Notes
Sunday 5 July 2020 - Saturday 11 July 2020
[Notebook: DB 85 Science]
Sunday 5 July 2020
[page 21]
Monday 6 July 2020
Here comes a radical ansatz. The conventional approach to quantum mechanics assumes that Minkowski space is the domain of Hilbert space so that when we set out to devise the relativistic version of quantum theory we have to perform Lorentz transformations on the Hilbert space. Here we take the opposite view, that Minkowski space is the consequence of applying
[page 22]
the mathematical theory of communication to Hilbert space which has the effect of "building in" the Minkowski space into inertial space. The route to this solution is that both Hilbert space and communication spaces are function spaces one complex and the other real. How we pull this off I do not yet know, but this is the ghost of a very productive plan which will come clearer when I read Veltman for the nth time since this idea has been cooking in my head since I got Veltman in 2000. Martinus Veltman: Diagrammatica: The Path to the Feynman Rules
Thinking about implementing evolution in function space, complex [numbers] as used by von Neumann, real as used by Shannon. Each of these little ideas feel as though they getting a bit closer to getting somewhere. Claude Shannon: Communication in the Presence of Noise
On the bus. Why do people do things? Same reason as atoms do things and right back down to the very beginning due to the principle of requisite variety: mostly the past cannot control the future because it is more complex; random = uncontrolled, the source of quantum randomness is the combination of eigenvalues and lack of control.
In function space each point (vector) represents a function. In Hilbert space each vector represents a circle group (φ = eiθ)φ)which if digitized may represent the alphabet of a source cycling through its eigenfunctions.
Stability requires closure as we see in the de Broglie explanation of the stationary states in the Bohr atom.
[page 23]
The universe can be modelled by a point on the surface of an infinite dimensional sphere radius 1, the point moving around as events in the universe change. This is analogous to the mapping of qubits onto the Bloch sphere. The point is the superposition of all the [basis] vectors in the universal Hilbert space. The constraint is that the sum of all the probabilities of the available possibilities, that is only one thing (involving quantum of action) happens at a time, the source of normalization. This may be true if the quantum universe antedates space-time but in the real world many things happen at once so it is not normalized [or, given that the foundation of the universe is a one dimensional Hilbert space corresponding to the initial singularity which serves as the ultimate hardware layer, all universal process must pass through this channel, leading to global normalization]. Is the wave-function of the universe (Everett III) normalized? Is its evolution unitary? Insofar as the universe is increasing its entropy by observing itself it cannot be unitary, and insofar as it is increasing its entropy, it is creating space, given our irresistable assumption that the simultaneous existence of p andnot-p (entropy count 2) is the defining property of space. The argument for the creation of space seems foolproof and gorgeous and shows how the reality of representation causes quantum theory to create inertial space (I think [stay tuned]). Keep cooking, its looking good. Bloch sphere - Wikipedia, Hugh Everett III: The Many Worlds Interpretation of Quantum Mechanics
Tuesday 7 July 2020
One of the major clues for this quixotic effort to revise physics is the analogy between the formation of a black hole and the birth of the universe from the initial singularity. A black hole, according to the theory, is a gravitational potential well so deep that light cannot escape from it, so forcing the null geodesics of the contained photons to coalesce so destrroying the photons and
[page 24]
and the space-time in which they exist. The inverse process would be the creation of photons and space-time and we can imagine that right near the beginning (or end) the only structures in existence would be energy, quantum mechanics, quanta of action and photons, which argues for the close coupling between quantum mechanics and the origin of photons and spacetime. This line of argument, which ignores detail but proceeds on more general "principles" creates a framework which provides general clues about how they work. Here we find the general theory of relativity constraining the behaviour of quantum theory in a way that could turn out to help us firm a clearer picture of the initial stages in the emergence of the universe which serves here as a story about the complexification of the divinity. Whatever we have to say needs to fit into the general framework established by our observational experience of gravitation, particularly the interface between the universality of gravitation and the universality if quantum mechanics.
Haacaaluu Hundeessaa: The fundamental methodology of oppression is to kill the outstanding figures who oppose it: Inquisitions take note: the effect of their actions is to bring themselves down. Awol K Allo: Haacaaluu Hundeessaa: A towering musician and an Oromo icon, Hachalu Hundessa: Maalan Jira!
From a PR point of view the most powerful thing I could do would be to rebuild physics in the image of god, coupling theology to reality, but although I may never achieve this I can keep working toward it, registering my tiny steps here.
The role of science is to explain facts, ie observed events
[page 25]
in the world like things do not fall off our spherical earth. The role of quantum mechanics is to explain behaviour at the scale where the quantum of action is relevant. This is primarily microscopic, but there are macroscopic manifestations often associated with the behaviour of bosons, like laser light, superconductivity and Bose-Einstein condensation in general. From this point of view we might think that bosons appear prior to space and count the quantum of action as a boson [spin 1] so that my own actions, and all actions at whatever scale have a bosonic quality through which they are mapped onto the fermionic world of the exclusion principle, in space p excludes not-p while both nevertheless exist. Bose-Einstein condensate - Wikipedia
How does the velocity of light couple to the quantum of action? Spacetime is pixellated by the quantum of action, a situation illustrated by the "uncertainty" relations Δx.Δp ≈ ΔE.Δt ≈ h. The first point of contact is the Planck-Einstein relation E = hf where we may interpret f as 1/Δt, the time interval necessary to execute one quantum of action. Velocity is the ratio of distance to time and since the velocity of light, c is fixed, the product of wavelength λ [Δx.] and frequency is fixed, c = λ.f. The photon, although massless, has momentum which is related to the quantum of action by Δp = h/Δx, so we imagine the photon stepping through spacetime at frequency f each step taking time Δt and moving Δx, so c = Δx./Δt, the ratio of pixel size to pixel duration. There are no limits to the energy, frequency or wavelength of a photon (except the constancy of c) so its energy and momentum may vary from zero to infinity. In the primitive universe we can see no constraints on these
[page 26]
except the pixel size determined by the quantum of action which in spacetime is the product of energy and time or momentum and [distance]. Energy has momentum given by mv where m = E/c2 and v = c so p = E/c. Putting all this together we get a picture of the relationship between h and c which is so simple I cannot understand it. The heuristic of simplicity blinds me to the nature of my world [rather like Pseudo-Dionysius's claim that god can only be understood in the negative way]. When I copy this out I will try to get it right and couple it to the notion that the energy of a vector in Hilbert space is the rate of rotation of the associated circle group, E = ℏω. I'm so dumb I want to cry. What I see, though is that the velocity of light in 4-space is closely coupled to the quantum of action and the metric of 4-space reflects the fact that photons exist prior to space-time and appear in space-time on null geodesics.
