vol VII: Notes
2015
Notes
[Sunday 8 February 2015 - Saturday 14 February 2015]
[Notebook: DB 78: Catholicism 2.0]
[page 102]
Sunday 8 February 2015
curate / constable
A system becomes corrupt when it loses its orthogonality, so that processes that should be independent become dependent, reducing the entropy of the system at constant energy, leading
[page 103]
to instability. Why nations fail. Where is the boundary between coupling and independence. Does a hydrogen atom know that it is part of me? There is nowhere in it to store information at this scale, but it does communicate with the region around it by exchanging photons (mainly) and a tiny amount of nuclear and gravitational interaction. Acemoglu & Robinson
The constables are the face workers of the task of keeping the physical peace. The curates have to deal with the metaphysical peace, the states of the souls of member of members of their flocks. These two layers of human activity interact, good metaphysics leading to good physics and good physics enabling good metaphysics. This is the virtuous circle of error control, each reduction in error increasing the complexity (entropy) of the system. So we can run the internet because we can make digital processes almost error free motivated by Shannon's discoveries.
The history of mathematics has been dominated by the relationship between the arithmetic integers and the geometric continuum. Here we see it implemented on a recursive bass in the trsnsfinite numbers, and we see this as a consequence of order and permutation of the elements of a set. [ie ℵn+1 is continuous (unresolved) with respect to ℵn] These elements need not be [seen as] a dust but rather as degrees of freedom in a dynamic situation ('employees') and permutations map the different ways of employing the elemental processes. Here we take the elemental processes to be Turing computable functions. These functions may be coupled into a continuum [in the Aristotelian sense] by the simple requirement that the output onf one machine is the input of the next. We begin with the simplest machine of all, the non machine. A string of two of these machines leaves the original input unchanged. The next most comple machine which takes two inputs
[page 104]
and gives one output is the not-and machine. It can be shown that any machine can be constructed from a suitable space-time network of nands [which is established by the hardware clock and topology].
A world of elemental processes [angels, there are as many species as there are Turing machines].
All drugs can be dangerous because a drug has an effect rather disproportionate to its size so overdosing is easy, particularly in the absence of research based portion control. Centers for Disease Control and Prevention
The excluded middle: not(not(x)) = x. There is nothing between the integers, they are orthogonal like the transfinite numbers (almost). Their lack or orthogonality (due to shared hardware) is in the limit of measure zero. The limit is the Platonic world. In the real world, resolution is limited by the quantum of action. This is true of all sizes of action. The resolution of a high explosive bomb is limited, making something of a lie of the claim to 'precision bombing'.
The crunch comes when we want to apply 'digital to the core' to actual calculations. We begin with the assumption that an elemental halted computation corresponds to one quantum of action. From this we can expand to four, space, time, energy , momentum. Energy is the time rate of elemental computations, momentum the space rate of same, a vector in three space.
Quantum mechanics is an heuristic structure, a metaphysics, a phase space, a coordinate system, in which to model the world. Here we map it to the transfinite computer network.
The path integral method is normalized [so] that the action leading the system from ψA to ψB is one quantum, a stationary value.
[page 105]
Monday 9 February 2015
A recurrent thought is that I have bitten off more than I can chew and am doomed to die before I see my project go significantly forward. On the other hand I can see that the Church is in trouble and I can see that there is a problem of governance which leaves the Church flat-footed in the face of modernity. So, I imagine the clergy have been getting their sex from children since time immemorial and the basic advice has been don't get too obvious. But society has changed, and we are much more sensitive to the presence of dirty old men and have begun to listen to our children rather that deny them a voice as the Church is accustomed to do.
So there is definitely a governance problem, so we must turn to the state of the art, which is democracy. Democracy cannot work without science, because we are relying on individual members of the body politic to form and express opinions about the guidance of their group, class or nation. If the people are unscientific and misinformed, we can expect the government to be too, so a secure democracy must have universal science based education.
This means theology must become scientific. Carbon dioxide is a drug, like ice, that speeds things up out of control.
As things get faster, the probability of control drops, since the controller must have a bandwidth advantage over the controlled system if it is to succeed, ie eliminate error.
Having decided half a century ago that theology must become scientific, I now have a pretty good grip on a theological model that is consistent with both God and
[page 106]
the world. I am no Aquinas, Lonergan or Barth, but I have a conviction.
I am angry at the Church because it has turned out to be such a failure for me. But my anger is now directed toward motivating the development of a consistent, scientific theological position, vague but maybe sufficient to attract real scientists to theology. Perhaps as an intellectual I have a bit of politician in me, but that is the only way I can profit from my work and go on, by selling it, as is where is.
