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vol VII: Notes

1999

Notes

[Notebook BOOK 4/5/94 DB 50]

[Sunday 2 May 1999 - Saturday 8 May 1999]

[page 259]

Sunday 2 May 1999

ie do the world lines of the Universe fill the whole of the Cantor Universe?

Before the Galilean revolution in our conception of science, theology was the theory of everything. Being the theory of everything, it has greater inertia than any of the other sciences, so it has been very slow in its evolution. Evidence of theology is scripture. In the last century theologians have taken a scientific attitude to scripture, and begun to study the

[page 260]

origins and transmission of the Biblical texts in minute detail.

Monday 3 May 1999

THEOLOGY break from tradition/theology

Rename old home pages -> archives (here to keep old versions of some historical interest)

BUSINESS = securing input the input we want either directly or by exchange, direct or mediated by measurement (eg money)

Basic business system is the alimentary canal.

LOVE

LOVE - POTENTIAL

As in all scientific endeavours, changing the model has no effect on the data in themselves, but by putting them in a new context is gives them new meaning

[page 261]

No symbolic representation can be deterministic because there is an infinity of mappings between symbol and reality.

So the unconditional love of god which is at the core of Christianity easily survives in the new model of god as unconditional love of our environment, which makes existence possible. Environment also conditions (ie communicates with) my life, so some aspects of my environment may not please me.

We are all god together and god is no longer immutable. We can sculpt it to suit ourselves, as long as we treat ourselves and environment with respect and do not make changes that increase rather than decrease the environmental burden on human existence.

Unconditional love of god has a practical output whose most general

 

equilibrium never existed. The Universe is driven by an apparently inexhaustible power ...

[page 262]

In my experience the RCC employs a less optimal model of love in its expansion of Christianity into management.

Arrow leadership. Arrow Leadership

Love -> sculpting the world 1 sculpting people. / 2 sculpting not people.

Take the chosen ones from their families at an early age and put them in the care of previously chosen ones, who are theoretical eunuchs. This condition is expressed in the three vows of poverty, chastity and obedience. I made these three vows, in good faith, as a monk in the Roman Catholic Order of Preachers.

Catholic Order of Preachers.

St Thomas was all heart, taking on the big job. The big bureaucracy.

Rule of law - habeas corporis - identification.

Guardian Weekly.

[page 263]

The dimensions of human space.

energy
information
material

Rotate the axes

Politics Data matching
Data non-matching

Trust in a world wide data base can only come when corruption is overcome.

Consider the internet payments system.

Your card number is encrypted using an algorithm known only to you and your bank. We send this code to the bank together with a request for authorization and receive a simple yes or no, upon which we release/not the goods.

Dispassionate view = delocalized view (ie 'position independent' code).

Where do I stand in all this? The

[page 263]

amount of work to be done seems overwhelming, but as the size of the project grows in my mind, so does its promise, so that it has the potential to carry its own weight.

Steve Jobs.

Is it heaven to be deeply engaged in a task. Attracted by the feeling of achievement at the end if even one person can understand me (ie myself). Clarity comes from long observation.

What do I want? To be heard, ie to have something interesting to say. Why? because this has not happened to me ie I want it in the older sense. More than anything, a religious community? perhaps just a lover? more likely a helpmate to enhance the productivity of everyday life, so that life may become more relaxed. Is that the goal? Not greatly interested in politics except as a means to some (what?) end.

[p 265]

Am I in heaven? If not, what is missing? All is good except for a bit too much anxiety = drivenness = in the grip of a potential. So relaxation will come when the gradient of the potential becomes zero, ie at equilibrium. There is no equilibrium in life, so no point in being anxious about anxiety. Relax, do a good job, and accept the outcome.

So today I made a big fuckup at work, costing about three hours. Eyes off the ball, making the transition from carpenter to intellectual.

Tuesday 4 May 1999

So the ancient religious advice relax, the system will look after you even if (Job) things look really bad. There is no guarantee of that in the old sense of divine providence, but it is still sound advice because the system is so vast that we cannot foresee and control all the possibilities, so we must learn to accept the data and respond flexibly.

Dogma does not help.

Consistency does.

Performance anxiety (life is shortish)

What exactly are we trying to tell everybody? The space of human existence can be much bigger than we think. What is needed to realize this space is creative cooperation: we move from being independent organisms to becoming the cells of one body, and our powers are greatly enriched by the combinations and permutations thus made possible.

This is the fundamental message of religion.