So how do photons create spacetime, how do they create massive particles? This creation becomes possible in space-time.
We can identify Hilbert space with the quantum of action [and with the trinity via the identification of the quantum of action [ancient name actus purus] with the classical God [defined by Aquinas]. The simplest Hilbert space has one point in its domain and one value, corresponding to the initial singularity. Like quantum mechanics itself, Hilbert space is symmetrical with respect to complexity so any quantum state φ may be the superposition of an infinite number of [orthonormal] basis vectors in a Hilbert space and still, through normalization, be identified with one quantum of action [and with the communication theoretical definition of an information source]. Orthonormal basis - Wikipedia, Claude Shannon: Communication in the Presence of Noise
Another reversal: We suggest that photons are the source of
[page 27]
electrons and positrons.
Quantum state φ is also symmetrical with respect to energy, since φ = eiωφ where ω is the angular frequency and φ is the quantum of action so given the Planck-Einstein relation E = ℏω it does not matter in quantum mechanics where we place the zero of energy. The only intrinsic property of the quantum of action would seem to be spin.
Energy is the time rate of change of phase and momentum is the spatial rate of change of phase, so the differentiation of energy and momentum and potential and kinetic energy does not emerge until we have space and time.
The Leopard page 151: 'the double skavery of love and death' Tomasi Di Lampedusa; The Leopoard
The velocity of light bifurcates into distance and time, momentum and energy, light, spin 1, each photon carrying [being] a quantum of action. Is the world yielding some secrets to me or am I deluding myself?
We begin, therefore, with a 1 dimensional Hilbert space which represents pure act, the unmoved mover, the classical god and the initial singularity.
Wednesday 8 July 2020
Pam had a big 5 minute seizure this morning and looks very poor
[page 28]
today.
. . .
My idea is to rebuild the physics of nuclear death with a physics of childish creative love. I am relying on my naivete to carry me to a new vision of the world based on cooperation and creation rather than murder and oppression, following the work of Charles Dickens' A Christmas Carol. A Christmas Carol - Wikipedia
I, like everybody else, am a phenomenon to be explored, or at least an explanatory challenge.
We are thinking that the development of mental models of the world parallels the evolution of the world and is punctuated by episodes of discovery and eras of business as usual. I am trying to ferment an era of discovery based on the idea that the quantum of actin is the primordial atom both in a formal and a concrete sense and that the definition of action is the transition from p to not-p, or perhaps the addition of a space of not-ps to the space of p where p stands for any transfinite structure of any complexity, so beginning with p whose cardinal is ℵn we generate around it and from it an even bigger not-p whose cardinal is ℵn + 1, a small subset of which is ℵn [the underlying layer in the transfinite network]. What is happening here is that [my] old ideas that have stood alone are fusing together to form more complex and complete ideas with the long term idea of producing an alternative to quantum field theories in the form
[page 29]
of quantum network theories and seeing how the emergence of these ideas models the parallel emergence of real structure in the history of the world, which generally becomes more complex but occasionally takes a step back. Science is in a sense a step back because it is an attempt to see how things got the way they are through past events.
Networks ramify and connect, like fungal mycelia. Mycelium - Wikipedia, Merlin Sheldrake: Entangled Life: How Fungi Make Our Worlds, Change Our Minds, and Shape Our Futures
Thursday 9 July 2020
The irritant in quantum field theory around which I am trying to deposit a pearl is a combination of the need for renormalization [to get reasonable results from the theory] and the absurd values of cosmological constants [derived with the theory] which I am trying to cure by taking the view that the quantum of action is a real discrete particle, an item of embodied logic which creates new entities by, in effect, interfering with itself, either constructively in the case of bosons or . . . negatively to produce the exclusion principle or 'pseudo bosons' [the singlet state] in the case of [paired] fermions. The continuous approach to physics treats amplitude as a continuous variable. The approach I am trying to zoom in on treats action as a logical variable, either a creator or an annihilator but nothing in between [as we see in the application of the "ladder operator" to the quantum harmonic oscillator]. From this point of view the apparent continuity that we see in quantum interactions is a statistical artefact of the law of large numbers, since the measured results of our quantum physics experiments are the result of vast numbers of trials of what are in effect tosses of the quantum coin. Quantum harmonic oscillator - Wikipedia
[page 30]
The [other] foundation of my pearl is the view that quantum mechanics precedes the emergence of space-time. Quantum field theories built in the space-time domain take the view that the quantum pixels we see in space-time which have the dimension of angular momentum obey the rule ΔE.Δt ≈ h, so that when we go to very high energies actions take place in very short times and when we go to high momenta actions occur over very short distances. This leads to trouble when the assumption that spacetime is continuous encourages the view that quantum interactions take place at a point, which means at infinite energy and momentum, which leads to physical nonsense which must be cured by renormalization, ie introducing artificial cutoffs in energy and momentum, in order to get reasonable results.
It is often difficult to find the words of symbols to express an idea but once this is achieved things begin to appear quite straight forward, although felicitous expression are not necessarily true, just a comfortable resolution to some mental stress or potential, what Descartes would call a clear and distinct idea. He appears to have been a bit deluded by the notion that god guarantees the truth of clear and distinct ideas. Meditations IIII. Manley & Taylor: Descartes Meditations - Trilingual Edition
Physicists and mathematicians may have created a problem for themselves by maintaining that the solutions to the quantum wave equation are deterministic and so determine the probability distribution of the outcomes of quantum measurement without being able to determine the outcome in time so, for instance, we are able to establish a half life for a radioactive nucleus
[page 31]
by determining the probability that it will tunnel through the potential maintaining its stability, the moment at which the decay actually occurs is not determined [as it would be in a classical theory, suggesting that quantum events are not coupled to time in the same was as classical events, a circumstance that led Einstein to feel that quantum mechanics is incomplete].