Cybernetics explains how we keep on course by error correction. To do this we need a well defined course, a mechanism that can detect when we deviate from that course and a mechanism to correct the deviation.
Did the Catholic Church make me kinky? It seems to have succeeded in embedding a fear of women in me that took a long while to root out, if in fact I have done.
Metaphysics: abstract theology; mathematical theology.
Tuesday 10 February 2015
Writing is now the principal means of reproduction available to me. I wish to construct a representation of my view of the world for others to examine and criticize. This has been going on for a long time and I have written millions o words in the last fifty years, but the story is not yet complete in the sense that it can stand alone without its historical formwork. I am led on by the feelings that that day will actually come, and will build upon itself once it becomes intelligible enough to attract other workers. Fides quaerens
[page 107]
intellectum, a feeling seeking expression.
The appendix [to Francis, letters 2014] is a body of doctrine, a new fiction to replace the old one and the letters would explain the consquences of implementing the new fiction, both in terms of 'reaction' and 'progress'.
The government thinks it runs the place, but most of it is self controlled, locally [households].
Science fights corruption [by shining lights in dark places].
Wednesday 11 February 2015
Turing machines: the spanning set of tools for the Universe. Turing machine - Wikipedia
The resource we all want is entropy / freedom / definition. The quantum mechanical resource, a result of low cardinality and locality, as in Einstein, Podolsky and Rosen. What exactly was their problem? Entropy - Wikipedia, Einstein, Podolsky and Rosen
Each morning I try to load my car with a complete set of resources for the task in hand, tools and materials.
Christianity had a certain amount of trouble dealing with its historical foundation in Judaism and the Old Testament. [The authors of the New Testament did well to portray themselves as the fulfilment of ancient prophecies.] We can eliminate this by going back to the first God common to us all, the divine Universe.
Why did not matter and antimatter entirely annihilate each other? How were they created in the first place? Wiki 'the presence of remaining matter, and the absence of detectable remaining antimatter
[page 108]
also called baryon asymmetry, is attributed to CP violation: a violation of the CP symmetry relating matter to antimatter. The exact mechanism of the violation during baryogensis remains a mystery.' Antimatter - Wikipedia
Thursday 12 February 2015
It is taking me a long time to become a productive theologian but have plenty of time ahead of me yet for development and propagation.
It is time to couple the transfinite numbers more closely to reality. Mathematics is all about functions and functions are all about transformations, so the natural lace t study motion is function space. Function space - Wikipedia
Appendix: [to Francis letters] begin with Wigner - then progress from mathematical physics to mathematical theology by following the complexity invariant features of the universal network from the initial singularity to now and beyond.
Complexity invariance explains the development of more complex systems by bringing attention to the fixed points in the physical layer that have their metaphysical echoes in theology.
The key lies in the requirement that information is represented physically.
My biggest problem with God was (and is) how can a completely simple entity know and control the extraordinary complexity of the world as we know it, from quantum mechanics on up, ie from 1 state to ℵn
[page 109]
The quantum mechanical state [Turing machine] is the elemental unit in the Universe. [it is a countable set of functions beginning with NOP, NOT, NAND . . . ]
An epistemologica question. Is the Universe true in the sense of being internally consistent, or is it damaged and corrupt, as proponents of the Fall appear to preach.
Is it that capitalists do not understand the nature of work? Work is the physical implementation of their capitalist desires, to construct a real money making system that works.
Formally, anti-matter is the logical contradiction of matter, so that when the two structures meet they annihilate each other into an integral which produces a single number as a measure of an infinite dimensional space. [Feymann sees anti-matter as matter travelling back in time. Antiparticle - Wikipedia]
Increasing entropy = moving leftwards towards more complex social networks.
Friday 13 February 2015
Sydney Melbourne.
Saturday 14 February 2015
|
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Further reading
Books
Click on the "Amazon" link below each book entry to see details of a book (and possibly buy it!)
Acemoglu, Daron, and James Robinson, Why Nations Fail: The Origins of Power, Prosperity and Poverty, Crown Business 2012 "Some time ago a little-known Scottish philosopher wrote a book on what makes nations succeed and what makes them fail. The Wealth of Nations is still being read today. With the same perspicacity and with the same broad historical perspective, Daron Acemoglu and James Robinson have retackled this same question for our own times. Two centuries from now our great-great- . . . -great grandchildren will be, similarly, reading Why Nations Fail." —George Akerlof, Nobel laureate in economics, 2001
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Bergson, Henri, and Arthur Mitchell (translator), Creative Evolution, Rowman & Littlefield 1983 Amazon Book Description: 'Creative Evolution, originally published in 1911 by Henry Holt and Company, is the work which catapulted Bergson from obscurity into world-wide fame. A study of the philosophical implications of biological evolutionary theory, the impact of this book reached far beyond biology and seemed to many to herald a new age in philosophy and the sciences.'
