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Notes

[Notebook Turkey, DB 55]

[Sunday 30 December 2001 - Saturday 5 January 2001]

[page 19]

Sunday 30 December 2001

Murder on the Orient Express: a very strange hypothesis which nevertheless (and by Agatha's design) is consistent with all the evidence, physical and psychological. Christie.

The existence of the 'Cantor transition' shows that any system, no

[page 20]

matter how small (and binary is our base, since 1n = 1, so 1 will not do. In the reals, any n > 1 will do) can, through combination and permutation, grow into a system of unlimited size. We have seen how binary processing has grown to encompass the world.

The technical side of this story is very succinct. Applying it to the real world, or better, fitting it to the real world is the time consuming part. In the end the model will find favour when each of many people find that it fits every little circumstance in their life and provides a respectable estimate of the best thing to do in the circumstances. From a marketing point of view we proceed by testimonials and word of mouth. Since I am promoting this plan the first thing to do is to show its application in my own life.

This is done, in general terms, by the difference between the painful life reflected in the early notebooks and the gradual quiescence as a new post-Catholic view began to grow in me and find formal expression in the transfinite network. The transfinite network provides a outline of meaning (heuristic structure) for all my experience. Most particularly it shows that I am a partly free agent in a divine world, and consequently (if I extend the same concept to everybody) it is within our power to build heaven on earth, that is to correct all the errors of human existence (ie war, disease, poverty, hatred etc) to whatever degree of fineness we choose simply by constraining ourselves to the minimal disciplines required for error free communication.

Nevertheless, writing down the technicalities is taking a long time. At present I am going through my notebooks trying to see the history of my development in order to discover the best starting point for an exposition of my position (expression of my state vector). These notebooks are in effect data for my thesis, and hence my decision to publish excerpts despite their banality. Raw data, in general, makes up in volume for what it lacks in easily discernible interpretation.

[page 21]

Concrete divinity is incompressibly complex (and so apparently random), so that every event (point, moment) is unique and meaningful (as Lonergan requires of god). Chaitin, Lonergan. The difference here (my Copernican Revolution) is not in the data but in the model. The potency-act model used by Thomas and Lonergan is wrong in that it makes act prior to potency, when they are in fact just two equal (peer) manifestations of the same thing (energy). Aquinas. Here again, we have [historically] confused the model and the reality and preferred the model over the reality [idealism]. We are constrained to act on our models, which we have derived from the real and tested in action. But as the differences between Newton and Einstein show, two entirely different models may be observationally indistinguishable over quite a wide range of conditions, but ultimately we will find situations (eg black holes) where the differences are manifest.

Physics puts potential and kinetic energy on the same footing, and integrates their difference through the lifetime of an event to arrive at a [numerical] measure of the event called the Lagrangian. It finds, after careful measurement of many events, that nature acts so as to bring the Lagrangian to an extreme value (maximum or minimum). What actually transpires in an event is determined by the form of the potential associated with the event and potential energy becomes kinetic and vice versa according to the constraints imposed by potential and extremalisation.

We can represent a potential by a string of symbols. This text sets up a potential which moves your mind. The form or shape of this potential arises from my mind as I try to capture in English the form of my mind. I encode the potential, you decode the potential. What I have written may or may not move you, depending on whether you read it or not and how you read it. All interactions involve two or more potentials (eg the orbits of the components of the solar system are a product of the gravitational potential that they collectively create). This potential is dominated by the sun, but planets, moons, asteroids and even dust all add their share of influence and collectively move according to the changing form of the potential thus created.

And it is clear from our own experience that

[page 22]

in any human interaction, all those present contribute to the potential milieu in which they move. This paradigm can extend to large numbers of people, nations or a planet. And it is clear that the quality of life of individuals in a collective depends very much on the form (esprit de corps) of the collective.

A computing machine is an arrangement of potentials that transforms an input vector (of particles coupled to the machine potentials) into an output vector.

Monday 31 December 2001
Tuesday 1 January 2002

Having spent the best part of December contemplating web publication of these notes verbatim as a data set for the theology page. I have decided against it [and changed my mind again later]. First, they are far too voluminous and fragmented. And second, unintelligible and often banal, reflecting the minutiae of experience that can best be accessed by general reference to the experiences of the reader. Also much of it seems to have a whingeing tone which, while it represents the pains that I have suffered in coming to terms with the world, is not necessarily part of the solution.