The answer, it seems, may be in symmetry. We can predict predict exactly that each face of a fair die will appear in one sixth of an infinite number of fair rolls, but the symmetry of the die and the finite number of its faces explain this outcome, since we know that it is guaranteed to settle into one of its six stationary states [but these events are in no way coupled to time]. The stationary states of electrons in an atom play a similar role, although the picture is much more complex, but the eigenvalue equation gives us a list of possible outcomes and the Born rule provides a metric for computing the probabilities of the possible outcomes which will be reflected in the "line weights" associated with each possible transition, which is determined by the requirement that each change of state is accompanied by precisely one quantum of action.
From the point of view of action, all state changes are discrete events which which are logically coupled by the quantum. The interest of physicists is in calculating the energy changes associated with these changes of state reflected in the frequencies of the photons emitted or absorbed in the process, and the question for science is how is the photon energy coupled to the quantum logic? Does the idea that quantum mechanics underlies space-time provide any help in doing the calculations, both for physicists and for nature?
Feynman's methods show that the probabilities of quantum events arise from the superposition of many different channels of communication. We may get a clue from the nervous system where the input to a neuron is a superposition of the effects of many excitatory and inhibitory synapses. What we are looking
[page 32]
for is the simple mechanism that underlies each of these channels which Feynman sees as a path integral and which I feel must always involve discrete events involving one quantum each.
Friday 10 July 2020
Big setback. Is my dream all a dream? Can I reproduce all the properties of current theory from my point of view. Maybe I have to accept current theory and devise a new interface between quantum field theory and natural theology / cognitive cosmology, working in the classical domain, but trying to reimagine the interface between quantum and classical, ie reinterpret quantum mechanics. Maybe my bridge is too far and retreat is required, so back to the drawing board and all the other cliches. New plan by next Monday.
Stars say: 'Don't be too hard on yourself if something you attempt goes wrong today. No one expects you to get it right very single time so why should you expect it yourself? Keep your standards high, but don't forget you are human like everybody else.' How do the stars say this? A Darwinian tautology.
The creation of energy is analogous to the creation of money and a measure of the creation of meaning by bonding and trust.
Why do we think the processes of quantum mechanics are
[page 33]
deterministic? Is it due to not knowing cybernetics since according to von Neumann observation increases entropy and therefore the results cannot be controlled by the participants.
De Broglie may have put his finger on it. The establishment of fixed and stable structures in the world is determined by the requirement that quanta of action be closed to create standing waves which means in effect the creation of codecs where decoding algorithms is the inverse of the encoding algorithm. I say this again and again in one way or another and it is slowly sinking in as my thought quanta gain closure and fit together into a network process. I have to learn how the eigenvalue equation really works to stop the ceaseless dynamics of the quantum process and extract a fixed stationary point.
BUT it is hard to renounce the instinct which brought me to the transfinite network. The payoff is so big that it is irresistably attractive. And I still have 20 years to do the job. Just have to map the transfinite computer network onto the assumption that the universe cannot do anything that is not turing computable so, like quantum mechanics and gravitation, there must be a way to put them together.
[page 34]
We imagine that one of the principal roles of the human brain is language processing, ie it is in effect a codec encoding our personal experience into language which someone using the same language can decode to share the experience [within the tacit envelope of shared humanity]. If we are going to indulge in cognitive cosmology we would like to see how fermions encode messages in bosons and transmit them to other fermions, gauge theory, or better phase theory. So the firing of a neuron is a matter of phase, as is the function of an atom receiving and transmitting photons. A quantum of action is a unit of phase, 2π.
We may think of the era when quantum mechanics was the only game in town, before the emergence of space-time as the domain of classical physics (theology and everything else), as the logical era and a good place to go back to think about this [is the work of] J. M. Jauch Josef-Maria Jauch - Wikipedia
Dirac: the existence of superposition is responsible for the striking difference between quantum and classical behaviour. de Ronde, Domenech & Freytes: Quantum Logic in Historical and Philosophical Perspective
Classically a superposition is a space containing different sets of data which may be accessed sequentially. Quantum superpositions are supposed to exist outside space time [and their most interesting feature is their linearity which seems to indicate that they do not enjoy concrete representation (?)].
Saturday 11 July 2020
Kuhlman; 'operator valued' = algorithm valued [represented by code]. Meinard Kuhlmann (Stanford Encyclopedia of Philosophy): Quantum Field Theory
A particle is a message [necessarily discrete, as required by information theory, if it is to convey information].
Kuhlmann, Conclusion:
. . . one has to recall why the ontological interpretation of quantum field theory is so difficult
[page 35]
is the fact that it is exceptionally unclear which part of the formalism are to be taken to represent anything physical in the first place. And it looks as though this problem will persist for quite some time.
The written work is a vehicle for ideas ie a [physical] representation of states in the mind of the writer. We know, from the vast complexity of the brain and the chain of communication through brain to muscles to pen, that the neural input to a sentence like this is from an information theoretical point if view millions of time more complex (as a count of the data needed to represent it) than the resultant sentences, and if we go deeper to physical quanta of action we see that each spike in the nervous system and each contraction of a muscle fibre is represented by millions of quanta of action. Looking in the opposite direction, from the readers point of view, each of these sentences motivates an equally complex response in the person decoding the sentences and we guess that at best, the concepts elicited in the recipient mind are only approximately equivalent to the states of mind that generate the sentences in the first place. In other words, we have a very flexible joint between two minds which is surrounded by a large realm of uncertainty which we see as analogous to the uncertainty we see in quantum theory [due to underdetermination in the communication link between system and observer].