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Churchill, Winston S, A History of the English Speaking People (Volume 1), Cassell Reference 2002 Amazon Product Description
'Volume I tells the story of Britain from pre-history to the Battle of Bosworth - the last of the battles of the Wars of the Roses in 1485 - and describes the strife and turmoil in the making of a nation. When this volume begins, tribal law was supreme; when it ends, Brtiain had become a nation and stood on the threshold of those adventures overseas which were to make an empire. Along the way we encounter a plethora of closely observed characters - William the Conqueror, Alfred the Great, Richard the Lionheart, Joan of Arc - and Churchill analyses the beginnings of Parliament, the Church and the monarchy with an eye as sharp as his legenday wit.'
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Churchill, Winston S, A History of the English Speaking People (Volume 1), Cassell Reference 2002 Amazon Product Description
'Volume I tells the story of Britain from pre-history to the Battle of Bosworth - the last of the battles of the Wars of the Roses in 1485 - and describes the strife and turmoil in the making of a nation. When this volume begins, tribal law was supreme; when it ends, Brtiain had become a nation and stood on the threshold of those adventures overseas which were to make an empire. Along the way we encounter a plethora of closely observed characters - William the Conqueror, Alfred the Great, Richard the Lionheart, Joan of Arc - and Churchill analyses the beginnings of Parliament, the Church and the monarchy with an eye as sharp as his legenday wit.'
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Coughlan, G D, and J E Dodd and B M Gripaios, The Ideas of Particle Physics: An Introduction for Scientists, Cambridge University Press 2006 Amazon Product Description
'The third edition of this well-received book is a readable introduction to the world of particle physics. It bridges the gap between traditional textbooks on the subject and popular accounts that assume little or no background knowledge. Carefully revised and updated, this new edition covers all of the important concepts in our modern understanding of particle physics. The theoretical development of the subject is traced from the foundations of quantum mechanics and relativity through to the most recent particle discoveries and the formulation of modern string theory. It includes a full description of the prospects for the Large Hadron Collider at CERN, which will allow many key ideas to be tested. The book is intended for anyone with a background in the physical sciences who wishes to learn more about particle physics. It is also valuable to students of physics wishing to gain an introductory overview of the subject.'
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Dodd, J E, and G D Coughlan, The Ideas of Particle Physics: An Introduction for Scientists, Cambridge UP 1991 Jacket: 'This book is intended to bridge the gap between traditional textbooks on particle physics and the popular accounts of the subject ... Although entirely self contained, it assumes a greater familiarity with the basic physics concepts than is usually the case in popular texts. This then allows a fuller discussion of more modern developments.'
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Einstein, Albert, and Robert W Lawson (translator) Roger Penrose (Introduction), Robert Geroch (Commentary), David C Cassidy (Historical Essay) , Relativity: The Special and General Theory, Pi Press 2005 Preface: 'The present book is intended, as far as possible, to give an exact insight into the theory of relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics. ... The author has spared himself no pains in his endeavour to present the main ideas in the simplest and most intelligible form, and on the whole, in the sequence and connection in which they actually originated.' page 3
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Feldman, , Joel S, and Thomas R Hurd, Lon Rosen, Jill D Wright, QED: A Proof of Renormalizability, Springer Verlag 1988
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| Hacklin, J, and Clement Huart, Raymonde Linossir, H de Wilman-Grabowska, Charles-Henri Marchal, Henri Maspero, Serge Eliseev and Paul-Louis Couchoud (Introduction), Asiatic Mythology: A Detailed Description and Explanation of the Mythologies of all the Great Nations of Asia, Crown Publishers Crescent Books Jacket: Asiatic Mythology was a great pioner work when it was first published [1932] and it has been ever since. . . . The Introduction says, "To penetrate to the heart of a civilization we ought to begin with a knowledge of its gods." Asiatic Mythology does indeed penetrate to the heart of civilizations that are drawing nearer to us than ever before. Therefore the book is today more significant and valuable than ever.' back |
Hoddeson, Lillian, and Laurie Brown, Michael Riodan & Max Dresden (editors), The Rise of the Standard Model, Cambridge University Press 1997 Review
'... a beautifully produced collection of essays by most of the leading scientists involved - including no fewer than eight Nobel laureates - and several eminent historians ... both practitioners and knowledgeable bystanders can draw inspiration from these reflections on what may turn out to have been the golden age of particle physics.' Graham Farmelo, New Scientist 'The volume is informative and useful to historians of physics.' Helge Kragh, Centaurus '... this book is ... worthwhile , timely and valuable.' R. Barlow, European Journal of Physics
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Kauffman, Stuart, At Home in the Universe: The Search for Laws of Complexity, Oxford University Press 1995 Preface: 'As I will argue in this book, natural selection is important, but it has not laboured alone to craft the fine architectures of the biosphere . . . The order of the biological world, I have come to believe . . . arises naturally and spontaneously because of the principles of self organisation - laws of complexity that we are just beginning to uncover and understand.'