Really I do feel quite content. I feel that the natural religion project p is moving along, and can see that it is better for it to become robust and viable and well formed, than stillborn through prematurity. All that is required is steady work for about another ten years, given all the distance travelled in the last thirty.

[p 267]

The key to my serenity is a reconciliation between dynamic unity and static complexity, ie relating the simplicity of god to the complexity of the observed Universe. A point in a space is a unity whose complexity is measured by the complexity of its spatial matrix = dimensionality?

differentiation | integration
{symbols} whole

QM Dirac transformation theory = permutation theory (groups and QM)

Wednesday 5 May 1999
Thursday 6 May 1999
Friday 7 May 1999

The hardest part of this is continuing in an intellectual vacuum, that is not being able to established links with similarly cultured individuals. (This is written in some ancient diary where I contemplated trying to find the intelligentsia of London.) What is lacking and what I seek is a community devoted to things beyond everyday life. Though I sometimes falter, poverty and loneliness keep me going through the thin spots where the excitement of

[page 268]

what I am seeing is not powerful enough. So the stick grows when the carrot fails, and there is always hope, faith and charity.

. . .

THEOLOGY = the motion of god. Potential and Action are equivalent and oscillate (in the harmonic oscillator) indefinitely.

Finish this article with the problems of god PURE ACT = COMPLETED BEING

Via negativa : words.

TECHNOLOGY The browser is technology, a transformer. 1 TOOL 2 WASTE 3 MIND.

Theology technology of the whole, transform anything into anything.

THEOLOGY 1 Existence of God. 2 Evolution (completion vs progress) (Mind of Go

The Christian edifice is a magnificent hypothesis still embodied by a good

[page 269]

proportion of the world's people, but like the phlogiston theory and the notion that the earth is at the centre of the Universe, it is difficult top fit it to the evidence. As Xian fundamentalists realize, their biggest problem is the theory of evolution. Since the Church has recognized the reality of this theory, it must now begin to come to terms with its consequences.

Saturday 8 May 1999

We have been building a castle in the air, that is a model. Although the castle is rather skeletal, but we have now reached the apex of the theoretical structure, where we meet the force that turns possibilities into reality, love. The second half of the story is grounding this castle so that it becomes reality. The force that turns dreams into reality is love.

Theology is specifically concerned with conscious personal experience. This creates a dichotomy between theology and the other sciences.

[page 270]

There are still some big leaps necessary before we got to theological heaven.

. . ..

Let us suppose that theology is the science whose specific data arise from private conscious experience. Theological data arise form introspection. This specifically differentiates theology from the other sciences. But it raises a fundamental question: How do my experiences of being human relate to this gigantic physical structure I call my body. We know that our mental functions are concentrated in the central nervous system. How does personal experience relate to the physical functioning of the central nervous system.

The traditional answer is that it doesn't.

Descartes founded the present era.

[p 271]

. . .

Stability and the attractors of life.

Stable: resists force and does not change
Labile: responds to force and does change

Quickness of mind: how fast I can process all the puzzles and find the ANSWER ie the INVERSE, so QUESTION x ANSWER = 1.
QUESTION + ANSWER = 0
QUESTION abstract operator ANSWER = I ie answer = q-1.

This is to be our understanding of problem and insight which gives rise to the fundamental 'multiplied' structure of the Universe (quadratic)

To mind of god

The ancients used the versatility of mind to propose a new form of reality called spirit. This was necessary because their model of matter, which made it inert and without structure, made it incompatible with subjective mental experience (pleonasm?)

[page 272]

So god's mind must be omnino immaterial

Our picture of the Universe is somewhat different. We learn from QM that the Universe is an infinite lattice of states which may or may not be occupied by a particle. Such a system is obviously suited to representing data and performing computations on it.

MIND = SUPERPOSITION = NETWORK

Probability density functions on a network.

Just as the unified motion of an engine is a superposition of all its components.

Technology : mapping. The search for insight is a technology.

A dream comes true when all conditions are fulfilled, that is when all the necessary inputs are available from the environment to realize the dream, a chip, a house, a love affair, even reproduction.

[page 273]

Once we have a physical law we have a window to pushing the Universe's buttons.

Make haste slowly. Thee is an optimum rate of development (motion) and life will be most beautiful if everything is adjusted to this rate (Theorem 1)

Statistical mechanics relates energy distributions to probability density functions.

