Sunday 24 January 2021 - Saturday 30 January 2021
[Notebook: DB 86: Hilbert / Minkowski]
[page 36]
Sunday 24 January 2021
Time to 'rationalize' my portfolio of websites, making them into a mini-network centered on jeffreynicholls.net, the 'personal brand'.
Monday 25 January 2021
Plato the politician saw the world as a puppet of the heavens. Aristotle accepted that the world has a nature of its own, but was driven by the unmoved mover. Aquinas, true to his faith, put the unmoved mover outside the world, but made god also omnipresent so making god a local mover while maintaining an artificial distinction between god and the world. Copernicus simplified the system by putting the Sun at the centre which enabled Kepler to conceive and state his laws. Newton simplified this by boiling it down to three laws of motion and universal gravitation.
Lagrange and Hamilton brought Newton down to earth. Carnot
[page 37]
introduced entropy which Maxwell and Boltzmann showed how to compute with Newtonian dynamics. This laid the foundation for quantum mechanics. This with Einstein's invariance made Dirac's transformation theory possible. Von Neumann introduced a new spatial domain for the universe, Hilbert space, but the idea [remained] that Minkowski space is the domain of quantum field theory, leading to unnecessary complications by mapping Hilbert space onto Minkowski space. A way out of this problem may be to think in terms of quantum computation and communication, leading to cognitive cosmology as the current state of the art. The biggest step forward may have been Aquinas's decision to make the unmoved mover ubiquitous and prior to space-time. Can this be worked out and science overcome Plato's initial political decision to see the world as a puppet of a ruling divinity rather than an autonomous entity? The Churches, like Plato, think they own god and their ideas clearly take precedence over the autonomous reality. We might like to think that the era of power corrupting science will end when theology is liberated from politics in the post-trump era, at the cost of half a million American lives. Thomas Aquinas, Summa, I, 8, 1: Is God in all things?
Tuesday 26 January 2021
Wednesday 27 January 2021
Still dreaming of making Hilbert space the foundation of the universe and trying to make it the source of Minkowski space [which you would think would be pretty straightforward, given the analogy with Euclidean space]. A chalLenge for the last few months, but still to get a grip on it. Hoping to find a route through Nielsen and Chuang. Nielsen & Chuang: Quantum Computation and Quantum Information
I want a picture in my mind which matches the functioning of the world. We can pretty much rule quantum electrodynamics out on two points, the spurious infinities and the lack of representation of the
[page 38]
functioning structures [which seem to be Platonic abstract forms]. Everything seems to come down to mass and energy, that is frequency which is captured by Hilbert space which does not capture distance, so the infinities arising from zero distances must be spurious. So we think everything comes down to timing in the Hilbert world, and timing is maintained when space emerges because it takes time to travel through space and we can imagine that the velocity of light is determined by the need to neutralize space by null geodesics in order to keep the timing right. I harp on this, but if I keep tossing it round like a Rubik's cube it might come out [and then when I know the process I can repeat it at will]. Meinard Kuhlmann (Stanford Encyclopedia of Philosophy): Quantum Field Theory
Plato and Parmenides' idea that stillness is the foundation of truth is completely wrong. The system is inherently dynamic and the stillnesses we see are merely the fixed points in the dynamic mappings which are in some way representative of cosmic harmonies whose essence lies in phase [as suggested by gauge theories where the 'gauge' is phase measured by a complex exponential]. Stationary structures like space-time are manifestations of standing waves, an idea that goes back to Duke de Broglie. Louis de Broglie - Wikipedia
Dreaming of answers. The velocity of light is a fixed point. Space is not. So?
Only the Animals Peter Bradshaw: Only the Animals review - audacious web of love and strangeness
Kuhlman Stanford on QFT: It does not work because it is trying to mix oil and water, ie quantum theory and special relativity. The answer (I hope) is to synthesize space-time out of Hilbert space in order to get consistency. Just need
[page 39]
the magic word and for a long time now it has been fixed point theory. Just have to twist it into the right shape.
Sitting at the bus stop listening to the birds. Can heaven be any better than this? We are trained by the entertainment industry to always look for extreme experiences.
The notion [is] that the creation of space-time is related to the bifurcation of energy into energy and momentum. Pixellation carries through but the venue changes from time to space and the coupling seems to be through null geodesics. So these ideas have been with me for about three [to six] months [when I began trying to revise Scientific Theology chapter 6: Constructing a Divine World. Null geodesic is the point where space meets time, ie it is the home of Hilbert space.
So we might say the emergence of mass breaks the null geodesic into space and time.
Thursday 28 January 2021
Friday 29 January 2021
The structure and nature of the physical world imposes logic on how we must act to achieve our goals, like navigating the streets of a city or using a flux to help solder wet a metal. Flux (metallurgy) - Wikipedia
The notion that Hilbert space lies in the null geodesic has a reassuring ring to it and feels like a platform for further progress,
[page 40]
a symmetry to act as a building block for both quantum theory (time / energy) and relativity (space / momentum). Somewhat exciting but could be an ephemeral flash in the cranium.
A next step: how does the Lagrangian formulation of dynamics apply to Hilbert space per se ie without the presence of space and time. In essence the action is the time integral of something between two states represented by points in time and in the absence of space-time such an integral is simply an account of the discrete quanta of action needed to move from state a to state b, and the minimum count is 1, as opposed to zero, when nothing happens, a sample of eternity.
Kuhlmann: 'Quantum Field Theory (QFT) is the mathematical and conceptual framework for contemporary elementary particle physics.' Meinard Kuhlmann (Stanford Encyclopedia of Philosophy): Quantum Field Theory (link above)
'QFT taken seriously in its metaphysical implications seems to give a picture of the world which is at variance with the central classical conceptions of particles and fields and even with some features of quantum mechanics (QM).' As we might expect, since classical is history.
'1. What is QFT
' . . . there is no canonical definition of what QFT is. . . . the interpretation of QFT is particularly obscure . . . '
'Historically, QFT resulted from the successful reconciliation of QM and special relativity theory (SRT).'