Waffling around with the notes has been valuable and it is interesting to see in retrospect how quietly each new element of the model has crept in even though many of the insights were very exciting at the time of occurrence. Rather than subjecting the reader to the confusing course I followed to get here, I would do a lot better to be able to produce an ordered and scientifically neutral account of my theological model of the world. This means a formal exposition, which means also some concentrated thought and writing. So we drop Notebooks but keep Synopsis and History.

Another advantage of this decision is that I am no longer writing here for publication, and so can be more honest, keeping the human personal details of The Theology Company behind the veil of incorporation where it belongs and dealing with the outside world through the medium of published literature in every medium and genre that is available.

And I don't want everyone reading some of the stuff I've written in these books, at least till I am dead. I thought for a while that it might be necessary to put up with this embarrassment in order to chart my course, but now I see that public resources are far richer and more appropriate through having undergone careful distillation by their editors, reviewers and authors. I can exhibit myself in the present by dancing or talking, and it is where I am that counts.

Back again to the 'article' which has been in preparation now for about twenty years, but I have been unable to dissect it out of its passionate matrix, so I can't help slagging the Church. We have to grow out of that and approach the whole question in a formal manner, taking the problems and their proposed solutions as they comes.

Science, as it is practised by people publishing papers in (eg) Nature has two distinct phases, which we might call modelling and fitting.

Wednesday 2 January 2002

Let the summary follow the outlines of the Summa, highlighting the differences between us and Thomas. Aquinas.

One worries a bit. I am getting older and perhaps losing my powers. But losses are balanced by gains: a slower mind and body by a wiser and more methodical approach. Wiser means dealing with more complex situations, ie avoiding unnecessary symmetrization. Method: don't panic.

Thinking time overcomes panic because it shows how good may be done and evil (error) avoided. Engineers and the like are concerned with the avoidance of error, while artists are dreaming up the goods to be constructed, like perhaps peace, happiness, etc. Part of our problem here comes from our rather strong and dangerous relationship with nature (which is threatening to burn us out), but part of it also comes from our relationship with one another. Something which could change much more rapidly (because of its abstract nature - lightness.

[page 24]

So the Theology Company is devoted to bringing about a sort of phase change in human attitudes to one another by altering the thermodynamic conditions under which people operate. This is called the cooperation/competition boundary.

TTC competes by cooperating and vice versa, like all other organisms. This situation is possible, because effective cooperation can yield net gain to all.

What is our goal? Let us say happy people living sustainably. This is a stable situation, to, in dynamic terms the goal of theology is to seek stable social and educational situations in the space determined by human nature and the nature of the planet.

This all seems high falutin', but can be made practical by finding algorithms at local level that 'complete' the process, like driving in a nail. The broad proposition is 'institute some degree of communal sharing = bonding'. So the global tax network.

What will this achieve? Should we devote the whole of TTC to this proposition.

The Theology Company - Prospectus.

Economic activity is based on the use of various resources to achieve certain ends. These ends fall into two classes which we might call agent and product. The agent (we assume) is concerned to achieve its own survival and growth. To do this it needs certain inputs (products) from other agents in the system (economy).

This book applies the methods of physics to the problems of theology. That such an approach is possible tells us a lot about the nature of our world. What we see around us and within us are structures with layer after layer of complexity, beginning as an undifferentiated point (the initial singularity) and expanding through

[page 25]

time into unlimited complexity. From a physical point of view the point of maximum complexity is the classical heat death scenario, when every point in the Universe is at the same temperature and its entropy is at a maximum. Such a point is a long way off. From a theological point of view, heat death is not the point of maximum entropy, but rather some other more structured state whose complexity (entropy) comes from ordered structure rather than sheer mass. Here we have the fundamental structural component in our Universe, the relationship between numbers and their more powerful representation as exponents and logarithms. These things are operations that distinguish points in spacetime.

We model the logical NOT with physical ORTHOGONALITY.

A is not-B tells us just one point in A's existence, B, where it is not. It tells us nothing about all the other points in the Universe, U, of which A and B are part. We distinguish Universes by their cardinal numbers aleph(n), so to say A = not-B in aleph(n) is to determine one out of aleph(n) points relative to another.

The only point that is defined in [the peer group with cardinal number] aleph(n) is aleph(n-1), the cardinal of the set from which it is derived. So in any cardinal peer group aleph(n) we can define not-aleph(n) as the point aleph(n-1) from which it was generated. By this means we are able to say that the peer groups aleph(not = n) are all orthogonal to aleph(n), but this must also take into account that aleph(n) contains aleph(< n). This is overcome by noticing that naming sets by their cardinal numbers is very abstract. In the concrete world the transfinite ordinal numbers are large enough to map onto the space of real events and their meanings.