It can take a long time to form and express a clear and distinct idea although in normal conversation the encoding snd decoding of speech is almost instantaneous because the context of the conversation provides much of the tacit background to what is being said. In the creative realm, however it may take years or centuries and many minds to
[page 36]
[page 36]
clearly formulate something like classical mechanics which was for a number of centuries our principal key to physical dynamics, and it seems clear from articles like Kuhlmann quoted above that fundamental physics is very far from clear and distinct and fraught with internal contradictions each of which serves as a starting point for a new debate on how to get things right. One thing that sustains me is that I rarely see any trace of the logical / cognitive approach to understanding the world that has become my staple, though it seems fully consistent with ancient ideas about the whole of reality being alive [as we expect god to be]. One reason for this is the tendency of scientists to ridicule hypotheses that do not explicitly meet the requirement of experimental refutation and are considered too soft to build a science on. When we look at physics we see that there are so many ideas and theories and alternative pictures that we get less guidance from theory in the development of complex technology than we do from simple trial and error, the approach I am taking here, putting things down as they occur to me so that I have a big selection of pieces from which to construct my jigsaw.
The quantum of action is the fundamental metric of space-time, defining for instance the size of an atom through the pixel of angular momentum. MIT Open Courseware: Heisenberg Uncertainty
Dirac page 3: '. . . there is a limit to our powers of observation and the smallness of the accompanying disturbance – a limit which is in the nature of things and can never be surpassed by improved technique or increased skill on the part of the observer.' ie the minimum message or particle, measured by the quantum of action if the qubit. Paul Dirac: The Principles of Quantum Mechanics (4th ed), Qubit - Wikipedia
[page 37]
Dirac page 4: 'A new set of accurate laws of nature is required. One of the most fundamental and drastic of these is The Principle of Superposition of States.'
We understand superposition in terms of waves but we can also provide logical explanations: and = addition, nand = subtraction.
page 9: '. . . the wave function gives information about one photon being in one place and not the probable number of photons in that place.'
page 10: '. . . all particles can be made to exhibit interference effects and all wave motion has its energy in the form of quanta.' So the wave is not necessarily continuous?
page 12: 'Any state may be considered as the superposition of two or more states, and indeed in an infinite number of ways' a consequence of assuming continuous amplitudes.
'There is an entirely new idea involved to which one must get accustomed and in terms of which one must proceed to build up an exact mathematical theory without having any detailed classical picture.' [ie no concrete representation ?]
So what is really going on with superposition and all that? The interesting bit is linearity and the ability to generate an infinity of states out if a two dimensional Hilbert space, something reminiscent of Cantor's generation of ℵn + 1 out of ℵn. I like sentences like this which can open up a whole new perspective on the relationship between quantum mechanics and creation via Cantor. Such pleasure. Now to make something of it.
[page 38]
As of Friday 10 I had concluded that my plan to graft quantum mechanics onto a digital computer network was dead, but my new perspective on superposition from reading Dirac again suggests that it [is] still showing signs of life through a possible link between the multiplication of states by superposition and Cantor's transfinite numbers. How is this going to work? The first step might be to break superposition down from a continuous process to a rational process, that is to make the coefficients a and b in ψ = a|0> + b|1> into rational, that is discrete, numbers with the same cardinal ℵn as the set of natural numbers. This conflicts somewhat with the normalization a2 + b2 = 1 but we can possibly deal with this by making a and b complex roots of unity.
The association of waves with particles is to say that a particles is a process comprising discrete event which is in effect a definition of a wave, ie wave mechanics = discrete event mechanics = logical mechanics = computation, wave = clock pulse.
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Further readingBooks
Di Lampedusa, Tomasi, The Leopard, Vintage Books / Penguin Random House 1958, 2007 Jacket: 'In the spring of 1860, Fabrizio, the charismatic Prince of Salina, still rules over thousands of acres and hundreds of people, including his own numerous family, in mingled splendour and squalor. Then comes Garibaldi's landing in Sicily and the Prince must decide whether to resist the forces of change or come to term with them. "Perhaps the greatest novel of the century" L.P. Hartley'
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Dirac, P A M, The Principles of Quantum Mechanics (4th ed), Oxford UP/Clarendon 1983 Jacket: '[this] is the standard work in the fundamental principles of quantum mechanics, indispensible both to the advanced student and the mature research worker, who will always find it a fresh source of knowledge and stimulation.' (Nature)
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Everett III, Hugh, and Bryce S Dewitt, Neill Graham (editors), The Many Worlds Interpretation of Quantum Mechanics, Princeton University Press 1973 Jacket: 'A novel interpretation of quantum mechanics, first proposed in brief form by Hugh Everett in 1957, forms the nucleus around which this book has developed. The volume contains Dr Everett's short paper from 1957, "'Relative State' formulation of quantum mechanics" and a far longer exposition of his interpretation entitled "The Theory of the Universal Wave Function" never before published. In addition other papers by Wheeler, DeWitt, Graham, Cooper and van Vechten provide further discussion of the same theme. Together they constitute virtually the entire world output of scholarly commentary on the Everett interpretation.'
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Khinchin, Aleksandr Yakovlevich, Mathematical Foundations of Information Theory (translated by P A Silvermann and M D Friedman), Dover 1957 Jacket: 'The first comprehensive introduction to information theory, this book places the work begun by Shannon and continued by McMillan, Feinstein and Khinchin on a rigorous mathematical basis. For the first time, mathematicians, statisticians, physicists, cyberneticists and communications engineers are offered a lucid, comprehensive introduction to this rapidly growing field.'
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Neuenschwander, Dwight E, Emmy Noether's Wonderful Theorem, Johns Hopkins University Press 2011 Jacket: A beautiful piece of mathematics, Noether's therem touches on every aspect of physics. Emmy Noether proved her theorem in 1915 and published it in 1918. This profound concept demonstrates the connection between conservation laws and symmetries. For instance, the theorem shows that a system invariant under translations of time, space or rotation will obey the laws of conservation of energy, linear momentum or angular momentum respectively. This exciting result offers a rich unifying principle for all of physics.'
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Pais, Abraham, 'Subtle is the Lord...': The Science and Life of Albert Einstein, Oxford UP 1982 Jacket: In this . . . major work Abraham Pais, himself an eminent physicist who worked alongside Einstein in the post-war years, traces the development of Einstein's entire ouvre. . . . Running through the book is a completely non-scientific biography . . . including many letters which appear in English for the first time, as well as other information not published before.'
Amazon
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Sheldrake, Merlin, Entangled Life: How Fungi Make Our Worlds, Change Our Minds, and Shape Our Futures, Random House. 2020 Jacket: 'When we think of fungi, we likely think ofmshrooms. But muchrooms are inly fruiting bodies, analogous to apples on a tree. Most fungi live out if sight yet make up a massively diverse kingdom of organisms that support and sustain nearly all living systems. Fungi provide a key to understanding the planet on which we live and the ways we think,feel and behave.'