Think of love as an attractor (eg a potential minimum), then to be in love is to be in a state of stable equilibrium. To be out of love is to be in an unstable state (unless the surrounding romantic landscape is perfectly flat) with a tendency to move down the steepest available gradient. [distinguish determined and stochastic systems] Let us postulate that Goedel's theorem requires any sufficiently complex phase space to have undecidable (ie random) patches, so that we experience both stochastic and classical forces, eg genetic vs romantic love. Also stochastic = flat because thee is no environmentally determined direction of motion. All are equally probable. Read E on Brownian

[page 274]

motion. The above looks like a stunning series of insights, helping to open the link between theology and the other sciences, carrying me a big step toward my goal. The measure of the distance I have to travel (on my stochastic path to my new religion)

. . . .

The Transfinite network is the phase space of logic. Its permutational structure means that it can encompass all possible sequences of any conceivable number of symbols.

When I am building, as I labour in the trenches to put in the foundations and underground services, I imagine the structure that is to rise above. As I build I gradually penetrate this space until I have completed the outer envelope of the building.

Few of us can handle n > 3 physical space in our imagination, but Descartes showed us how to convert geometry into arithmetic [and algebra].

[page 275]

. . .

Or is this too detailed. No. Stepping stone to QM which both defines its own states (so we do not need an artificial coordinate system) and predicts probabilities of occupation. Yes, leave it out. They can look in book. We don't avoid technicality here. What must be eliminated is any kind of prejudice or talking down to people. So

. . .

The whole of society maybe modelled by a horse race and a totalizator. Serendipidity. Just read EB 'pari-mutuel'. Editors: Encyclopaedia Britannica

QM is not confined to microscopic systems. If quantum computers are feasible (and it seems so) then quantum states must become macroscopically observable. This is known to happen in BE condensates, but we need a large space of macroscopic states to build a computer. Bose-Einstein Condensate - Wikipedia

The phase space is like a blank page. PHASE SPACE = MEMORY SPACE.

[page 276]

One variable location per dimension, so the memory becomes a vector and a computation becomes a rotation of that vector.

ie

Applying the phase space idea to computation.

How does it feel. I am being ridden by a demanding rider, but at least I have direction. A horse's job is to go where the rider wants it to go.

Reinterpret the doctrine of substance and accidents (Aristotle, Met 11:8). One person's accident is another person's substance, and the whole reality is the superposition of all these points of view.

network = superpositions.

The mind of god is the superposition of all human minds.

[page 277]

>Bayes and conditional probability. The probability of the hypothesis, given the data p(H|D) relates to the prior probability of the hypothesis by

p(H|D) = p(H) p(D|H) / p(H) p(D|H) + p(not H) p(D|not H). Bayes' theorem - Wikipedia

Model -> love Indicative reasoning (Algorithms for detecting the environment)
Love -> model Deontic reasoning (Algorithms for calculating what to do) [Cummins p 40]

At every point supervisory programs (measurers of the gain in fitness provided by any activity) are ordering tasks and subtasks. (ie planning my day) so that I waver between reading (gathering information) writing (recording information) publishing (distributing information) and domestic tasks of multiple sorts from doing dishes to telling stories.

[page 278]

Time budget, self management etc. The longer the planning perspective the tighter the packing of deterministic futures.

Mind is parallel processor (that is a network) responding to varying inputs and outputs. Both inputs and outputs are parallel (eg multiples sensors, multiple muscles), but there must be crosstalk (ie network activity) to unify all these activities into a fit package.

Now my day changes because NN's tank has sprung a leak and dropped all its water.

. . .

My best description of what is going on is that I am babbling. Babies and young songbirds go through a babbling phase when they are learning to make the sounds of their language by using them as toys rather than tools. Understanding comes later. Here I babble furiously, hoping later to talk perfectly coherent mathematical theology. The pieces are around me, but understanding comes slowly. Like a jigsaw, there are the easy edge pieces, the slow midsection and the rush to the finish when pieces are few.

[279]

Model/theory/the tree of life

Data flows in the tree of life. How a tree becomes a network.

New logo: the transfinite tree.

Peer nodes in a tree form a group.

How do we map time tree onto space trees and yield special Relativity? Time division multiplexing vs space division multiplexing (same data)

Sensation is digital and symbolic input just like reading. So what I see as I sit here is a symbolically represented space (landscape) mostly coded as photons.

Matter and form are relative terms.

FORM is

When time division multiplexing + space division multiplexing match, we get reality (p = 1)

[page 280]

There exists a symbolic representation of the world which can be traced in an unbroken line from quantum mechanics to writing such as this.