[page 41]
'. . . ultimately the characterization of QFT on the one hand, as the quantum mechanical description of systems with an infinite number of degrees of freedom, and on the other hand as the only way to reconcile QM with SRT, are intimately connected with one another.' The infinite degrees of freedom seems to be the fundamental problem, and is an artefact of using Minkowski space (assumed to be continuous) as the mathematical domain for the theory. We correct this by making separable Hilbert space as primary.
Note that gauge invariance is a kind of symmetry that does not come about by space-time transformations [but by transformation of the vector potential (which is not observable)].
'In order to link thr notion of gauge invariance to the Lagrangian formulation of QFT one needs a more general form of gauge tranformatios which applies to the field operator φ which is supplied by φ → e-i Λφ, φ* → e-i Λφ* where Λ is an arbitrary real constant.'
'these global gauge transformations go to a (local) transformation e-iα(x)φ(x).'
'the analogy [is] to general relativity where (there is a local) gauge symmetry (general covariance).'
'2.4 Effective Field Theories (EFTs) and Renormalization.'
'EFTs are inherently approximative and change with the range of energy considered.'
The computer network model suggests that all that changes with energy scale is the rate at which processes occur. This does not appear to be true, since different phenomena appear at different enemies. Where
[page 42]
do we go from here? The notion that everything depends on timing may provide a route, since higher energy means higher frequency which may open the way to introducing more detailed and complex sub-processes that can fit in with slower processes at the lower energy end of the spectrum (so higher energy experiments may reveal these processes).
Kuhlmann: 'Influences from higher energy processes contribute to average values but they cannot be described in detail.' A further problem is that higher energy scales would appear to be relevant to simpler and more primitive processes emerging earlier in the life of the universe.
'The main idea of EFTs in particular the Lagrangians, depend on the energy of the phenomena which are analyzed.'
'3.1 Quantum Gravity'
'. . . gravitation is according to GRT (general relativity theory) not an interaction that takes place in space-time but gravitational forces are identified with the curvature of space-time itself.
[page 43]
Thus quantizing gravitation would amount to quantizing space-time, and it is not at all clear what this could mean. ' In other words, it is its own domain. Or better, Hilbert space is the domain of the universe, including gravitation. Space-time is already pixellated by Planck's constant through the uncertainty relations ΔE.Δt ≈ Δp.Δx ≈ ℏ.
The 'emergence of space-time (Kiefer 2007) Claus Kiefer: Quantum Gravity
Kuhlmann: 3.2 String Theory
'The pivotal consequence that strings interact at an extended distance and not at a point.' Which assumes that space-time and distance already exist. Not deep enough.
4. Axiomatic Reformulations
4.1: Operationalism (Measurability?)
'The mathematical aspect of the problem is that a field at a point φ(x) is not an operator on Hilbert space. The physical counterpart of the problem is that it would take an infinite amount of energy to measure a field at a point in space-time.' Still stuck on doing everything in Minkowski space-time using smeared 'test functions'. (Streater & Wightman) Streater & Wightman: PCT, Spin, Statistics and All That
Haag (1996) Rudolf Haag; Local Quantum Physics; Fields, Particles, Algebra
4.2 Mathematical Rigour
'. . . the quest toward a concise axiomatic formulation, instead of the grab
[page 44]
bag of conventional QFT, with its numerous mathematically dubious, even though successful, approximation techniques.
1. choice of entities to axiomatize - eg quantum of action p → ¬p
2. Choice of axioms
3. Proof that this works
' "To be turned away from the standard model by Algebraic QFT is sheer madness" 'David Wallace (2011): Taking Particle Physics Seriously: a Critique of the Algebraic Approach to Quantum Field Theory, page 21
Kuhlmann: ''The empirical success of renormalization in Conventional QFT (CQFT) leaves the physical reasons for this success in the dark, argues Fraser (2011) unlike in condensed matter physics where its success is due to the fact that matter is discrete at atomic length scales' But it is also discrete at the level of the quantum of action. Blinded by continuity for the nth time!!
. . .
4.3 Inequivalent Representations
'In quantum field theory, however, von Neumann’s uniqueness theorem loses its validity since here one is dealing with an infinite number of degrees of freedom. Now one is confronted with a multitude of unitarily inequivalent representations (UIRs) of the CCRs and it is not obvious what this means physically and how one should cope with it.'
So 'algebras of observables rather than the observables themselves in a particular representation should be taken as the basic entities in the mathematical description of QFT . . . '
4.4 Algebras, Inequivalent Representations and the Physical-Content Question
"Hilbert space conservatists” and “algebraic imperialists” (Arageorgis 1995 and Ruetsche 2002 coined these terms). To be ultimately conquered by the logical cosmologists!
'topology defines what is meant by the neighbourhood of an element'.
Theorem Fell 1960: J. M. G. Fell (1960): The Dual Spaces of C* Algebras
The existence of UIRs suggests that it has not yet sunk in that the universe is self consistent. Problem once again arises from infinity and continuity in Minkowsky space which is a furphy. The computational foundation of the universe is (as von Neumann will tell us) cardinal ℵ0, and all the higher infinities as develped by Cantor are digitized by their creation out of the natural numbers. Quantum computation and communication still looks the way to go.
4.5 Interpretative Impact of Accelerated Observers and Interacting Systems
'Unruh effect: as uniformly accelerated observer in a Minkowski vacuum should detect a thermal bath of particles' (Unruh 1976, Unruh & Wald, 1984). Unruh & Wald
[page 46]
Kuhlmann: 'It seems that the very existence of the basic entities of an ontology should not depend on the state of motion of the detectors.' Stupid in a dynamic universe: The Plato Parmenides error again [that truth is eternal].
5. Further Philosophical Issues
5.1 Candidate ontologies
'Ontology is concerned with the most general features, entities and structures of being.' ie god and the quantum of action.
What is a particle? what is a field? a quantum field?
5.1.1: Particle interpretation
Could it be more appropriate not to think of eg, particles, as the most fundamental entities at all, but rather of properties, processes or events [eg quantum of action]?