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Lederman 1, Leon, and Dick Teresi, The God Particle: If the Universe is the Answer, What is the question, Mariner Books 2006 '. . . Part history, part autobiography, part polemic, with sideswipes on mystics onthe way, the book is a strange hotch-potch held together more by Lederman's outsize personality than any logic. . . . ' Roland Pease Nature 362, 302 (25 Mar 1993)
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Lederman 1, Leon, and Dick Teresi, The God Particle: If the Universe is the Answer, What is the question, Mariner Books (June 26, 2006)
• Language: English
• ISBN-10: 0618711686
• ISBN-13: 978-0618711680 2006 '. . . Part history, part autobiography, part polemic, with sideswipes on mystics onthe way, the book is a strange hotch-potch held together more by Lederman's outsize personality than any logic. . . . ' Roland Pease Nature 362, 302 (25 Mar 1993)
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Maxwell, James Clerk, Treatise on Electricity and Magnetism (vol 1), OUP 1998 First published 1873
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Maxwell, James Clerk, Treatise on Electricity and Magnetism (vol 2), OUP 1998 First published 1873
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Maxwell, James Clerk, Treatise on Electricity and Magnetism (vol 1), OUP 1998 First published 1873
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Maxwell, James Clerk, Treatise on Electricity and Magnetism (vol 2), OUP 1998 First published 1873
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Ricks, Thomas E, Fiasco, The American Military Adventure in Iraq, 2003 - 2005, Penguin (Non-Classics) 2007 Amazon.com Review
'Fiasco is a more strongly worded title than you might expect a seasoned military reporter such as Thomas E. Ricks to use, accustomed as he is to the even-handed style of daily newspaper journalism. But Ricks, the Pentagon correspondent for the Washington Post . . . has written a thorough and devastating history of the war in Iraq from the planning stages through the continued insurgency in early 2006, and he does not shy away from naming those he finds responsible. His tragic story is divided in two. The first part--the runup to the war and the invasion in 2003--is familiar from books like Cobra II and Plan of Attack, although Ricks uses his many military sources to portray an officer class that was far more skeptical of the war beforehand than generally reported. But the heart of his book is the second half, beginning in August 2003, when, as he writes, the war really began, with the bombing of the Jordanian embassy and the emergence of the insurgency. His strongest critique is that the U.S. military failed to anticipate--and then failed to recognize--the insurgency, and tried to fight it with conventional methods that only fanned its flames. What makes his portrait particularly damning are the dozens of military sources--most of them on record--who join in his critique, and the thousands of pages of internal documents he uses to make his case for a war poorly planned and bravely but blindly fought. . . . ' Tom Nissley
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Ricks, Thomas E, The Gamble: General David Petraeus and the American Military Adventure in Iraq, 2006-2008, Penguin Press 2009 Amazon product description: 'The Gamble offers news breaking information, revealing behind-the-scenes disagreements between top commanders. We learn that almost every single officer in the chain of command fought the surge. Many of Petraeus’s closest advisers went to Iraq extremely pessimistic, doubting that the surge would have any effect, and his own boss was so skeptical that he dispatched an admiral to Baghdad in the summer of 2007 to come up with a strategy to replace Petraeus’s. That same boss later flew to Iraq to try to talk Petraeus out of his planned congressional testimony. The Gamble examines the congressional hearings through the eyes of Petraeus and Ambassador Ryan Crocker, and their views of the questions posed by the 2008 presidential candidates.
For Petraeus, prevailing in Iraq means extending the war. Thomas E. Ricks concludes that the war is likely to last another five to ten years—and that that outcome is a best case scenario. His stunning conclusion, stated in the last line of the book, is that “the events for which the Iraq war will be remembered by us and by the world have not yet happened."'
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Ricks, Thomas E, The Gamble: General David Petraeus and the American Military Adventure in Iraq, 2006-2008, Penguin Press HC, The (February 10, 2009)
• Language: English
• ISBN-10: 1594201978
• ISBN-13: 978-1594201974 2009 Amazon product description: 'The Gamble offers news breaking information, revealing behind-the-scenes disagreements between top commanders. We learn that almost every single officer in the chain of command fought the surge. Many of Petraeus’s closest advisers went to Iraq extremely pessimistic, doubting that the surge would have any effect, and his own boss was so skeptical that he dispatched an admiral to Baghdad in the summer of 2007 to come up with a strategy to replace Petraeus’s. That same boss later flew to Iraq to try to talk Petraeus out of his planned congressional testimony. The Gamble examines the congressional hearings through the eyes of Petraeus and Ambassador Ryan Crocker, and their views of the questions posed by the 2008 presidential candidates.