My lifeline to the outside world is Nature magazine, which I await each week with ?? can't think of the word apprehension? anticipation?

In metaphysical situations the sender may keep a copy of the transmitted message so that the text is multiplied by communication. In physical situations only one copy of each occupied state exists, so that the sender loses (annihilates) its copy when it transmits (creates) it into the receiver. No cloning theorem - Wikipedia

This fact appears as a conservation of fundamental elements of each particle change (ie interactivity) energy, momentum, angular momentum.

Superposition is metaphysical and perhaps explains all complex structure in the Universe.

Copyright:

You may copy this material freely provided only that you quote fairly and provide a link (or reference) to your source.


Further reading

Books

Click on the "Amazon" link below each book entry to see details of a book (and possibly buy it!)

Aquinas, Thomas, Summa Theologica (translated by Fathers of the English Dominican Province), Tabor Publishing 1981 'Brother Thomas raised new problems in his teaching, invented a new method, used new systems of proof. To hear him teach a new doctrine, with new arguments, one could not doubt that God, by the irradiation of this new light and by the novelty of this inspiration, gave him the power to teach, by the spoken and written word, new opinions and new knowledge.' (William of Tocco, T's first biographer) 
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Augustine, 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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Casti, John L, Five Golden Rules: Great Theories of 20th-Century Mathematics - and Why They Matter, John Wiley and Sons 1996 Preface: '[this book] is intended to tell the general reader about mathematics by showcasing five of the finest achievements of the mathematician's art in this [20th] century.' p ix. Treats the Minimax theorem (game theory), the Brouwer Fixed-Point theorem (topology), Morse's theorem (singularity theory), the Halting theorem (theory of computation) and the Simplex method (optimisation theory). 
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Chaitin, Gregory J, Information, Randomness & Incompleteness: Papers on Algorithmic Information Theory, World Scientific 1987 Jacket: 'Algorithmic information theory is a branch of computational complexity theory concerned with the size of computer programs rather than with their running time. ... The theory combines features of probability theory, information theory, statistical mechanics and thermodynamics, and recursive function or computability theory. ... [A] major application of algorithmic information theory has been the dramatic new light it throws on Goedel's famous incompleteness theorem and on the limitations of the axiomatic method. ...' 
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Chaitin, Gregory J, Algorithmic Information Theory, Cambridge UP 1987 Foreword: 'The crucial fact here is that there exist symbolic objects (i.e., texts) which are "algorithmically inexplicable", i.e., cannot be specified by any text shorter than themselves. Since texts of this sort have the properties associated with random sequences of classical probability theory, the theory of describability developed . . . in the present work yields a very interesting new view of the notion of randomness.' J T Schwartz 
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Chaitin, Gregory J, "Goedel's Theorem and Information" in Information, Randomness & Incompleteness: Papers on Algorithmic Information Theory, Reprinted from the International Journal of Theoretical Physics (1982) 22, 941-954., World Scientific 1987 Abstract: 'Goedel's theorem may be demonstrated using arguments having an information-theoretic flavour. In such an approach, it is possible to argue that if a theorem contains more information than any given set of axoms, then it is impossible for the theorem to have been derived from the axioms. In contrast with the traditional proof based on the paradox of the liar, this new viewpoint suggests that the incompleteness phenomenon discovered by Gödel is natural and widespread rather than pathological and unusual.' 
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Clancy, Susan A, The trauma Myth: The Truth About Sexual Abuse of Chiudren-- and its Aftermath, Basic Books 2010 From Booklist 'Clancy argues the controversial position that survivors of childhood sexual abuse are victimized not only by their abusers, whose acts often leave them more confused (due to incomprehension) than frightened, but also and inadvertently by well-intentioned health professionals, whose interpretations of abusive experiences are often more traumatic than actual events and effects. Well-meaning practitioners emphasize abuse’s violence, fear, and threats, which “do not characterize the experiences that most victims have.” Challenging the traumatogenic model’s assumptions and origins, Clancy questions the “repression” concept of “recovered” memories as oddly selective compared to conceptions of other major traumas. Skillfully interweaving case studies, statistics, and technical data, she disputes that abusive acts destabilize neurobiology as in other traumas. Positing that the trauma model damages victims with inaccurate predictions and ineffective treatments, she recommends tracking consequences via cognitive, behavioural, and developmental pathways because “what hurts most victims is not the experience itself but the meaning of the experience—how victims make sense of what happened . . . how these understandings make them feel about themselves and others.”' --Whitney Scott 
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Davis, Martin, Computability and Unsolvability, Dover 1982 Preface: 'This book is an introduction to the theory of computability and non-computability ususally referred to as the theory of recursive functions. The subject is concerned with the existence of purely mechanical procedures for solving problems. . . . The existence of absolutely unsolvable problems and the Goedel incompleteness theorem are among the results in the theory of computability that have philosophical significance.' 