Silliness: 'The so called self-energy of a point particle [with a field?] is infinite.'
Pure particle ontology → action at a distance (?) collision?
Why QFT seems to be about particles:
1. Fourier analyze vector potential into a countable infinity of normal modes (induced by periodic boundary conditions [where do these come from]);
2. Each mode described independently as a harmonic oscillator.
5.1.2: Field interpretation
' Field (in [conventional] Minkowski space) has infinite degrees of freedom φ(x, t). Classical field specified by real numbers, quantum field by operators
[page 47]
attached to space-time points, φ( x, t) → φ̂ ( x, t) '
Teller, "quantum field" is "perverse reading" of the notion of field since no definite physical values whatsoever are assigned to space-time points.
(i) Teller definite values exist when state is determined
(ii) Vacuum expectation value
(iii) Wave functional interpretation
5.1.3 Ontic Structural Realism (OSR)
' . . . most fashionable ontological framework for modern physics.'
Invariants of structure: mass, spin, charge.
'A trope bundle is not individuated by spatio-temporal co-localization but because of the particularity of its constitutive tropes.'
[insert from page 49] We are wondering, in the light of the heuristic of simplicity, why the high energy structure revealed in baryons and mesons is so complex and the answer may be that whereas once space-time emerges identical particles can have separate identities by being separated in space-time whereas the initial proton may have come into existence before space-time so that the fundamental particles had to have complex personalities in order to differentiate themselves.
Kuhlmann: 5.2 Did Wigner Refine the Particle Concept?
'. . . the state space of an elementary system shall have no internal structure with respect to relativistic transformations.'
'The requirement that a state space has to be relativistically invariant means that starting from any of its states it must be possible to get to all the other states by superposition of these states which result from relativistic transformations of the state one started with.' But what if states are deeper than space-time, so relativity has no effect on them? (Kuhlman 2010 sec 8.1.2) Meinard Kuhlman: The Ultimate Constituents of the Material World: In Search of an Ontology for Fundamental Physics
[page 48]
Kuhlmann: 5.3 Non Localizability Theorems
5.4 The role of symmetries
Symmetries are entities that remain unchanged under some transformation, ie the meaning of a sentence is symmetric under accurate linguistic transformation
a) space-time transformations - Lorentz
b) internal transformation
eg 'the only Lorentz invariant and gauge invariant renormalizable Lagrangian for photons is precisely the original Dirac Lagrangian'.
5.5 Taking Stock
Particles??
Fields quantum states as such are not spatio-temporally defined.
'Ontic Structural Realism [OSR] takes the paramount significance of symmetry groups to indicate that symmetry structures as such have ontological primacy over objects. However, since most OSRists are decidedly against Platonism it is not altogether clear how symmetry structures could be ontologically prior to objects if they only exist in concrete realizations, namely in those objects that exhibit these symmetries.' Try network layering.
Dispositional Trope Ontology [DTO] Properties understood
[page 49]
as particulars called tropes.
'In conclusion one has to recall that one reason why the ontological interpretation of QFT is so difficult is the fact that it is exceptionally unclear which parts of the formalism should be taken to represent anything physical in the first place. And it looks as if that problem will persist for some time.
Saturday 30 January 2020
From the philosophical point of view recorded above, QFT is a mess. It is not even clear what it is. It was developed under pressure of war (since many believed that the Nazis were on the way to a nuclear weapon) and like most technological tasks the research budget was probably about 5% and the development by trial and error 95%. It is probable that military secrecy still hides a lot of workplace injuries caused by the error and the physics industry still seems to owe its huge budgets to its past successes in weapons and continued work in nuclear weapons, delivery systems and other high technology contributions to "defence". I feel that I have carte blanche to go my own way in quantum theology. One of the most surprising featured of physics now is that very little mention is made of the initial discovery of the quantum of action, which appears to me, following Aristotle and Aquinas, to be the fundamental divine symmetry on the world.
We are wondering, in the light of the heuristic of simplicity why the high energy structure revealed in baryons and mesons is so complex and the answer may be that whereas once space-time emerges identical particles can have separate identities by being separated in space-time whereas the initial proton may have come into existence before space-time so that the fundamental particles had to have complex personalities in order to differentiate themselves.
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Further readingBooks
Bateson, Gregory, and Mary Catherine Bateson, Steps to an Ecology of Mind: Collected Essays in Anthropology, Psychiatry, Evolution and Anthropology, University of Chicago Press 2000 Jacket: 'This collection amounts to a retrospective exhibition of a working life. ... Bateson has come to this position during a career that carried him not only into anthropology, for which he was first trained, but into psychiatry, genetics, and communication theory. He . . . examines the nature of the mind, seeing it not as a nebulous something, somehow lodged in the body of each man, but as a network of interactions relating the individual with his society and his species and with the universe at large.' D W Harding, New York Review of Books
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Chaitin, Gregory J, Algorithmic Information Theory, Cambridge UP 1987 Foreword: 'The crucial fact here is that there exist symbolic objects (i.e., texts) which are "algorithmically inexplicable", i.e., cannot be specified by any text shorter than themselves. Since texts of this sort have the properties associated with random sequences of classical probability theory, the theory of describability developed . . . in the present work yields a very interesting new view of the notion of randomness.' J T Schwartz
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Darwin, Charles, The Autobiography of Charles Darwin and Selected Letters, Dover 1958 back |
Davis, Martin, Computability and Unsolvability, Dover 1982 Preface: 'This book is an introduction to the theory of computability and non-computability ususally referred to as the theory of recursive functions. The subject is concerned with the existence of purely mechanical procedures for solving problems. . . . The existence of absolutely unsolvable problems and the Goedel incompleteness theorem are among the results in the theory of computability that have philosophical significance.'