For Petraeus, prevailing in Iraq means extending the war. Thomas E. Ricks concludes that the war is likely to last another five to ten years—and that that outcome is a best case scenario. His stunning conclusion, stated in the last line of the book, is that “the events for which the Iraq war will be remembered by us and by the world have not yet happened."'
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Rose, Paul Lawrence, Heisenberg and the Nazi Atomic Bomb 1939-1945: A Study in German Culture, University of California Press 1998 Amazon Editorial Review
From Booklist
'Of the controversies surrounding the dawn of the atomic age, ranking near the top is the matter of Werner Heisenberg and his team's failure to put a bomb in Hitler's hands. Two principal explanations exist. One view, presented in Thomas Powers' Heisenberg's War (1993), is that Heisenberg hindered research, and, in any event, was not ordered to go all out for the bomb; Rose adopts the opposing contention that Heisenberg failed not because of moral compunctions but because he miscalculated the moderator required by a plutonium-producing reactor and the critical mass for a U235 bomb. That Rose spitefully condemns Powers' popular book as "entirely bogus" indicates the passion he brings to arraigning Heisenberg and his historical defense; and on bomb technology, the strictly technical side, Rose bests Powers. However, his attempted clinching of the argument by digressions into German patriotism and Heisenberg's mindset is too speculative to be convincing. Deeply researched scholarship for serious students.' Gilbert Taylor
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Streater, Raymond F, and Arthur S Wightman, PCT, Spin, Statistics and All That, Princeton University Press 2005 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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The Trinity, Saint, and Edmond Hill (Introduction, translation and notes), and John E Rotelle (editor), The Trinity, New City Press 1991 Written 399 - 419: De Trinitate is a radical restatement, defence and development of the Christian doctrine of the Trinity. Augistine's book has served as a foundation for most subsequent work, particularly that of Thomas Aquinas.
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Wittgenstein, Ludwig, and David Francis Pears, Brian McGuinness, Bertrand Russell
, Tractatus Logico-Philosophicus, Routledge 2001 'This as a most imortant book containing original ideas on a large range of topics, forming a coherent system, which, whether or not it be, as the author claims, in its essentials the final solution of the problems dealt with, is of extraordinary interest and deserves the attention of all philosophers.' Frank Ramsey, 'Critical Notice of L Wittgenstein's Tractatus Logico-Philosophicus', Mind, XXXII, no 128 (October 1923) pp 465-78.
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Papers
| Lederman, Leon, "The God particle et al.", Nature, 448, 7151, 17 July 2007, page 310-312. 'The birth of particle physics -- that is high energy physics -- can be dated to about 1950, offspring of the marriage between nuclear physics and the study of cosmic rays. It exploited techniques and technology from both disciplines, and its objective was to identify the primordial particles of nature -- those from which all matter is made -- and codify the laws of physics that oversee their propperties and social behaviours.'. back |
| Neder, I, N Ofek, Y Chung, M Heiblum, D Mahalu & V Umansky, "Interference between two indistinguishable electrons from independent sources", Nature, 448, 7151, 19 July 2007, page 333 - 337. 'Very much like the ubiquitous quantum interference of a single particle with itself, quantum interference of two independent, but indistinguishable, particles is also possible. For a single particle, the interference is between the amplitudes of the particle's wavefunctions, whereas the interference between two particles is a direct result of quantum exchange statistics. Such interference is observed only in the joint probability of finding the particles in two separated detectors, after they were injected from two spatially separated and independent sources. Experimental realizations of two-particle interferometers have been proposed; in these proposals it was shown that such correlations are a direct signature of quantum entanglement between the spatial degrees of freedom of the two particles ('orbital entanglement'), even though they do not interact with each other. In optics, experiments using indistinguishable pairs of photons encountered difficulties in generating pairs of independent photons and synchronizing their arrival times; thus they have concentrated on detecting bunching of photons (bosons) by coincidence measurements. Similar experiments with electrons are rather scarce. Cross-correlation measurements between partitioned currents, emanating from one source, yielded similar information to that obtained from auto-correlation (shot noise) measurements. The proposal of ref. 3 is an electronic analogue to the historical Hanbury Brown and Twiss experiment with classical light. It is based on the electronic Mach–Zehnder interferometer that uses edge channels in the quantum Hall effect regime. Here we implement such an interferometer. We partitioned two independent and mutually incoherent electron beams into two trajectories, so that the combined four trajectories enclosed an Aharonov–Bohm flux. Although individual currents and their fluctuations (shot noise measured by auto-correlation) were found to be independent of the Aharonov–Bohm flux, the cross-correlation between current fluctuations at two opposite points across the device exhibited strong Aharonov–Bohm oscillations, suggesting orbital entanglement between the two electron beams.. back |
| 't Hooft, Gerard, "The making of the standard model", Nature, 448, 7151, 19 July 2007, page 271 - 273. 'The standard model of particle physics is more than a model. It is a detailed thoery that encompasses nearly all that is known about the subatomic particles and forces in a concise set of principles and equations.. back |
Links