The fact that the fundamental theological position of the Christian religion is false (if it is true) means that in a consistent Universe, no evidence can be found in favour of it. In other words the only way that it can be maintained in existence is violence. It shares this feature with many other false theological, religious, political and economic beliefs and practices. The authoritarian and self-

[page 26]

serving attitude that lies behind these defenses of the indefensible appear to be the source of all the violence on earth. In contrast, it may be postulated, beliefs and actions that are true to the nature of reality lead away from violence to peace.

The violence need not be physical. It can be psychological, and takes the general form of those in authority refusing to listen to their subjects. This appears to be the central feature of the Australian Catholic University's response to ideas put to it: they are beyond hearing. Outside the pale. Heresy.

But heresy means sticking to something counterfactual as described above. One does not have to stick to the truth, but flows along with it. TTC is the good guys, RCC are the heretics. But to make this stick requires a bit of very clear and faultless science, which is not yet available to me though the general drift is there. Is the Universe Divine can be divided into many questions, the first of which are how big is god? and Is the Universe as big as god?

So how big is god? We begin with the transfinite neural network. Is this as big as god? God contains all possible reality, that is (we shall say) all possible structure. Now the term structure implies complexity, and it is well established that god is omnino simplex. How does one measure a perfectly simple thing? The digression to deal with this question deals with the relationship of static and dynamic structure, revealing the orthogonal spectra of complexity and lifetime, the Universe of frequency,

Understanding, lifetime and the eternity of science. When I come back from Turkey all this will be just that much clearer.

We can learn about things by looking at them, as it were, from a great height. Since the beginning of recorded

[page 27]

history, people have been trying to stand far enough back from life on earth to get a good glimpse of what it is all about. The scientific method is aimed to give us the greatest possible independence from preconceptions about the world around us. It achieves independence by relying on the data alone, giving secondary importance to the way the data are currently classified and understood. So TTC is open to hypotheses that Christianity will not consider.

Science is the study of connection = communication through spacetime.

Thursday 3 January 2002
Friday 4 January 2002

Is the Universe as big as god? Quantum computation, fitted to the transfinite network, says yes. Could this be wrong? We begin at the coarsest level, studying peer particles classified by cardinal number, ie the naturals and the alephs, which are images on one another. Behind the cardinal structure, and explaining it, is the ordinal structure. Its first task must be to explain special relativity.

Special relativity tells us the consequences of the fact that communications in spacetime are ordered locally but not globally. Something like this, but arguments about simultaneity apply to all systems where distance is measured by delay, in some way. This can be seen as spatial distance measuring how different structures are and time distances being the number of operations need to convert one into the other.

ACT = {CREATION, ANNIHILATION} with conservation of c (velocity of light) h (quantum of action) energy, momentum, spin and a whole lot of other 'constants'. Both creation and annihilation are proper to the divinity, and so QM falls in naturally with the idea that the Universe is divine.

The clincher (it must be) is that the qubit is a universal computer in the Turing etc sense, on the assumption that the complex numbers are really ordered pairs of real numbers. Lo.

And why not?

Complex numbers are operators in Hilbert space, and can be expanded by constructing more dimensions, ie independent degrees of freedom, into a structure as big as the transfinite network.

Saturday 5 January 2002

Related sites:


Concordat Watch
Revealing Vatican attempts to propagate its religion by international treaty

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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!)