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Feynman, Richard P, What do You Care What Other People Think: Further Adventures of a Curious Character, Unwin Hyman 1988 Jacket: 'Feynman died on 15 February 1988, after a long battle with cancer. During his final years he and his friend Ralph Leighton prepared this manuscript, his last literary legacy. It is at once wise and reminiscent, even serious in parts. Here is the story of how two people most influenced Feynman's early years - his father who taught him to think and his first wife Arlene who taught him to love even as she lay dying in Alberquerque hospital while Feynman worked nearby, on the atomic bomb in Los Alamos. . . . The second half of the book . . . is Feynman's behind the scenes account of the investigation that followed the space shuttle Challenger's explosion in January 1986. . . . We come to know in detail, through the eyes of a great scientist, the confusion and misjudgement that have plagued NAA in recent years.'
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Guareschi, Giovanni, and Una Vicenzo Troubridge (transpator), The Little World of Don Camillo, Image (Doubleday) 1986 Amazon Customer Reiew Humorous lessons in tolerance, October 7, 2000
By Guillermo Maynez
'I first read Don Camilo when I was 13. The thing that I have always liked the most about this book is its central lesson: it is possible to fight about ideologies, but when the community is in danger, we must forget the fight and help our neighbors. We'll continue the fuss later. Episode after episode, Don Camilo, the local priest, and Peppone, the communist mayor, confront each other, sometimes in a serious and violent way. But every time, both men negotiate their way out of trouble. That is a related lesson: public enemies / private friends. When you finish the book, indeed, you get a feeling that these two enemies and rivals have developed, over the years and innumerable shared experiences, a friendship that is deeper than most people's relationships. I like very much the parts when, in the midst of a crisis, Peppone and Don Camilo run secret negotiations in the middle of the night. But if you think this is a "rosy" book, full of childish situations, you are wrong. The problems that both characters have to solve are often deep and painful. This is the best kind of educational book, because it does not really have a "moral". The intelligent reader -and most children are- gets his own conclusions in a funny and humorous way. Those are the lessons likely to stay for life. A lovely book.'
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Haag, Rudolf , Local Quantum Physics; Fields, Particles, Algebra, Springer-Verlag 1996 'This textbook gives a comprehensive account of local quantum physics, understood as the synthesis of quantum theory with the principle of locality. Centered on the algebraic approach it describes the physical concepts, the mathematical structures, and their consequences. These include the emergence of the particle picture, general collision theory covering the cases of massless particles and infraparticles, and the analysis of possible charge structures and exchange symmetries, including braid group statistics.'
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Hawking, Steven W, and G F R Ellis, The Large Scale Structure of Space-Time, Cambridge UP 1975 Preface: Einstein's General Theory of Relativity . . . leads to two remarkable predictions about the universe: first that the final fate of massive stars is to collapse behind an event horizon to form a 'black hole' which will contain a singularity; and secondly that there is a singularity in our past which constitutes, in some sense, a beginning to our universe. Our discussion is principally aimed at developing these two results.'
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Hofstadter, Douglas R, and Daniel C Dennett, The Mind's I: Fantasies and Reflections on Self & Soul, Bantam 1985 Jacket: 'In this unique, mind-jolting book, DH, the author of G¨del, Escher, Bach, the intellectual best seller that won the 1980 Pulitzer Prize, and Philosopher Daniel Dennett, author of the widely acclaimed Brainstorms, explore the meaning of self and consciousness through the perspectives of literature, artificial intelligence, psychology and much more. . . . '
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Kiefer, Claus, Quantum Gravity, Oxford University Press 2012 ' The search for a quantum theory of the gravitational field is one of the great open problems in theoretical physics. This book presents a self-contained discussion of the concepts, methods and applications that can be expected in such a theory. The two main approaches to its construction — the direct quantisation of Einstein's general theory of relativity and string theory — are covered. New to this Edition:
. . . new chapters or sections on quantum gravity phenomenology, Horava-Lifshitz quantum gravity, analogue gravity, the holographic principle, affine quantum gravity, and other topics.
Presents updates on loop quantum cosmology, the LTB model, asymptotic safety, various discrete approaches, and other topics.
contains pedagogical extensions throughout the text.'
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Kuhlman, Meinard , The Ultimate Constituents of the Material World: In Search of an Ontology for Fundamental Physics , Ontos Verlag 2010 ' Today, quantum field theory (QFT) is the best starting point for analyzing the fundamental building blocks of the material world. QFT yields a picture of the world that is at variance with central classical conceptions. The core of Kuhlmann’s investigation consists in the analysis of various ontological interpretations of QFT. Eventually, Kuhlmann proposes a dispositional trope ontology, according to which particularized properties and not things are the most basic entities.
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Marks, John , The Search for the 'Manchurian Candidate': The CIA and mind control, W W Norton & Co 1991 Amazon: 'This book is probably the most quoted book I've seen on the topic of government experimentation on mind control. However, John Marks only follows the trail of the CIA. Many other branches/units of the government and military were involved in MK-Ultra. The Army, Navy, Air Force, NSA, DOD, DOE. Would be nice to see all resources pooled together to have one complete story of these experiments instead of just one small segment of it. In spite of the single focus, it is the best information out there for documentation...especially since many of the other agencies involved destroyed all or most of their MK-Ultra documents (which is another conspiracy in itself). Thank heavens for the persistence of John Marks to find these documents! ' A reader from Pennsylvania.