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Steinbeck, John, and Robert DeMott (Editor and Introduction), Sweet Thursday, Penguin Classics 2008 Amazon Product Description
'In Monterey, on the California coast, Sweet Thursday is what they call the day after Lousy Wednesday, which is one of those days that are just naturally bad. Returning to the scene of Cannery Row—the weedy lots and junk heaps and flophouses of Monterey, John Steinbeck once more brings to life the denizens of a netherworld of laughter and tears—from Fauna, new headmistress of the local brothel, to Hazel, a bum whose mother must have wanted a daughter.'
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Veltman, Martinus, Diagrammatica: The Path to the Feynman Rules, Cambridge University Press 1994 Jacket: 'This book provides an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics. The aim is to make clear what the physical foundations of present-day field theory are, to clarify the physical content of Feynman rules, and to outline their domain of applicability. ... The book includes valuable appendices that review some essential mathematics, including complex spaces, matrices, the CBH equation, traces and dimensional regularization. ...'
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Weinberg, Steven, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, Wiley 1972 Amazon customer review: 'The Best Exposition on General Relativity:
'Weinberg is a master. His style is efficent. His words not wasted. His insights are inspiring. Behind each statement dwells a reservoir of thought. His selection and organization of the material seems non-improvable. Completion of the book yields general relativity in a comprehensive manner.
In addition to his methods, I am wholeheartedly biased towards his approach of basing general relativity on empiricism rather than geometry. Reading this book is almost synonomous with sitting at the feet of a master.
The methods utilized are standard tensor analysis, which yields the best results and understanding of the physics in a first exposure. MTW, in contrast, uses different mathematical approaches and moreover does so in an inconsistent manner. Weinberg is the BEST book, existing today, on general relativity period.' A Customer
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Links
A Christmas Carol - Wikipedia, A Christmas Carol - Wikipedia, the free encyclopedia, ' A Christmas Carol. In Prose. Being a Ghost Story of Christmas, commonly known as A Christmas Carol, is a novella by Charles Dickens, first published in London by Chapman & Hall in 1843 and illustrated by John Leech. A Christmas Carol recounts the story of Ebenezer Scrooge, an elderly miser who is visited by the ghost of his former business partner Jacob Marley and the spirits of Christmas Past, Present and Yet to Come. After their visits, Scrooge is transformed into a kinder, gentler man. ' back |
Adelard of Bath - Wikipedia, Adelard of Bath - Wikipedia, the free encyclopedia, 'Adelard of Bath (Latin: Adelardus Bathensis) (c. 1080 – c. 1152) was a 12th-century English natural philosopher. He is known both for his original works and for translating many important Greek and Arab scientific works of astrology, astronomy, philosophy and mathematics into Latin from Arabic versions, which were then introduced to Western Europe. He is known as one of the first to introduce the Hindu–Arabic numeral system to Europe. He stands at the convergence of three intellectual schools: the traditional learning of French schools, the Greek culture of Southern Italy, and the Arabic science of the East.' back |
Adrian Vermeule, Why conservative justices are more likely to defect, ' There is a third theory that has more explanatory force: The justices are indeed acting faithfully to law, but not by enforcing the written Constitution and laws. Rather what they enforce is our real, unwritten constitution, a set of understandings that underlies and shapes our interpretation of the law. Justices interpret open-ended provisions (“due process of law”) in light of this unwritten constitution. And because the background small-c constitution embodies a liberal order, it is unsurprising that their decisions do as well.' back |
Amino acid - Wikipedia, Amino acid - Wikipedia, the free encyclopedia, 'In chemistry, an amino acid is a molecule containing both amine and carboxyl functional groups. These molecules are particularly important in biochemistry, where this term refers to alpha-amino acids with the general formula H2NCHRCOOH, where R is an organic substituent.' back |
Andrew Hamilton, The Border Force Act's disquieting parallels, 'On July 1 the Australian Border Force Act 2015 became law. Detention centre staff are now forbidden to speak about human rights abuses, with a two year jail penalty applying. It is perhaps appropriate to recall the secrecy of the security apparatus of Stalinist Russia, Apartheid South Africa, and Chile and Argentina under the Generals, where victims were denigrated and information prevented from leaking out.' back |
Australian Government, Australian Border Force Bill 2015, 'Type
Government
Portfolio
Immigration and Border Protection
Originating house
House of Representatives
Status
Act
Parliament no
44
Summary
Introduced with the Customs and Other Legislation Amendment (Australian Border Force) Bill 2015, the bill: establishes the statutory office and role of the Australian Border Force (ABF) Commissioner; provides for the exercise of powers of the commissioner and the ABF employees; provides for the issue of binding written directions in relation to the administration and control of the ABF and the department respectively, and the performance of functions or exercise of powers; provides the ability to require immigration and border protection workers to undergo alcohol and prohibited drug screening tests; establishes secrecy and disclosure provisions; and provides for the management of serious misconduct by employees. back |
Awol K Allo, Haacaaluu Hundeessaa: A towering musician and an Oromo icon, ' When Haacaaluu was assassinated by unidentified assailants on June 29 in Addis Ababa, Ethiopia lost not just a strikingly talented musician, but also a political and cultural icon. His assassination sent shockwaves across the country, particularly in Oromia, the Oromo-majority region of Ethiopia, and triggered major protests in Addis Ababa and elsewhere.
At least 160 people have been killed in the ensuing clashes and more than 1,000 arrested, including leading figures of the Oromo opposition parties, such as Jawar Mohammed, Bekele Gerba, Shigut Geleta, and others.' back |
Bicknell & Pates, 'Living fossils': we mapped half a billion years of horseshoe crabs to save them from blood harvest, ' Fossil records for horseshoe crabs extend back about 480 million years. This is well over 200 million years before the dinosaurs.
More recently, horseshoe crabs have greatly helped advance modern medicine. Their blood is used to identify endotoxins in solutions. These are toxins found in bacteria, so anyone who has had an injection or surgery has been kept safe from dangerous toxins thanks to these creatures.