Christie, Agatha, Murder on the Orient Express, Berkley Publishing Group 2000 Amazon: 'This beautifully crafted murder mystery ranks among Agatha Christie's finest. The dapper Belgian detective finds himself investigating the murder of an American businessman on board the Simplon Orient Express. The death occurs in a a manner that implicates one of the twelve passengers in the Stamboul-Calais coach. Poirot carefully interviews the suspects, all of whom have cast-iron alibis. The case appears impossible to solve, until Poirot, using nothing but his wits and a few tiny, seemingly insignificant clues (including a monogrammed handkerchief, a pipe-cleaner, and a Hungarian passport), assembles one of his most brilliant explanations.' A reader from Anaheim, California. 
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Clark, Edmund M., and Orna Grumberg, Doron A. Peled, Model Checking, MIT Press 1999 Jacket: 'Model checking is a technique for verifying finite-state systems such as sequential circuit designs and communication protocols. It has a number of advantages over traditional approaches that are based on simulation, testing and deductive reasoning. In particular model checking is automatic and usually quite fast. Also, of the design contains an error, model checking will produce a counter=example that can be used to pinpiont the error. . . . ' 
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Hardy, Godfrey Harold, and C P Snow (foreword), A Mathematician's Apology, Cambridge University Press 1940-2008 Jacket: G H Hardy was one of the twentieth century's finest mathematical thinkers, renowned among his contemporaries as 'a real mathematician . . . the purest of the pure'. This 'apology', written poignantly as his mathematical powers were declining, offers a brilliant and engaging account of mathematics as very much more than science, When it was first published, Graham Greene hailed it alongside Henry James's notebooks as 'the best account of what it is like to be a creative artist. C P Snow's foreword gives sympathetic and witty insights into Hardy's ife, with its rich store of anecdotes concerning his academic life as well as his passion for cricket.' 
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Khinchin, A I, Mathematical Foundations of Information Theory (translated by P A Silvermann and M D Friedman), Dover 1957 Jacket: 'The first comprehensive introduction to information theory, this book places the work begun by Shannon and continued by McMillan, Feinstein and Khinchin on a rigorous mathematical basis. For the first time, mathematicians, statisticians, physicists, cyberneticists and communications engineers are offered a lucid, comprehensive introduction to this rapidly growing field.' 
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Lo, Hoi-Kwong, and Tim Spiller, Sandra Popescu, Introduction to Quantum Computation and Information, World Scientific 1998 Jacket: 'This book provides a pedagogical introduction to the subjects of quantum information and computation. Topics include non-locality of quantum mechanics, quantum computation, quantum cryptography, quantum error correction, fault tolerant quantum computation, as well as some experimental aspects of quantum computation and quantum cryptography. A knowledge of basic quantum mechanics is assumed.' 
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Lonergan, Bernard J F, Insight : A Study of Human Understanding (Collected Works of Bernard Lonergan : Volume 3), University of Toronto Press 1992 '... Bernard Lonergan's masterwork. Its aim is nothing less than insight into insight itself, an understanding of understanding' 
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Sacks, Oliver, Uncle Tungsten: Memories of a Chemical Boyhood, Vintage 2002 Amazon editorial review From Publishers Weekly 'Sacks, a neurologist perhaps best known for his books Awakenings (which became a Robin Williams/Robert De Niro vehicle) and The Man Who Mistook His Wife for a Hat, invokes his childhood in wartime England and his early scientific fascination with light, matter and energy as a mystic might invoke the transformative symbolism of metals and salts. The "Uncle Tungsten" of the book's title is Sacks's Uncle Dave, who manufactured light bulbs with filaments of fine tungsten wire, and who first initiated Sacks into the mysteries of metals. The author of this illuminating and poignant memoir describes his four tortuous years at boarding school during the war, where he was sent to escape the bombings, and his profound inquisitiveness cultivated by living in a household steeped in learning, religion and politics (both his parents were doctors and his aunts were ardent Zionists). But as Sacks writes, the family influence extended well beyond the home, to include the groundbreaking chemists and physicists whom he describes as "honorary ancestors, people to whom, in fantasy, I had a sort of connection." Family life exacted another transformative influence as well: his older brother Michael's psychosis made him feel that "a magical and malignant world was closing in about him," perhaps giving a hint of what led the author to explore the depths of psychosis in his later professional life. For Sacks, the onset of puberty coincided with his discovery of biology, his departure from his childhood love of chemistry and, at age 14, a new understanding that he would become a doctor. Many readers and patients are happy with that decision. (Oct.)Forecast: This book is as well-written as Sacks's earlier works, and should get fans engrossed in the facts of his life and opinions. Look for an early spike on the strength of his name, and strong sales thereafter.' Copyright 2001 Cahners Business Information, Inc. 
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Saint Aubyn, Alan, and Walt Wheeler, A Fellow of Trinity, British Library, Historical Print Editions 2011  