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Nielsen, Michael A, and Isaac L Chuang, Quantum Computation and Quantum Information, Cambridge University Press 2000 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, 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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Von Goethe, Johann Wolfgang, Conversations of Goethe with Johann Eckermann, Da Capo Press 1988 'German poet, dramatist, novelist, translator, scientist, and musician, Johann Wolfgang von Goethe (1749–1832) was the last universal genius of the West and a master of world literature, the author of The Sorrows of Young Werther, Wilhelm Meister, and Faust. Nowhere else can one encounter a more penetrating, many-sided, and personal Goethe than in the extraordinary Conversations (1836) by Johann Peter Eckermann (1792–1854), a German author and scholar as well as Goethe's friend, archivist, and editor. . . . '
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West, Morris, The Ambassador, New English Library 1970 Jacket: 'Out of every international crisis comes at least one great book. From the explosive, bitter and savage battlefront of Vietnam comes THE AMBASSADOR. . . . "
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Links
Adrian G. Dyer et al, Fragmentary Blue: Resolving the Rarity Paradox in Flower Colours, ' Flowers did not evolve under the pressure of human color vision, so modeling pollinator vision with established techniques may provide a less biased insight into color mediated interaction between animal observers and plants that enable biotic pollination. Indeed, when considering harsh environments like high altitude in the Himalayan mountains, we observe that short wavelength blue flowers do indeed become more frequent (Figure 9), suggesting that biotic pollination is a key factor that must always be considered in mapping flower biodiversity. Thus, whenever considering biological factors influencing flowers color signaling, or including abiotic factors reported on by researchers, care must be taken as to what observer is most relevant to a particular question, and how different observers may need to be considered to understand how and why blue flower colors exist in complex natural environments. back |
Al Jazeera & Agencies, Russia arrests thousands amid unprecedented pro=Navalny protests, ' Security forces detained more than 3,000 people and violently broke up rallies across Russia as tens of thousands of protesters ignored extreme cold and police warnings to demand the release of Kremlin critic Alexei Navalny.
Prosecutors in St Petersburg said in a statement late Saturday they were probing violations including “on the part of law enforcement” and the use of force against an unidentified woman.' back |
Australia Day - Wikipedia, Australia Day - Wikipedia, the free encyclopedia, 'Australia Day is the official National Day of Australia. Celebrated annually on 26 January, it marks the anniversary of the 1788 arrival of the First Fleet of British Ships at Port Jackson, New South Wales, and the raising of the Flag of Great Britain at Sydney Cove by Governor Arthur Phillip.' back |
Australian Government Office of the Chief Scientist, The Importance of Advanced Physical and Mathematical Sciences to the Australian Economy, 'The report estimates that the direct contribution of
the advanced physical and mathematical sciences is
equal to 11% of the Australian economy (that is, about
$145 billion per year). Along with the direct contribution,
the report estimates additional and flow-on benefits of
another 11%, bringing total benefits to just over 22%
(around $292 billion per year). Importantly, the report
points out that this estimate of the contribution of
advanced physical and mathematical sciences is likely to be
conservative, and sets out several other areas of benefit that
are harder to measure.' back |
Australian Office of the Chief Scientist, Media Relase: Science — A Major Contributor to the Economy, 'Professor Chubb has issued a joint media release with the Australian Academy of Science on a report showing the value of advanced physical and mathematical sciences to the Australian economy.' back |
Born rule - Wikipedia, Born rule - Wikipedia, the free encyclopedia, 'The Born rule (also called the Born law, Born's rule, or Born's law) is a law of quantum mechanics which gives the probability that a measurement on a quantum system will yield a given result. It is named after its originator, the physicist Max Born. The Born rule is one of the key principles of the Copenhagen interpretation of quantum mechanics. There have been many attempts to derive the Born rule from the other assumptions of quantum mechanics, with inconclusive results. . . . The Born rule states that if an observable corresponding to a Hermitian operator A with discrete spectrum is measured in a system with normalized wave function (see bra-ket notation), then
the measured result will be one of the eigenvalues λ of A, and
the probability of measuring a given eigenvalue λi will equal <ψ|Pi|ψ> where Pi is the projection onto the eigenspace of A corresponding to λi'. back |
Cantor's theorem - Wikipedia, Cantor's theorem - Wikipedia, the free encyclopedia, ' In elementary set theory, Cantor's theorem is a fundamental result which states that, for any set A, the set of all subsets of A (the power set of A, denoted by P(A) ) has a strictly greater cardinality than A itself. For finite sets, Cantor's theorem can be seen to be true by simple enumeration of the number of subsets. Counting the empty set as a subset, a set with n members has a total of 2n subsets, so that if card (A) = n, then card (P(A)) = 2 n , and the theorem holds because 2n > n for all non-negative integers. ' back |
Claude E Shannon, A Mathematical Theory of Communication, 'The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point. Frequently the messages have meaning; that is they refer to or are correlated according to some system with certain physical or conceptual entities. These semantic aspects of communication are irrelevant to the engineering problem. The significant aspect is that the actual message is one selected from a set of possible messages.' back |
Code of Canon Law 333, The Roman Pontiff, ' Can. 333 §1. By virtue of his office, the Roman Pontiff not only possesses power over the universal Church but also obtains the primacy of ordinary power over all particular churches and groups of them. Moreover, this primacy strengthens and protects the proper, ordinary, and immediate power which bishops possess in the particular churches entrusted to their care.
§2. In fulfilling the office of supreme pastor of the Church, the Roman Pontiff is always joined in communion with the other bishops and with the universal Church. He nevertheless has the right, according to the needs of the Church, to determine the manner, whether personal or collegial, of exercising this office.
§3. No appeal or recourse is permitted against a sentence or decree of the Roman Pontiff.' back |
Computable function - Wikipedia, Computable function - Wikipedia, the free encyclopedia, 'Computable functions (or Turing-computable functions) are the basic objects of study in computability theory. They make precise the intuitive notion of algorithm. Computable functions can be used to discuss computability without referring to any concrete model of computation such as Turing machines or register machines. Their definition, however, must make reference to some specific model of computation.' back |
David Wallace, In Defence of Naiveté: The Conceptual Status of Lagrangian Quantum Field Theory, ' ABSTRACT. I analyse the conceptual and mathematical foundations of Lagrangian quantum field theory (QFT) (that is, the 'naive' (QFT) used in mainstream physics, as opposed to algebraic quantum field theory). The objective is to see whether Lagrangian (QFT) has a sufficiently firm conceptual and mathematical basis to be a legitimate object of foundational study, or whether it is too ill-defined. The analysis covers renormalisation and infinities, inequivalent representations, and the concept of localised states; the conclusion is that Lagrangian QFT (at least as described here) is a perfectly respectable physical theory, albeit somewhat different in certain respects from most of those studied in foundational back |
David Wallace (2011), Taking Particle Physics Seriously: a Critique of the Algebraic Approach to Quantum Field Theory , ' I argue against the currently-prevalent view in philosophy of physics that algebraic quantum field theory (AQFT) is the correct framework for philosophy of quantum field theory and that "conventional" quantum field theory (CQFT), of the
sort used in mainstream particle physics, is not suitable for foundational study. In doing so, I defend the position that AQFT and CQFT, understood in an appropriate sense, ought to be understood as rival programs to resolve the mathematical and physical pathologies of renormalization theory, and that CQFT has succeeded in this task and AQFT has failed. I also defend CQFT from recent criticisms
made by Doreen Fraser.' back |
DOBBY, I Can't Breather (feat BARKAA), ' "I Can't Breathe" were the last words of both George Floyd in Minneapolis, and Dunghutti man David Dungay Jr in Long Bay Prison (Sydney, Australia) right before they were murdered at the hands of police. Five years since his (filmed) murder, not one officer in the footage of David Dungay's murder has been convicted. In this song DOBBY and BARKAA call for immediate action to bring justice to the families of the 438 Indigenous people who died in police custody since the 1991 Royal Commission into Indigenous Deaths In Custody.