Unfortunately, the harvesting of their blood for this purpose is one reason horseshoe crabs are becoming an endangered group. Our research published today in Frontiers in Earth Science will hopefully aid conservation efforts to protect these enigmatic creatures.' back |
Bloch sphere - Wikipedia, Bloch sphere - Wikipedia, the free encyclopdia, ' The Bloch sphere is a unit 2-sphere, with antipodal points corresponding to a pair of mutually orthogonal state vectors. The north and south poles of the Bloch sphere are typically chosen to correspond to the standard basis vectors | 0 ⟩ {\displaystyle |0\rangle } and | 1 ⟩ {\displaystyle |1\rangle } , respectively, which in turn might correspond e.g. to the spin-up and spin-down states of an electron. This choice is arbitrary, however. The points on the surface of the sphere correspond to the pure states of the system, whereas the interior points correspond to the mixed states. back |
Bose-Einstein condensate - Wikipedia, Bose-Einstein condensate - Wikipedia, the free encyclopedia, ' A Bose–Einstein condensate (BEC) is a state of matter (also called the fifth state of matter) which is typically formed when a gas of bosons at low densities is cooled to temperatures very close to absolute zero (-273.15 °C). Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which point microscopic quantum phenomena, particularly wavefunction interference, become apparent macroscopically. A BEC is formed by cooling a gas of extremely low density, about one-hundred-thousandth (1/100,000) the density of normal air, to ultra-low temperatures.
This state was first predicted, generally, in 1924–1925 by Albert Einstein following and crediting a pioneering paper by Satyendra Nath Bose on the new field now known as quantum statistics.' 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 |
Carnot heat engine - Wikipedia, Carnot heat engine - Wikipedia, the free encyclopedia, 'A Carnot heat engine is a hypothetical engine that operates on the reversible Carnot cycle. The basic model for this engine was developed by Nicolas Léonard Sadi Carnot in 1824. The Carnot engine model was graphically expanded upon by Benoît Paul Émile Clapeyron in 1834 and mathematically elaborated upon by Rudolf Clausius in the 1850s and 60s from which the concept of entropy emerged.' back |
Chongyi Feng, 'The rot goes right up to Beiing': Why detained professor Xu Zhangrun is such a threat to China's leadership, 'In Xu’s final essay, China as a Lone Ship, he called for a change in leadership – one which now seems virtually impossible.
Enough, the mouldy campaigns of deification and personality cult; enough, the monstrous lies and endless sufferings; enough the blood-sucking red dynasty and greedy party-state; enough, the absurd policies and practices in trying to put the clock back [to a more Mao-style leadership] over the past seven years; enough, the mountains of bodies and seas of blood resulting from the red tyranny over the past 70 years.'
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Chris Turney & Chris Fogwill, Marine life fount in ancient Antarctica ice helps solve a carbon dioxide puzzle from the ice age, ' Evidence of minute amounts of marine life in an ancient Antarctic ice sheet helps explain a longstanding puzzle of why rising carbon dioxide (CO₂) levels stalled for hundreds of years as Earth warmed from the last ice age.
Our study shows there was an explosion in productivity of marine life at the surface of the Southern Ocean thousands of years ago.' back |
Claude Shannon, Communication in the Presence of Noise, 'A method is developed for representing any communication system geometrically. Messages and the corresponding signals are points in two “function spaces,” and the modulation process is a mapping of one space into the other. Using this representation, a number of results in communication theory are deduced concerning expansion and compression of bandwidth and the threshold effect. Formulas are found for the maximum rate of transmission of binary digits over a system when the signal is perturbed by various types of noise. Some of the properties of “ideal” systems which transmit at this maximum rate are discussed. The equivalent number of binary digits per second for certain information sources is calculated.' [C. E. Shannon , “Communication in the presence of noise,” Proc. IRE,
vol. 37, pp. 10–21, Jan. 1949.] back |
de Ronde, Domenech & Freytes, Quantum Logic in Historical and Philosophical Perspective, ' Quantum Logic (QL) was developed as an attempt to construct a propositional structure that would allow for describing the events of interest in Quantum Mechanics (QM). QL replaced the Boolean structure, which, although suitable for the discourse of classical physics, was inadequate for representing the atomic realm.' back |
Dianna Theodora Kennedy, God, religion and fundamentalismL an unholy trinity, 'Who falls prey to fundamentalist messages? I have developed an algorithm:
Fundamentalism = fear + magical thinking + social and political forces that create psychological vulnerability, rage, hate, envy, alienation and marginalisation + cognitive narrowing (for example, indoctrination).
As a result, the disenfranchised, embattled, denigrated and rejected, deprived and needy, traumatised and dispossessed, envious, hateful and rageful members of society are all fair game for the message of fundamentalist religious and politico-religious ideologies.' back |
Differential form - Wikipedia, Differential form - Wikipedia, the free encylopedia, 'In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates. Differential forms provide a unified approach to defining integrands over curves, surfaces, volumes, and higher dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications, especially in geometry, topology and physics.' back |
Dominic Kelly, Conservatives' collective tantrum over the pope has been a wonder to behold. , 'These discoveries played out in the Australian’s coverage, which was kicked off by its environment editor, Graham Lloyd. Amid a collection of key points from the encyclical, Lloyd quotes a media release from James Grant, Catholic priest and adjunct fellow at the Institute of Public Affairs, reassuring Catholics that they “can feel safe in being sceptical about the pope’s opinion”.
Yes, a Catholic priest working for a climate denialist thinktank issued a media release telling Catholics how they should react to the pope’s views about climate change. back |
E J Dionne Jr, Liberated by Grace: The African-American Christian Tradition, 'And the scholar Jonathan Rieder noted in his book about Martin Luther King Jr.’s ministry, The Word of the Lord Is Upon Me, that the Resurrection and the Exodus stories were rich sources of hope, especially in the movement’s darkest moments. “God will make a way out of no way” was King’s answer to those whose spirits were flagging.