| Antimatter - Wikipedia, Antimatter - Wikipedia, the free encyclopedia, 'In particle physics, antimatter is material composed of antiparticles, which have the same mass as particles of ordinary matter but have opposite charge and other particle properties such as lepton and baryon number, quantum spin, etc. Encounters between particles and antiparticles lead to the annihilation of both, giving rise to varying proportions of high-energy photons (gamma rays), neutrinos, and lower-mass particle–antiparticle pairs. . . . There is considerable speculation as to why the observable universe is apparently composed almost entirely of ordinary matter, as opposed to a more symmetric combination of matter and antimatter. This asymmetry of matter and antimatter in the visible universe is one of the greatest unsolved problems in physics.[2] The process by which this asymmetry between particles and antiparticles developed is called baryogenesis.' back |
| Aquinas 165, Summa I, 28, 1: Are there real relations in God?, 'Reply to Objection 4. Relations which result from the mental operation alone in the objects understood are logical relations only, inasmuch as reason observes them as existing between two objects perceived by the mind. Those relations, however, which follow the operation of the intellect, and which exist between the word intellectually proceeding and the source whence it proceeds, are not logical relations only, but are real relations; inasmuch as the intellect and the reason are real things, and are really related to that which proceeds from them intelligibly; as a corporeal thing is related to that which proceeds from it corporeally. Thus paternity and filiation are real relations in God.' back |
| Aquinas 20, Summa I, 3, 7: Whether God is altogether simple? , 'I answer that, The absolute simplicity of God may be shown in many ways.
First, from the previous articles of this question. For there is neither composition of quantitative parts in God, since He is not a body; nor composition of matter and form; nor does His nature differ from His "suppositum"; nor His essence from His existence; neither is there in Him composition of genus and difference, nor of subject and accident. Therefore, it is clear that God is nowise composite, but is altogether simple. . . . ' back |
| Centers for Disease Control and Prevention, Prescription Drug Overdose on the United States: Fact Sheet, 'Deaths from drug overdose have been rising steadily over the past two decades and have become the leading cause of injury death in the United States.1 Every day in the United States, 120 people die as a result of drug overdose,8 and another 6,748 are treated in emergency departments (ED) for the misuse or abuse of drugs.2 Nearly 9 out of 10 poisoning deaths are caused by drugs.' back |
| Circle group - Wikipedia, Circle group - Wikipedia, the free encyclopedia, 'In mathematics, the circle group, denoted by T (or in blackboard bold by ), is the multiplicative group of all complex numbers with absolute value 1, i.e., the unit circle in the complex plane.' back |
| Clay Millennium Prize - Atiyah, Michael Atiyah Lecture, back |
| Clay Millennium Prize - Tate, Lecture by John Tate, back |
| Dark energy - Wikipedia, Dark energy - Wikipedia, the free encyclopedia, 'In physical cosmology & Astronomy, dark energy is a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe. Dark energy is the most popular way to explain recent observations that the universe appears to be expanding at an accelerating rate. In the standard model of cosmology, dark energy currently accounts for 74% of the total mass-energy of the universe.' back |
| Diffeomorphism - Wikipedia, Diffeomorphism - Wikipedia, the free encyclopedia, 'In mathematics, a diffeomorphism is an isomorphism of smooth manifolds. It is an invertible function that maps one differentiable manifold to another, such that both the function and its inverse are smooth. . . . They are Cr diffeomorphic if there is an r times continuously differentiable bijective function between them whose inverse is also r times continuously differentiable. back |
| Einstein, Podolsky and Rosen, Can the Quantum Mechanical Description of Physical Reality be Considered Complete?, A PDF of the classic paper. 'In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system. In quantum mechanics in the case of two physical quantities described by non-commuting operators, the knowledge of one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these two quantities cannot have simultaneous reality. Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that if (1) is false then (2) is also false, One is thus led to conclude that the description of reality given by the wave function is not complete.' back |
| Elementary particle - Wikipedia, Elementary particle - Wikipedia, the free encyclopedia, 'In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which all other particles are made. In the Standard Model, the quarks, leptons, and gauge bosons are elementary particles.' back |
| Entropy - Wikipedia, Entropy - Wikipedia, the free encyclopedia, 'Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when converting energy to work. During this work, entropy accumulates in the system, but has to be removed by dissipation in the form of waste heat.' back |
| Function space - Wikipedia, Function space - Wikipedia, the free encyclopedia, 'In mathematics, a function space is a set of functions of a given kind from a set X to a set Y. It is called a space because in many applications, it is a topological space or a vector space or both' back |
| Gauge boson - Wikipedia, Gauge boson - Wikipedia, the free encyclopedia, 'In particle physics, gauge bosons are bosonic particles that act as carriers of the fundamental forces of nature.[1][2] More specifically, elementary particles whose interactions are described by gauge theory exert forces on each other by the exchange of gauge bosons, usually as virtual particles.' back |
| Gauge theory - Wikipedia, Gauge theory - Wikipedia, the free encyclopedia, 'In physics, gauge theory is a quantum field theory where the Lagrangian is invariant under certain transformations.