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Davis, Martin, The Undecidable : Basic Papers on Problems Propositions Unsolvable Problems and Computable Functions, Raven Press 1965 Description: '[Includes] ... the basic papers of Gödel, Church, Turing, and Post in which the class of recursive functions was singled out and seen to be just the class of functions that can be computed by terminating processes. Also presented is the work of Church, Turing, and Post in which problems from the theory of abstract computing machines, from mathematical logic, and finally from algebra are shown to be unsolvable in the sense that there is no terminating process for dealing with them. Finally, the book presents the work of Kleene and of Post initiating the classification theory of unsolvable problems. Already the standard reference work on the subject, The Undecidable is also ideally suited as a text or supplementary text for courses in logic, philosophy, and foundations of mathematics.'  
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Dawkins, Richard, Climbing Mount Improbable, W. W. Norton & Company 1997 Amazon editorial review: 'How do species evolve? Richard Dawkins, one of the world's most eminent zoologists, likens the process to scaling a huge, Himalaya-size peak, the Mount Improbable of his title. An alpinist does not leap from sea level to the summit; neither does a species utterly change forms overnight, but instead follows a course of "slow, cumulative, one-step-at-a-time, non-random survival of random variants" -- a course that Charles Darwin, Dawkins's great hero, called natural selection. Illustrating his arguments with case studies from the natural world, such as the evolution of the eye and the lung, and the coevolution of certain kinds of figs and wasps, Dawkins provides a vigorous, entertaining defense of key Darwinian ideas.' 
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Feynman, Richard P, and Robert B Leighton, Matthew Sands, The Feynman Lectures on Physics (volume 3) : Quantum Mechanics, Addison Wesley 1970 Foreword: 'This set of lectures tries to elucidate from the beginning those features of quantum mechanics which are the most basic and the most general. ... In each instance the ideas are introduced together with a detailed discussion of some specific examples - to try to make the physical ideas as real as possible.' Matthew Sands 
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Feynman, Richard P, and Robert B Leighton et al, The Feynman Lectures on Physics (volume 1) : Mainly Mechanics, Radiation and Heat, Addison Wesley 1963 Foreword: 'This book is based on a course of lectures in introductory physics given by Prof. R P Feynman at the California Institute of Technology during the academic year 1961-62. ... The lectures constitute a major part of a fundamental revision of the introductory course, carried out over a four year period. ... The need for a basic revision arose both from the rapid development of physics in recent decades and from the fact that entering freshmen have shown a stewady incrase in mathematical ability as a result of improvements in high school mathematical course content.' 
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Gödel, Kurt, and Solomon Feferman et al (eds), Kurt Gödel: Collected Works Volume 1 Publications 1929-1936, Oxford UP 1986 Jacket: 'Kurt Goedel was the most outstanding logician of the twentieth century, famous for his work on the completeness of logic, the incompleteness of number theory and the consistency of the axiom of choice and the continuum hypotheses. ... The first volume of a comprehensive edition of Goedel's works, this book makes available for the first time in a single source all his publications from 1929 to 1936, including his dissertation. ...' 
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Goedel, Kurt, and B Meltzler (translator), R B Braithwaite (Introduction), On Formally Undecidable Propositions of Principia Mathematica and Related Systems, Dover 1992 A translation of Uber Formal Unentscheidbare Satze der Principia Mathematica und Verwandter Systeme I, Monatshefte fur Mathematik und Physic, 38(1931) 173-198. Jacket: 'In 1931 a young Austrian mathematician published an epoch making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Gödel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will mot give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th century mathematics.' 
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Goedel, Kurt, "On formally undecidable propositions of Principia Mathematica and related systems, I" in Solomon Fefferman et al (eds) Kurt Goedel: Collected Works Volume 1 Publications 1929-1936, Oxford UP 1986 Jacket: 'Kurt Goedel was the most outstanding logician of the twentieth century, famous for his work on the completeness of logic, the incompleteness of number theory and the consistency of the axiom of choice and the continuum hypotheses. ... The first volume of a comprehensive edition of Goedel's works, this book makes available for the first time in a single source all his publications from 1929 to 1936, including his dissertation. ...' 
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Nielsen, Michael A, and Isaac L Chuang, Quantum Computation and Quantum Information, Cambridge University Press 2000 Review: A rigorous, comprehensive text on quantum information is timely. The study of quantum information and computation represents a particularly direct route to understanding quantum mechanics. Unlike the traditional route to quantum mechanics via Schroedinger's equation and the hydrogen atom, the study of quantum information requires no calculus, merely a knowledge of complex numbers and matrix multiplication. In addition, quantum information processing gives direct access to the traditionally advanced topics of measurement of quantum systems and decoherence.' Seth Lloyd, Department of Quantum Mechanical Engineering, MIT, Nature 6876: vol 416 page 19, 7 March 2002. 
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von Campenhausen, Hans, and (English translation revised by L A Garrard), The Fathers of the Greek Church, Adam and Charles Black 1963 Professor of Ecclesiastical History, Heidelberg Universityback
Papers