No shootings, no bombings, no fires can destroy this faith.' back |
George Monbiot, Greece is the latest battleground in the financial elite's war on democracy, 'The Maastricht treaty, establishing the European Union and the euro, was built on a lethal delusion: a belief that the ECB could provide the only common economic governance that monetary union required. It arose from an extreme version of market fundamentalism: if inflation were kept low, its authors imagined, the magic of the markets would resolve all other social and economic problems, making politics redundant. Those sober, suited, serious people, who now pronounce themselves the only adults in the room, turn out to be demented utopian fantasists, votaries of a fanatical economic cult.' back |
Good news (Christianity) - Wikipedia, Good news (Christianity) - Wikipedia, the free encyclopedia, 'In Christianity, the good news or evangelium (from Koine evengelion– also translated as "gospel", "glad tidings" and variants) is the message of Jesus, the Christ (the Messiah), specifically his atoning death on the cross and resurrection, the descent of the Holy Spirit at Pentecost as "helper" (paraclete), and the resulting promise and hope of salvation for the faithful.' back |
Google search - Wikipedia, Google search - Wikipedia, the free encyclopedia, 'Google search is a web search engine owned by Google Inc. and is the most-used search engine on the Web [3]. Google receives several hundred million queries each day through its various services.[4] Google search was originally developed by Larry Page and Sergey Brin in 1997.' back |
Gregory Melluish, Australia's Constitution works because it doesn't define national identity, 'It is very important to realise that the Australian Constitution has nothing to do with identity politics. It does not deal with substantive issues, as do other constitutions, such as the Irish Constitution – which was why the Irish people needed to hold a referendum on same-sex marriage. The Australian Constitution’s focus is procedural.
The one concession to identity was the inclusion of God in the preamble. It was something that many ordinary Australians desired but was not particularly favoured by convention delegates. Edmund Barton, in particular, spoke against it. Section 116, forbidding government support of any religion, ensured that it would have no legal implications.' back |
Hachalu Hundessa, Maalan Jira!,
Comment: Abdi Wardere 6 days ago
' I was born in Ogaden, Ethiopia but left Ethiopia in tears because as a young boy Ethiopian soldiers used to beat us indiscriminately because of our ethnicity. We Somalis and our beloved brothers of Oromia are never accepted in Ethiopia as equals. I am Oromia and Oromia is from me. Brother Hachalu, RIP for you are one of us. ' back |
Jessica Burkett, What the Dog-Fish and Camel-Bird can tells us about how our brains work, 'One implication that arises from this research by Google is that simulating intelligence requires an additional organisational component beyond just consolidated feature detection. Yet it’s still unclear how to successfully replicate this function within deep learning models.' back |
Jim Yardley and William Neuman, In Bolivia. Pope Francis Apologizes for Curch's 'Grave Sins', 'SANTA CRUZ, Bolivia — Pope Francis offered a direct apology on Thursday for the complicity of the Roman Catholic Church in the oppression of Latin America during the colonial era, even as he called for a global social movement to shatter a “new colonialism” that has fostered inequality, materialism and the exploitation of the poor.
Speaking to a hall filled with social activists, farmers, garbage workers and Bolivian indigenous people, Francis offered the most ambitious, and biting, address of his South American tour.' back |
John Keane, Julian Assange on Google, surveillance and predatory capitalism, '“Three years ago, Google finally joined the ranks of top-spending Washington lobbyists,” Assange tells me. “It’s a list usually stalked by such giants as the US Chamber of Commerce, military contractors, and the petro-carbon leviathans. Google is now at the top of the company list.” It annually spends more on lobbying than such military aerospace giants Lockheed Martin, Raytheon and Boeing.' back |
Josef-Maria Jauch - Wikipedia, Josef-Maria Jauch - Wikipedia, the free encyclopedia, ' Josef Maria Jauch (September 20, 1914 in Lucerne – August 30, 1974 in Geneva) was a Swiss/American theoretical physicist.
He studied mathematics and physics at ETH Zürich, earning his diploma in 1938. He then received his doctorate in 1940 from the University of Minnesota under Edward Lee Hill, for a dissertation entitled On Contact Transformations and Group Theory in Quantum Mechanical Problems. . . .
His work focused on quantum scattering theory, the process of measurement in quantum mechanics, causality, irreversible phenomena, and gauge theories. His contribution to the axiomatization of quantum field theory is a mathematical model of rigor. While in the U.S., he became interested in the theory of symmetry groups and their applications in the field of particle physics, a subject whose importance was not appreciated until the 1960s with the introduction of the SU(3) group by Murray Gell-Mann and Yuval Ne'eman.' back |
Kenneth P. Birnham et al, Overcoming Communications Challenges in Software for Monitoring and Controlling Power Systems, 'The restructuring of the electric power grid has created new control and monitoring requirements for which classical technologies may be inadequate. The
most obvious way of buiding such systems, using TCP connections to link monitoring systems with data sources, gives poor scalability and exhibits instability precisely when information is most urgently required. Astrolabe, Bimodal Multicast and
Gravitational Gossip, technologies of our own design,
seek to overcome these problems using what are called “epidemic” communication protocols. This paper
evaluates a hypothetical power monitoring scenario involving the New York State grid, and conclude
s that the technology is well matched to the need.' 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 |
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 |
MIT Open Courseware, Heisenberg Uncertainty, Slides 17, 18: 'Quantum mechanics tells us that an ATOM COULD NEVER COLLAPSE as it would take an infinite energy to locate the electron on top of the proton. . . . By preventing localization of the electron near the proton, the Uncertainty Principle RETARDS THE CLASSICAL COLLAPSE OF THE ATOM, PROVIDES THE CORRECT DENSITY OF MATTER,and YIELDS THE PROPER BINDING ENERGY OF ATOMS'
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Mycelium - Wikipedia, Mycelium - Wikipedia, the free encyclopedia, ' Mycelium is the vegetative part of a fungus or fungus-like bacterial colony, consisting of a mass of branching, thread-like hyphae. The mass of hyphae is sometimes called shiro, especially within the fairy ring fungi. Fungal colonies composed of mycelium are found in and on soil and many other substrates. A typical single spore germinates into a monokaryotic mycelium, which cannot reproduce sexually; when two compatible monokaryotic mycelia join and form a dikaryotic mycelium, that mycelium may form fruiting bodies such as mushrooms. A mycelium may be minute, forming a colony that is too small to see, or may grow to span thousands of acres as in Armillaria.' back |
Open Notebook Science - Wikipedia, Open Notebook Science - Wikipedia, the free encyclopedia, 'Open Notebook Science is the practice of making the entire primary record of a research project publicly available online as it is recorded. This involves placing the personal, or laboratory, notebook of the researcher online along with all raw and processed data, and any associated material, as this material is generated. The approach may be summed up by the slogan 'no insider information'. It is the logical extreme of transparent approaches to research and explicitly includes the making available of failed, less significant, and otherwise unpublished experiments; so called 'Dark Data'.' back |
Orthonormal basis - Wikipedia, Orthonormal basis - Wikipedia, the free encyclopedia, 'In mathematics, an orthonormal basis of an inner product space V (i.e., a vector space with an inner product), or in particular of a Hilbert space H, is a set of elements whose span is dense in the space, in which the elements are mutually orthogonal and of magnitude 1. Elements in an orthogonal basis do not have to have a magnitude of 1 but must be mutually perpendicular. It is easy to change the vectors in an orthogonal basis by scalar multiples to get an orthonormal basis, and indeed this is a typical way that an orthonormal basis is constructed.' back |
Peano axioms - Wikipedia, Peano axioms - Wikipedia - the free encyclopedia, 'In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are a set of axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano. These axioms have been used nearly unchanged in a number of metamathematical investigations, including research into fundamental questions of whether number theory is consistent and complete.' back |
Peter Hannam, Abbott government's 'blue tape' costs consumers billions, report finds, 'Businesses taking part in the federal Energy Efficiency Opportunities (EEO) were on track to save $786 million a year from implemented or intended investments to curb energy use, the report notes, citing Industry Ministry figures.