The transformations (called local gauge transformations) form a Lie group which is referred to as the symmetry group or the gauge group of the theory. For each group parameter there is a corresponding vector field called gauge field which helps to make the Lagrangian gauge invariant. The quanta of the gauge field are called gauge bosons.
If the symmetry group is non-commutative, the gauge theory is referred to as non-abelian or Yang-Mills theory.' back |
| Goldstone boson - Wikipedia, Goldstone boson - Wikipedia, the free encyclopedia, 'In particle and condensed matter physics, Goldstone bosons (also known as Nambu-Goldstone bosons) are bosons that appear in models with spontaneously broken symmetry.' back |
| Google.org, Google names Larry Brilliant as Executive Director of Google.org, 'Mountain View, CA - February 22, 2006 - Google Inc. (NASDAQ: GOOG) today announced the appointment of Dr. Larry Brilliant as Executive Director of Google.org, which administers Google's philanthropic activities. In this role he will work with the company's co-founders Larry Page and Sergey Brin to define the mission and strategic goals of Google's philanthropy. Dr. Brilliant is a founder and director of The Seva Foundation, a Policy Advisory Council Member at the University of California, Berkeley School of Public Health, and a member of the Strategic Advisory Group of Kleiner-Perkin's Pandemic and Bio-Defense Fund.' back |
| Google.org, Searching for solutions, 'Google.org aspires to use the power of information and technology to address the global challenges of our age: climate change, poverty and emerging disease. In collaboration with experienced partners working in each of these fields, we will invest our resources and tap the strengths of Google's employees and global operations to advance our initiatives.' back |
| Henry IV, De Haeretico Comburenda, Statutes of the Realm, 2:12S-28: 2 Henry IV: ' . . . and they the same persons and every of them, after such sentence promulgate shall receive, and them before the people in an high place cause to be burnt, that such punishment may strike fear into the minds of others, . . . ' back |
| Higgs boson - Wikipedia, Higgs boson - Wikipedia, the free encyclopedia, 'The Higgs boson or Higgs particle is a proposed elementary particle in the Standard Model of particle physics. The Higgs boson is named after Peter Higgs who, along with others, proposed the mechanism that predicted such a particle in 1964.The existence of the Higgs boson and the associated Higgs field explain why the other massive elementary particles in the standard model have their mass.' back |
| John Wycliffe - Wikipedia, John Wycliffe - Wikipedia, the free encyclopedia, 'Chair Jaimin John Wycliffe . . . also spelled Wyclif, Wycliff, Wiclef, Wicliffe, or Wickliffe) (mid-1320s – 31 December 1384) was an English theologian, lay preacher[1], translator and reformist.' back |
| Ludwig Wittgenstein - SEP, Ludwig Wittgenstein (Standord Encyclopedia of Phlosophy), 'Considered by some to be the greatest philosopher of the 20th century, Ludwig Wittgenstein played a central, if controversial, role in 20th-century analytic philosophy. He continues to influence current philosophical thought in topics as diverse as logic and language, perception and intention, ethics and religion, aesthetics and culture.' back |
| Mass gap - Wikipedia, Mass gap - Wikipedia, the free encyclopedia, 'In quantum field theory, the mass gap is the difference in energy between the vacuum and the next lowest energy state. The energy of the vacuum is zero by definition, and assuming that all energy states can be thought of as particles in plane-waves, the mass gap is the mass of the lightest particle.