Shannon, Claude E, "Communication in the Presence of Noise", Proceedings of the IEEE, 86, 2, February 1998, page 447-457. Reprint of Shannon, Claude E. "Communication in the Presence of Noise." Proceedings of the IEEE, 37 (January 1949) : 10-21. '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 this maximum rate are discussed. The equivalent number of binary digits per second of certain information sources is calculated.' . back
Zurek, Wojciech Hubert, "Quantum origin of quantum jumps: Breaking of unitary symmetry induced by information transfer in the transition from quantum to classical", Physical Review A, 76, 5, 16 November 2007, page . Abstract: '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 a framework for 'wave-packet collapse', designating terminal points of quantum jumps and defining the measured observable by specifying its eigenstates. In quantum Darwinism, they are the progenitors of multiple copies spread throughout the environment &mdash the fittest quantum states that not only survive decoherence, but subvert the environment into carrying information about them &mdash into becoming a witness.'. back
Zurek, Wojciech Hubert, "Decoherence, einselection, and the quantum origins of the classical", Review of Modern Physics, 75, , 2003, page 715-775. The manner in which states of some quantum systems become effectively classical is of great significance for the foundations of quantum physics, as well as for problems of practical interest such as quantum engineering. In the past two decades it has become increasingly clear that many (perhaps all) of the symptoms of classicality can be induced in quantum systems by their environments. Thus decoherence is caused by the interaction in which the environment in effect monitors certain observables of the system, destroying coherence between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly nonlocal “Schrödinger-cat states.” The classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit. Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation. Only the preferred pointer observable of the apparatus can store information that has predictive power. When the measured quantum system is microscopic and isolated, this restriction on the predictive utility of its correlations with the macroscopic apparatus results in the effective “collapse of the wave packet.” The existential interpretation implied by einselection regards observers as open quantum systems, distinguished only by their ability to acquire, store, and process information. Spreading of the correlations with the effectively classical pointer states throughout the environment allows one to understand “classical reality” as a property based on the relatively objective existence of the einselected states. Effectively classical pointer states can be “found out” without being re-prepared, e.g, by intercepting the information already present in the environment. The redundancy of the records of pointer states in the environment (which can be thought of as their “fitness” in the Darwinian sense) is a measure of their classicality. A new symmetry appears in this setting. Environment-assisted invariance or envariance sheds new light on the nature of ignorance of the state of the system due to quantum correlations with the environment and leads to Born’s rules and to reduced density matrices, ultimately justifying basic principles of the program of decoherence and einselection.. back
Links
Arrow Leadership, Home - Arrow Leadership, 'Arrow Australia is the premier Christian provider of training, in the non-tertiary sector, for emerging and mature leaders. At Arrow we facilitate development and learning that transforms the lives of tomorrow's leaders today, and shapes how they are able to transform the context of their work/vocation through their ministry and mission. The Arrow Leadership Program was established in Australia in 1995. Since then many groups have progressed though a two-year leadership and spiritual growth program with over 300 graduates.' back
Bayes' theorem - Wikipedia, Bayes' theorem - Wikipedia, the free encyclopedia, 'In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule) relates current to prior belief. It also relates current to prior evidence. It is important in the mathematical manipulation of conditional probabilities. Bayes' rule can be derived from more basic axioms of probability, specifically conditional probability.' back
Bose-Einstein Condensate - Wikipedia, Bose-Einstein Condensate - Wikipedia, the free encyclopedia, 'A Bose–Einstein condensate (BEC) is a state of matter of a dilute gas of bosons cooled to temperatures very close to absolute zero (that is, very near 0 K or −273.15 °C[1]). Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which point macroscopic quantum phenomena become apparent. This state was first predicted, generally, in 1924–25 by Satyendra Nath Bose and Albert Einstein.' back
Bubble chamber - Wikipedia, Bubble chamber - Wikipedia, the free encyclopedia, 'A bubble chamber is a vessel filled with a superheated transparent liquid (most often liquid hydrogen) used to detect electrically charged particles moving through it. It was invented in 1952 by Donald A. Glaser,[1] for which he was awarded the 1960 Nobel Prize in Physics.[2] Anecdotally, Glaser was inspired by the bubbles in a glass of beer; however, in a 2006 talk, he refuted this story, saying that although beer was not the inspiration for the bubble chamber, he did experiments using beer to fill early prototypes.' back
CERN, LHC Homepage, 'The Large Hadron Collider (LHC) sits in a circular tunnel 27 km in circumference. The tunnel is buried around 50 to 175 m. underground. It straddles the Swiss and French borders on the outskirts of Geneva. The first collisions at an energy of 3.5 TeV per beam took place on 30th March 2010. The LHC is designed to collide two counter rotating beams of protons or heavy ions. Proton-proton collisions are foreseen at an energy of 7 TeV per beam. The beams move around the LHC ring inside a continuous vacuum guided by magnets. The magnets are superconducting and are cooled by a huge cryogenics system. The cables conduct current without resistance in their superconducting state. The beams will be stored at high energy for hours. During this time collisions take place inside the four main LHC experiments.' back