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Shannon, Claude, and Warren Weaver, The Mathematical Theory of Communication, University of Illinois Press 1949 'Before this there was no universal way of measuring the complexities of messages or the capabilities of circuits to transmit them. Shannon gave us a mathematical way . . . invaluable . . . to scientists and engineers the world over.' Scientific American 
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van der Waerden, B L, Sources of Quantum Mechanics, Dover Publications 1968 Amazon Book Description: 'Seventeen seminal papers, dating from the years 1917-26, in which the quantum theory as wenow know it was developed and formulated. Among the scientists represented: Einstein,Ehrenfest, Bohr, Born, Van Vleck, Heisenberg, Dirac, Pauli and Jordan. All 17 papers translatedinto English.' 
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von Neumann, John, and Robert T Beyer (translator), Mathematical Foundations of Quantum Mechanics, Princeton University Press 1983 Jacket: '. . . a revolutionary book that caused a sea change in theoretical physics. . . . JvN begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which JvN regards as the definitive form of quantum mechanics. . . . Regarded as a tour de force at the time of its publication, this book is still indispensable for those interested in the fundamental issues of quantum mechanics.' 
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Weisberg, Robert W, Creativity: Genius and Other Myths, W H Freeman 1985 Jacket: .In Creativity: Genius and Other Myths, Robert Weisberg shows that much of what we believe about creativity is not true. Beginning with an example of a creative solution to a simple real-life problem, he analyzes the traditional literature, arguing that creative responses evolve through a straight forward series of concious steps. 
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Papers
Chaitin, Gregory J, "Randomness and Mathematical Proof", Scientific American, 232, 5, May 1975, page 47-52. 'Although randomness can be precisely defined and can even be measured, a given number cannot be proved random. This enigma establishes a limit in what is possible in mathematics'. 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
Links
Camille Jordan - Wikipedia Camille Jordan - Wikipedia, the free encyclopedia 'Marie Ennemond Camille Jordan (January 5, 1838 – January 22, 1922) was a French mathematician, known both for his foundational work in group theory and for his influential Cours d'analyse. He was born in Lyon and educated at the École polytechnique. He was an engineer by profession; later in life he taught at the École polytechnique and the Collège de France, where he had a reputation for eccentric choices of notation.' back
Church-Turing thesis - Wikipedia Church-Turing thesis - Wikipedia, the free encyclopedia back
J B S Haldane - Wikipedia J B S Haldane - Wikipedia, the free encyclopedia 'John Burdon Sanderson Haldane FRS (5 November 1892 – 1 December 1964[1]), known as Jack (but who used 'J.B.S.' in his printed works), was a British-born geneticist and evolutionary biologist generally credited with a central role in the development of neo-Darwinian thinking (popularized by Richard Dawkins' 1976 work titled The Selfish Gene). A staunch Marxist, he was critical of Britain's role in the Suez Crisis, and chose to leave Britain, move to India and become an Indian citizen. He was also one of the founders (along with Ronald Fisher and Sewall Wright) of population genetics.' back
Lancelot Hogben - Wikipedia Lancelot Hogben - Wikipedia, the free encyclopedia 'Lancelot Thomas Hogben FRS[1] (9 December 1895 – 22 August 1975) was a versatile British experimental zoologist and medical statistician. He is best known for developing the African clawed frog (Xenopus laevis) as a model organism for biological research in his early career, attacking the eugenics movement in the middle of his career, and popularising books on science, mathematics and language in his later career.' back
Motorola 6809 - Wikipedia Motorola 6809 - Wikipedia, the free encyclopdia 'The Motorola 6809 is an 8-bit (with some 16-bit features) microprocessor CPU from Motorola, designed by Terry Ritter and Joel Boney and introduced 1978. It was a major advance over both its predecessor, the Motorola 6800, and the related MOS Technology 6502.' back
Ordinal number - Wikipedia Ordinal number - Wikipedia, the free encyclopedia 'In set theory, an ordinal number, or just ordinal, is the order type of a well-ordered set. They are usually identified with hereditarily transitive sets. Ordinals are an extension of the natural numbers different from integers and from cardinals. Like other kinds of numbers, ordinals can be added, multiplied, and exponentiated. Ordinals were introduced by Georg Cantor in 1883 to accommodate infinite sequences and to classify sets with certain kinds of order structures on them. He derived them by accident while working on a problem concerning trigonometric series—see Georg Cantor.' back
Renormalization group - Wikipedia Renormalization group - Wikipedia, the free encyclopedia 'In theoretical physics, renormalization group (RG) refers to a mathematical apparatus that allows one to investigate the changes of a physical system as one views it at different distance scales. In particle physics it reflects the changes in the underlying force laws as one varies the energy scale at which physical processes occur. A change in scale is called a "scale transformation" or "conformal transformation." The renormalization group is intimately related to "conformal invariance" or "scale invariance," a symmetry by which the system appears the same at all scales (so-called self-similarity).' back

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