"I’m so grateful to have created this track with sister BARKAA. Our I Can't Breathe video really captures that frustration of ignorance felt constantly in our community. There are staunch appearances by some very talented mob, and I’m so thankful to have them all a part of this. The direction and creative vision of Luke Currie-Richardson and Benjamin Ling resulted in a powerful, vibrant music video that screams of urgency". - DOBBY' back |
Flux (metallurgy) - Wikipedia, Flux (metallurgy) - Wikipedia, the free encyclopedia, ' In metallurgy, a flux (derived from Latin fluxus meaning "flow") is a chemical cleaning agent, flowing agent, or purifying agent. Fluxes may have more than one function at a time. They are used in both extractive metallurgy and metal joining. . . . In high-temperature metal joining processes (welding, brazing and soldering), flux is a substance which is nearly inert at room temperature, but which becomes strongly reducing at elevated temperatures, preventing oxidation of the base and filler materials. The role of a flux is typically dual: dissolving the oxides already present on the metal surface, which facilitates wetting by molten metal, and acting as an oxygen barrier by coating the hot surface, preventing its oxidation.' back |
Galileo affair - Wikipedia, Galileo affair - Wikipedia, the free encyclopedia, 'The Galileo affair was a sequence of events, beginning around 1610, during which Galileo Galilei came into conflict with both the Catholic Church, for his support of Copernican astronomy, and secular philosophers, for his criticism of Aristotelianism.' back |
Hausdorff space - Wikipedia, Hausdorff space - Wikipedia, the free encyclopedia, ' In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space where for any two distinct points there exist neighbourhoods of each which are disjoint from each other. Of the many separation axioms that can be imposed on a topological space, the "Hausdorff condition" (T2) is the most frequently used and discussed. It implies the uniqueness of limits of sequences, nets, and filters.
Hausdorff spaces are named after Felix Hausdorff, one of the founders of topology. Hausdorff's original definition of a topological space (in 1914) included the Hausdorff condition as an axiom. .' back |
Information theory - Wikipedia, Information theory - Wikipedia, the free encyclopedia, 'Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Historically, information theory was developed by Claude E. Shannon to find fundamental limits on compressing and reliably storing and communicating data. Since its inception it has broadened to find applications in many other areas, including statistical inference, natural language processing, cryptography generally, networks other than communication networks — as in neurobiology, the evolution and function of molecular codes, model selection in ecology, thermal physics, quantum computing, plagiarism detection and other forms of data analysis.' back |
J .P. Jones and Y. V. Matijasevic, Register Machine Proof of the Theorem on Exponential Diophantine Representations of Enumerable Sets, 'Introduction. The purpose of this paper is to give a new, simple proof of the theorem of M. Davis, H .Putnam and J .Robinson, which states that every recursively enumarable relation A(a1, . . . , An is exponential diophantine . . . ' back |
J M G Fell, The Structure of Algebras of Operator Fields, ' At the present time a great deal is known about the general theory of C*-algebras. However, little has been done to clarify the precise structure of specific non-commutative C*-algebras, for example, the group C*-algebras of particular non-commutative non- compact groups. In this paper we present a number of results which together constitute program for determining the structure of many specific C*-algebras; and apply them to describe completely the group C*-algebra of SL(2, C).' back |
J. M. G. Fell (1960), The Dual Spaces of C* Algebras, ' Introduction. The idea of the structure space (or dual space) A of an associative algebra A was introduced by Jacobson in [8]. The space A con- sists of all kernels of irreducible representations of A, with the hull-kernel topology: An ideal I in A is in the closure of a subset B of A if I contains the intersection of the ideals in B. For unrestricted infinite-dimensional A, the dual space need not be Hausdorff or even T1; and in many situations it is not very useful. However, Gelfand and others have shown that for commutative Banach algebras the dual space is a powerful tool. back |
James Mitchell Crow, The Bird Librarian, ' On the table in this photograph are the remains of more than 130 wedge-tailed eagles (Aquila audax) — Australia’s largest bird of prey. The birds had been poisoned, and I needed to confirm the species for a criminal case.