Compact space - Wikipedia, Compact space - Wikipedia, the free encyclopedia, 'In mathematics, more specifically general topology and metric topology, a compact space is an abstract mathematical space in which, intuitively, whenever one takes an infinite number of "steps" in the space, eventually one must get arbitrarily close to some other point of the space. Thus a closed and bounded subset (such as a closed interval or rectangle) of a Euclidean space is compact because ultimately one's steps are forced to "bunch up" near a point of the set, a result known as the Bolzano–Weierstrass theorem, whereas Euclidean space itself is not compact because one can take infinitely many equal steps in any given direction without ever getting very close to any other point of the space.' back
Convex set - Wikipedia, Convex set - Wikipedia, the free encyclopedia, 'In Euclidean space, an object is convex if for every pair of points within the object, every point on the straight line segment that joins them is also within the object. For example, a solid cube is convex, but anything that is hollow or has a dent in it, for example, a crescent shape, is not convex.' back
Daniel W Graham - Heraclitus, Heraclitus, 'A Greek philosopher of Ephesus (near modern Kuşadası, Turkey) who was active around 500 BCE, Heraclitus propounded a distinctive theory which he expressed in oracular language. He is best known for his doctrines that things are constantly changing (universal flux), that opposites coincide (unity of opposites), and that fire is the basic material of the world. The exact interpretation of these doctrines is controversial, as is the inference often drawn from this theory that in the world as Heraclitus conceives it contradictory propositions must be true.' back
Editors: Encyclopaedia Britannica, Pare-mutuel, 'Pari-mutuel, ( French: pari, “bet”; mutuel, “mutual”) plural pari-mutuels, or Paris-mutuels, method of wagering introduced in France about 1870 by Parisian businessman Pierre Oller. It became one of the world’s most popular methods of betting on horse races.' back
Erlangen program - Wikipedia, Erlangen program - Wikipedia, the free encyclopedia, 'An influential research program and manifesto was published in 1872 by Felix Klein, under the title Vergleichende Betrachtungen über neuere geometrische Forschungen. This Erlangen Program (Erlanger Programm) — Klein was then at Erlangen — proposed a new solution to the problem how to classify and characterize geometries on the basis of projective geometry and group theory.' back
Hexapla - Wikipedia, Hexapla - Wikipedia, the free encyclopedia, 'Hexapla (Ἑξαπλά: Gr. for "sixfold") is the term for an edition of the Bible in six versions. Especially it applies to the edition of the Old Testament compiled by Origen of Alexandria, which placed side by side: Hebrew Hebrew transliterated into Greek characters Aquila of Sinope Symmachus the Ebionite A recension of the Septuagint, with (1) interpolations to indicate where the Hebrew is not represented in the Septuagint -- these are taken mainly from Theodotion's text and marked with asterisks, and (2) indications, using signs called obeloi (singular: obelus), of where words, phrases, or occasionally larger sections in the Septuagint do not reflect any underlying Hebrew. Theodotion.' back
Holy See, Congregation for the Doctrine of the Faith, Profile: 'CONGREGATION FOR THE DOCTRINE OF THE FAITH Founded in 1542 by Pope Paul III with the Constitution "Licet ab initio," . . . The only curial organism which is older is the Secretariat of State, whose forerunner, the Apostolic Secretariat, was created by Innocent VIII on December 31, 1487, with the Constitution "Non debet reprehensibile." . . . Today, according to Article 48 of the Apostolic Constitution on the Roman Curia, 'Pastor Bonus,' promulgated by the Holy Father John Paul II on June 28, 1988, "the duty proper to the Congregation for the Doctrine of the Faith is to promote and safeguard the doctrine on the faith and morals throughout the Catholic world: for this reason everything which in any way touches such matter falls within its competence." The congregation is now headed by Prefect Cardinal Joseph Ratzinger. It has a secretary, Archbishop Tarcisio Bertone, S.D.B., named June 13, an under-secretary, Msgr. Jozef Zlatnansky, and a staff of 32, according to the 1995 "Annuario Pontificio" or "Pontifical Yearbook." It also has 23 members - cardinals, archbishops and bishops - and 27 consultors. Given the nature of its task, congregation work is divided into four distinct sections: the doctrinal office, the disciplinary office, the matrimonial office and that for priests. back
Homeomorphism - Wikipedia, Homeomorphism - Wikipedia, the free encyclopedia, 'In the mathematical field of topology, a homeomorphism or topological isomorphism (from the Greek words (homoios) = similar and (morph) = shape = form (. . . ) is a bicontinuous function between two topological spaces. Homeomorphisms are the isomorphisms in the category of topological spaces — that is, they are the mappings which preserve all the topological properties of a given space. Two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same.' back
Hypatia - Wikipedia, Hypatia - Wikipedia, the free encyclopedia, 'Hypatia (Greek: Ὑπατία, Hypatía, . . . born between AD 350 and 370; died March 415) was a Greek scholar from Alexandria, Egypt, considered the first notable woman in mathematics, who also taught philosophy and astronomy. She lived in Roman Egypt, and was killed by a Christian mob who falsely blamed her for religious turmoil.[ Some suggest that her murder marked the end of what is traditionally known as Classical antiquity, although others such as Christian Wildberg observe that Hellenistic philosophy continued to flourish until the age of Justinian in the sixth century.' back
IUPAC nomenclature - Wikipedia, IUPAC nomenclature - Wikipedia, the free encyclopedia, 'IUPAC nomenclature is a system of naming chemical compounds and of describing the science of chemistry in general. It is developed and kept up to date under the auspices of the International Union of Pure and Applied Chemistry (IUPAC). ...