Since exact energy eigenstates are infinitely spread out and are therefore usually excluded from a formal mathematical description, a more pedantic definition is that the mass gap is the greatest lower bound of the energy of any state which is orthogonal to the vacuum.' back |
| Method of Fluxions - Wikipedia, Method of Fluxions - Wikipedia, the free encyclopedia, 'Method of Fluxions is a book by Isaac Newton. The book was completed in 1671, and published in 1736. Fluxions is Newton's term for differential calculus (fluents was his term for integral calculus). He originally developed the method at Woolsthorpe Manor during the closing of Cambridge during the Great Plague of London from 1665 to 1667, but did not choose to make his findings known (similarly, his findings which eventually became the Philosophiae Naturalis Principia Mathematica were developed at this time and hidden from the world in Newton's notes for many years).' 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 |
| Renormalization - Wikipedia, Renormalization - Wikipedia, the free encyclopedia, 'In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities.' back |
| Spontaneous symmetry breaking - Wikipedia, Spontaneous symmetry breaking - Wikipedia, the free encyclopedia, 'Spontaneous symmetry breaking is a mode of realization of symmetry breaking in a physical system, where the underlying laws are invariant under a symmetry transformation, but the system as a whole changes under such transformations, in contrast to explicit symmetry breaking. It is a spontaneous process by which a system in a symmetrical state ends up in an asymmetrical state. It thus describes systems where the equations of motion or the Lagrangian obey certain symmetries, but the lowest energy solutions do not exhibit that symmetry. back |
| Tensor - Wikipedia, Tensor - Wikipedia, the free encyclopedia, 'Tensors are geometric objects that describe linear relations between vectors, scalars, and other tensors. Elementary examples of such relations include the dot product, the cross product, and linear maps. Vectors and scalars themselves are also tensors. A tensor can be represented as a multi-dimensional array of numerical values.' back |
| The Fall - Catholic Catechism: 385-421, Catechism of the Catholic Church, '391 Behind the disobedient choice of our first parents lurks a seductive voice, opposed to God, which makes them fall into death out of envy.266 Scripture and the Church's Tradition see in this being a fallen angel, called "Satan" or the "devil".267 The Church teaches that Satan was at first a good angel, made by God: "The devil and the other demons were indeed created naturally good by God, but they became evil by their own doing."' back |
| Turing machine - Wikipedia, Turing machine - Wikipedia, the free encyclopedia, 'Turing machines are extremely basic abstract symbol-manipulating devices which, despite their simplicity, can be adapted to simulate the logic of any computer algorithm (as we understand them). They were described in 1936 by Alan Turing. Though they were intended to be technically feasible, Turing machines were not meant to be a practical computing technology, but a thought experiment about the limits of mechanical computation; thus they were not actually constructed. Studying their abstract properties yields many insights into computer science and complexity theory.' back |
| Wu-Ki Tung, Bjorken scaling - Scholarpedia, 'Bjorken Scaling refers to an important simplifying feature (scaling) of a large class of dimensionless physical quantities in elementary particles, notably the structure functions in deep inelastic scattering, that implies observed strongly interacting particles (hadrons) are made of point-like constituents. It was first proposed by James Bjorken in 1968. This idea, along with the contemporaneous concept of partons by Feynman, and the subsequent experimental discovery of (approximate) scaling behavior, inspired the formulation of Quantum Chromodynamics (QCD), the modern fundamental theory of strong interactions, in 1974. Bjorken scaling is, however, not exact; it is mildly broken. The QCD theory can predict the logarithmic scale-breaking behavior of the relevant physical quantities; and these predictions have been fully confirmed by modern high energy experiments.' back |
| Yang-Mills theory - Wikipedia, Yang-Mills theory - Wikipedia, the free encyclopedia, 'Yang-Mills theory is a gauge theory of quantum field theory based on the SU(N) group. It was formulated by Yang and Mills in 1954[1] in an effort to extend the original concept of gauge theory for an Abelian group, as was quantum electrodynamics, to the case of a nonabelian group with the intention to get an explanation for strong interactions. This initial idea was not a success as the quanta of the Yang-Mills field must be massless in order to mantain gauge invariance but such massless particles should have had long range effects that are not seen in experiments. So, the idea was put aside till the start of 1960 when the concept of breaking of symmetry in massless theories, initially due to Jeffrey Goldstone, Yoichiro Nambu and Giovanni Jona-Lasinio, with particles acquiring mass in this way, was put forward.' back |
| Yoichiro Nambu - Wikipedia, Yoichiro Nambu - Wikipedia, the free encyclopedia, 'Yoichiro Nambu . . . born January 18, 1921) is a Japanese-born American physicist, currently a professor at the University of Chicago. Known for his contributions to the field of theoretical physics, he was awarded the Nobel Prize in Physics in 2008 for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics.' back |
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