As collection manager of ornithology at the Australian Museum in Sydney, I not only identify birds, but also give input on exhibits and educational programmes and provide other scientific services. The museum’s bird collection is the oldest and largest in Australia, containing about 100,000 specimens of species from all over both the country and the world. The oldest registered specimen is a northern pintail duck (Anas acuta), collected in 1828.' back |
John Horton Conway - Wikipedia, John Horton Conway - Wikipedia, the free encyclopedia, 'John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He has also contributed to many branches of recreational mathematics, notably the invention of the cellular automaton called the Game of Life. Conway is currently Professor Emeritus of Mathematics at Princeton University in New Jersey.' back |
Lia Harris, Parents and carers who emotionally abuse children face jail under new laws, 'NSW Child Abuse Squad acting superintendent Andrew Waterman said his detectives and other officers were often powerless to charge parents and carers who neglect their children’s emotional and developmental needs under existing laws
He said new laws would acknowledge that children needed more than just basic food and water to become functioning adults.' back |
Louis de Broglie - Wikipedia, Louis de Broglie - Wikipedia, the free encyclopedia, 'Louis-Victor-Pierre-Raymond, 7th duc de Broglie . . . 15 August 1892 – 19 March 1987) was a French physicist who made groundbreaking contributions to quantum theory. In his 1924 PhD thesis he postulated the wave nature of electrons and suggested that all matter has wave properties. This concept is known as the de Broglie hypothesis, an example of wave-particle duality, and forms a central part of the theory of quantum mechanics.' back |
Mark Mazetti and Mat Apuzzo, U.S. Relies Heavily n Saudi Money to Support Syrian Rebels, 'WASHINGTON — When President Obama secretly authorized the Central Intelligence Agency to begin arming Syria’s embattled rebels in 2013, the spy agency knew it would have a willing partner to help pay for the covert operation. It was the same partner the C.I.A. has relied on for decades for money and discretion in far-off conflicts: the Kingdom of Saudi Arabia.' back |
Massimo Faggioli, Lots of Politics, Little Vision, ' Right now, the USCCB is pretty much the opposite of synodality and collegiality between brother bishops, and between the bishops and the pope. Instead of behaving ecclesially, it has been behaving politically, and now it will be judged politically because it has lost the right to be judged ecclesially. On those terms, many Catholics (and non-Catholics) in the United States automatically dismiss whatever the bishops now say.' back |
Meinard Kuhlmann (Stanford Encyclopedia of Philosophy), Quantum Field Theory, ' Quantum Field Theory (QFT) is the mathematical and conceptual framework for contemporary elementary particle physics. In a rather informal sense QFT is the extension of quantum mechanics (QM), dealing with particles, over to fields, i.e. systems with an infinite number of degrees of freedom. (See the entry on quantum mechanics.) In the last few years QFT has become a more widely discussed topic in philosophy of science, with questions ranging from methodology and semantics to ontology. QFT taken seriously in its metaphysical implications seems to give a picture of the world which is at variance with central classical conceptions of particles and fields, and even with some features of QM.' back |
Peter Bradshaw, Only the Animals review - audacious web of love and strangeness, ' But now Moll has given us this audacious, witty and absorbing mystery thriller, a tale of adultery and amour fou with a gamey touch of the macabre – adapted by Moll and his longtime collaborator Gilles Marchand from the novel Seules Les Bêtes by Colin Niel. It is about five people and their relationship with a sixth person who is to meet a terrifying, arbitrary fate. The movie introduces us in turn to these six overlapping lives, with ingenious point-of-view shifts that will explain an apparent oddity or anomaly in the previous scene and set us up for a rug-pull in the next, letting us in on a secret, then coolly pushing us away.' back |
Peter Burnett, A major report excoriated Australia's environment laws. Sussan Ley's response s ocnfused and risky, 'It’s official: Australia’s natural environment and iconic places are in deep trouble. They can’t withstand current and future threats, including climate change. And the national laws protecting them are flawed and badly outdated.
You could hardly imagine a worse report on the state of Australia’s environment, and the law’s capacity to protect it, than that released yesterday. The review of the Environmental Protection and Biodiversity (EPBC) Act, by former competition watchdog chair Professor Graeme Samuel, did not mince words. Without urgent changes, most of Australia’s threatened plants, animals and ecosystems will become extinct.' back |
Peter Hannam, Australia sinks on 'most credible' environmental index in the world, 'Australia's global ranking has dived on an international survey that Environment Minister Greg Hunt had described as "the most credible, scientifically based" analysis in the world.
The 2016 Environmental Performance Index, released every two years by Yale University in the US, has dropped Australia's ranking by 10 places to 13th out of 180 nations in its latest update.' back |
Peter Seibel, Practical Common Lisp, 'This page, and the pages it links to, contain text of the Common Lisp book Practical Common Lisp published by Apress These pages now contain the final text as it appears in the book. If you find errors in these pages, please send email to book@gigamonkeys.com. These pages will remain online in perpetuity—I hope they will serve as a useful introduction to Common Lisp for folks who are curious about Lisp but maybe not yet curious enough to shell out big bucks for a dead-tree book and a good Common Lisp tutorial for folks who want to get down to real coding right away.' back |
Rand Richards Cooper, The Mourning After, ' During the Bush administration, Karl Rove infamously derided a journalist for being part of what Rove called “the reality-based community.” . . . Well, Rove said, you can forget about that! Here were his contemptuous words to the journalist: “We’re an empire now, and when we act, we create our own reality. And while you’re studying that reality—judiciously, as you will—we’ll act again, creating other new realities, which you can study too, and that’s how things will sort out.” ' back |
Satori - Wikipedia, Satori - Wikipedia, the free encyclopedia, 'Satori is a Japanese Buddhist term for "enlightenment." The word literally means "understanding." "Satori" translates as a flash of sudden awareness, or individual enlightenment, and while satori is from the Zen Buddhist tradition, enlightenment can be simultaneously considered "the first step" or embarkation toward nirvana.
Satori is typically juxtaposed with a related term known as kensho, which translates as "seeing one's nature." Kensho experiences tend to be briefer glimpses, while satori is considered to be a deeper spiritual experience. Satori is as well an intuitive experience and has been described as being similar to awakening one day with an additional pair of arms, and only later learning how to use them.' back |
Sir Robert Owen, The Litvinenko Inquiry: Report into the death of Alexander Litvinenko, '2.6 It has always been my view that the question of possible Russian State responsibility
for Mr Litvinenko’s death is one of the most important issues arising from his death. It
was an issue that I had intended to investigate at the inquest, but it did not seem right
to me to investigate this issue in the knowledge that government material that was
of great relevance had been excluded – albeit that it had been excluded for a good
reason.