This article treats the system of nomenclature in general, notably its aims and historical development. Separate articles treat the naming of organic compounds and inorganic compounds in more detail.' . . .

The primary function of chemical nomenclature is to ensure that the person who hears or reads a chemical name is under no ambiguity as to which chemical compound it refers to: each name should refer to a single substance. It is considered less important to ensure that each substance should have a single name, although the number of acceptable names is limited.' back

John Chrysostom - Wikipedia, John Chrysostom - Wikipedia, the free encyclopedia, 'John Chrysostom (c. 347–407, Greek: Ἰωάννης ὁ Χρυσόστομος), Archbishop of Constantinople, was an important Early Church Father. He is known for his eloquence in preaching and public speaking, his denunciation of abuse of authority by both ecclesiastical and political leaders, the Divine Liturgy of St. John Chrysostom, and his ascetic sensibilities. After his death (or, according to some sources, during his life) he was given the Greek surname chrysostomos, meaning "golden mouthed", rendered in English as Chrysostom.' back
No cloning theorem - Wikipedia, No cloning theorem - Wikipedia, the free encyclopedia, 'The no cloning theorem is a result of quantum mechanics which forbids the creation of identical copies of an arbitrary unknown quantum state. It was stated by Wootters, Zurek, and Dieks in 1982, and has profound implications in quantum computing and related fields.' back
Synesius - Wikipedia, Synesius - Wikipedia, the free encyclopedia, 'Synesius (Greek: Συνέσιος; c. 373 - c. 414), a Greek bishop of Ptolemais in the Libyan Pentapolis after 410, was born of wealthy parents, who claimed descent from Spartan kings, at Cyrene between 370 and 375.' back

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