However, the 2014 axing of the EEO by the Abbott government – for an annual saving in regulatory burden worth just $17.7 million – and other moves to cull efficiency efforts mean future energy savings are likely to fizzle out.' back |
Protein - Wikipedia, Protein - Wikipedia, the free encyclopedia, 'Proteins (also known as polypeptides) are organic compounds made of amino acids arranged in a linear chain. The amino acids in a polymer chain are joined together by the peptide bonds between the carboxyl and amino groups of adjacent amino acid residues. The sequence of amino acids in a protein is defined by the sequence of a gene, which is encoded in the genetic code.' back |
Quantum harmonic oscillator - Wikipedia, Quantum harmonic oscillator - Wikipedia, the free encyclopedia, 'The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary potential can usually be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics. Furthermore, it is one of the few quantum-mechanical systems for which an exact, analytical solution is known.' back |
Qubit - Wikipedia, Qubit - Wikipedia, the free encyclopedia, 'A quantum bit, or qubit . . . is a unit of quantum information. That information is described by a state vector in a two-level quantum mechanical system which is formally equivalent to a two-dimensional vector space over the complex numbers.
Benjamin Schumacher discovered a way of interpreting quantum states as information. He came up with a way of compressing the information in a state, and storing the information on a smaller number of states. This is now known as Schumacher compression. In the acknowledgments of his paper (Phys. Rev. A 51, 2738), Schumacher states that the term qubit was invented in jest, during his conversations with Bill Wootters.' back |
Roger Waters: Pink Floyd, The Wall, back |
Simon Campbell & Yerra Bharat Kumar, Revealed: the Sun's secret plan to become a lithium factory, ' Lithium is used in everything from medication to mobile phone batteries, but where does it come from? We know it is mined here on Earth, but where it is created in the universe is less well understood.
We studied hundreds of thousands of stars like our own Sun and found they produce huge amounts of lithium late in their lives. This discovery, published today in Nature Astronomy, was not predicted by our best models of stars, indicating that some physical process must be missing from stellar theory.' back |
Spencer Ackerman, US torture doctors could face charges after report alleges post 9/11 'colllusion', 'The largest association of psychologists in the United States is on the brink of a crisis, the Guardian has learned, after an independent review revealed that medical professionals lied and covered up their extensive involvement in post-9/11 torture. The revelation, puncturing years of denials, has already led to at least one leadership firing and creates the potential for loss of licenses and even prosecutions.' back |
Suzanne Goldberg, Exxon knew of climate change in 1981, email says - but it funded deniers for 27 more years, '“Exxon first got interested in climate change in 1981 because it was seeking to develop the Natuna gas field off Indonesia,” Lenny Bernstein, a 30-year industry veteran and Exxon’s former in-house climate expert, wrote in the email. “This is an immense reserve of natural gas, but it is 70% CO2”, or carbon dioxide, the main driver of climate change.' back |
User Datagram Protocol - Wikipedia, User Datagram Protocol - Wikipedia, the free encyclopedia, 'The User Datagram Protocol (UDP) is one of the core members of the Internet protocol suite. The protocol was designed by David P. Reed in 1980 and formally defined in RFC 768.
UDP uses a simple connectionless transmission model with a minimum of protocol mechanism. It has no handshaking dialogues, and thus exposes any unreliability of the underlying network protocol to the user's program. There is no guarantee of delivery, ordering, or duplicate protection. UDP provides checksums for data integrity, and port numbers for addressing different functions at the source and destination of the datagram.' back |
Wojciech Hubert Zurek, Quantum origin of quantum jumps: breaking of unitary symmetry induced by information transfer and the transition from quantum to classical, 'Submitted on 17 Mar 2007 (v1), last revised 18 Mar 2008 (this version, v3))
Measurements transfer information about a system to the apparatus, and then further on – to
observers and (often inadvertently) to the environment. I show that even imperfect copying essential in such situations restricts possible unperturbed outcomes to an orthogonal subset of all possible states of the system, thus breaking the unitary symmetry of its Hilbert space implied by the quantum superposition principle. Preferred outcome states emerge as a result. They provide framework
for the “wavepacket collapse”, designating terminal points of quantum jumps, and defining the
measured observable by specifying its eigenstates.' back |
Xu Zhangrun, Viral Alarm, ' The material offered here in translation is excerpted, annotated on the basis of Professor Xu’s ‘Lone Ship of State’ with the permission of the author. It is the latest chapter in ‘Viral Alarm’, the theme of China Heritage Annual 2020. For a table of contents and links to other chapters in the Annual, see here, and for the ‘Xu Zhangrun Archive’, see here.' back |
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