2.7
I therefore asked the Home Secretary to establish a Public Inquiry to replace the
inquest. The advantage of a Public Inquiry over the inquest was that the rules governing
an inquiry allow for sensitive evidence to be heard in closed session.' back |
Smiriti Mallapaty, Are COVID vaccination programmes working? Scientists seek first clues, ' As countries worldwide roll out COVID-19 vaccines, researchers are eagerly watching for early signs that they are having an impact on the pandemic. Last week, researchers in Israel reported preliminary figures suggesting that people vaccinated there were about one-third less likely to test positive for SARS-CoV-2 than people who had not received a shot. But scientists say that population-wide effects of immunization will take time to become clear.' back |
Sorting algorithm - Wikipedia, Sorting algorithm - Wikipedia, the free encyclopedia, 'A sorting algorithm is an algorithm that puts elements of a list in a certain order. The most-used orders are numerical order and lexicographical order. Efficient sorting is important for optimizing the use of other algorithms (such as search and merge algorithms) which require input data to be in sorted lists; it is also often useful for canonicalizing data and for producing human-readable output. More formally, the output must satisfy two conditions:
The output is in nondecreasing order (each element is no smaller than the previous element according to the desired total order);
The output is a permutation (reordering) of the input.' back |
Stefan R Underhill, Did I Sentence a Murderer or a Cooperative Witness, 'The tragedy of mass incarceration has recently focused much attention on the need to reform three-strikes laws, mandatory minimums and the federal-sentencing guidelines, which often direct judges to impose excessive sentences. We also need a mechanism for judges to re-evaluate the sentences they’ve imposed.' back |
Thanu Padmanabhan, Thermodynamical Aspects of gravity: New Insights, '(Submitted on 26 Nov 2009 (v1), last revised 19 Jan 2010 (this version, v2))
The fact that one can associate thermodynamic properties with horizons brings together principles of quantum theory, gravitation and thermodynamics and possibly offers a window to the nature of quantum geometry. This review discusses certain aspects of this topic concentrating on new insights gained from some recent work. After a brief introduction of the overall perspective, Sections 2 and 3 provide the pedagogical background on the geometrical features of bifurcation horizons, path integral derivation of horizon temperature, black hole evaporation, structure of Lanczos-Lovelock models, the concept of Noether charge and its relation to horizon entropy. Section 4 discusses several conceptual issues introduced by the existence of temperature and entropy of the horizons. In Section 5 we take up the connection between horizon thermodynamics and gravitational dynamics and describe several peculiar features which have no simple interpretation in the conventional approach. The next two sections describe the recent progress achieved in an alternative perspective of gravity. In Section 6 we provide a thermodynamic interpretation of the field equations of gravity in any diffeomorphism invariant theory and in Section 7 we obtain the field equations of gravity from an entropy maximization principle. The last section provides a summary.' back |
Thomas Aquinas, Summa, I, 8, 1, Is God in all things?, ' I answer that, God is in all things; not, indeed, as part of their essence, nor as an accident, but as an agent is present to that upon which it works. For an agent must be joined to that wherein it acts immediately and touch it by its power; hence it is proved in Phys. vii that the thing moved and the mover must be joined together. Now since God is very being by His own essence, created being must be His proper effect; as to ignite is the proper effect of fire. back |
Tony Abbott MHR, Federal Member for Warringah - Tony Abbott MHR, 'Tony Abbott was elected Member for Warringah at a by-election in March 1994. Prior to entering Parliament he was Executive Director of Australians for Constitutional Monarchy from 1993-94. From 1990-93 he was press secretary and political advisor to the Leader of the Opposition, Dr John Hewson. His previous career was in journalism, where he wrote as a feature writer for 'The Bulletin' and 'The Australian'.' back |
Trinity - Wikipedia, Trinity - Wikipedia, the free encyclopedia, 'The Christian doctrine of the Trinity (from Latin trinitas "triad", from trinus "threefold") defines God as three consubstantial persons, expressions, or hypostases: the Father, the Son (Jesus Christ), and the Holy Spirit; "one God in three persons". The three persons are distinct, yet are one "substance, essence or nature" homoousios). In this context, a "nature" is what one is, while a "person" is who one is.' back |
Unruh & Wald, What happens when an accelerating observer detects a Rindler particle, ' Abstract: (APS)
The nature of the interaction between a quantum field and an accelerating particle detector is analyzed from the point of view of an inertial observer. It is shown in detail for the simple case of a two-level detector how absorption of a Rindler particle corresponds to emission of a Minkowski particle. Several apparently paradoxical aspects of this process related to causality and energy conservation are discussed and resolved. back |
Voltaire, If God did not exist it would be necessary to invent him @ Everything2.com, 'A famous quote by Voltaire.' back |
Wiles' proof of Fermat's Last Theorem - Wikipedia, Wiles' proof of Fermat's Last Theorem - Wikipedia, the free encyclopedia, 'Andrew Wiles' proof of Fermat's Last Theorem is a proof of the modularity theorem for semistable elliptic curves released by Andrew Wiles, which, together with Ribet's theorem, provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the Modularity Theorem were almost universally considered inaccessible to proof by contemporaneous mathematicians, seen as virtually impossible to prove using current knowledge.' back |
William. G. Unruh, Notes on black-hole evaporation, ' This paper examines various aspects of black-hole evaporation. A two-dimensional model is investigated where it is shown that using fermion-boson cancellation on the stress-energy tensor reduces the energy outflow to zero, while other noncovariant techniques give the Hawking result. A technique for replacing the collapse by boundary conditions on the past horizon is developed which retains the essential features of the collapse while eliminating some of the difficulties. This set of boundary conditions is also suggested as the most natural set for a preexistent black hole. The behavior of particle detectors under acceleration is investigated where it is shown that an accelerated detector even in flat spacetime will detect particles in the vacuum. The similarity of this case with the behavior of a detector near the black hole is brought out, and it is shown that a geodesic detector near the horizon will not see the Hawking flux of particles. Finally, the work of Berger, Chitre, Nutku, and Moncrief on scalar geons is corrected, and the spherically symmetric coupled scalar-gravitation Hamiltonian is presented in the hope that someone can apply it to the problem of black-hole evaporation.' back |
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