natural theology > notes

Notes

[Notebook: DB 57 Language]

[Sunday 26 June 2005 - Saturday 2 July 2005]

[page 165]

Sunday 26 June 2005

Monday 27 June 2005

Tuesday 28 June 2005

Wednesday 29 June 2005

Science works because we can do the 'same things' over and over again. But every event in the Universe is unique, up to a point. There are symmetries in the Universe which give meaning to terms like same, similar, identical etc (even identical twins are unique, as is every particle interaction which ever has or ever will occur in the life of the

[page 166]

Universe. A model of the Universe (for natural theology a model of god) must be able to deal with this complexity. The structure we propose for the purpose is the Cantor Universe (CU) which we construct from a set of natural numbers. For practical purposes we can represent the set of all natural numbers (to which Cantor assigned the first transfinite cardinal ℵ₀) by any set with two or more elements.

Each set of natural numbers has a cardinal number. Finite sets have cardinal numbers like 0 (the empty set), 5 (the set of fingers remaining on my right hand) or n. For the set of all natural numbers, n = ℵ₀. Any set of natural numbers has a natural order starting with the smallest and growing toward the largest. Given any particular number from a set, we can, by examining the chosen number and all the other numbers, assign the chosen number to its proper place in the order. This property arises from our definition of cardinals by sets of objects.

From this basic order of a set of numbers, we can create permutations, that is reorderings of the numbers. We can achieve any possible reordering by swapping pairs of numbers. The number of permutations if n objects is n!, ie n x (n-1) x . . . x2 x 1. The cardinal of the set of permutations of a set is generally greater than the permuted set (which we will call the alphabet of the permutation). The cardinal of the set if permutations of an alphabet whose cardinal is ℵ₀ is the second transfinite cardinal, ℵ₁. These permutations have a natural

[page 167]

(alphabetical) order and so themselves can become the alphabet of a set of permutations measured by the third transfinite cardinal, ℵ₂, and so on without end, even unto transfinite subscripts on the transfinite symbols.

Alphabets make words, words sentences, sentences books and so on until we come to the level of complexity which we will label 'literature'. We may then thing of the CU as the space in which to define a literature.

Having defined a space that (we hypothesis) is large enough to address every event at every scale in the life of the Universe, we must now see if we can understand if we can see how this addressing works by fitting it to the Universe of experience. The proposed interface between the CU and everyday experience is the transfinite network.

It is customary to thing of abstract networks as two dimensional groups of nodes and edges joined in some subset of all possible ways. Real networks, however, are three dimensional structures because they are layered. At the bottom we have the physical layer, copper, silicon, photons, electrons and so on. On top of the physical layer network designers build layers of software that reach up to the user layers. An ISO standard, for instance, postulates seven layers of processing between physics and the user. Tanenbaum, USSG - Indiana University

[page 168]

First error correction, then transmission protocols etc. The user's input must bore down to the physical layer, travel whatever distance and then burrow back up to the user's output

Now we assume that all the in formation traded in the Universe is encoded and transmitted in physical form. Landauer

Now let u equate the physical layer and the natural numbers. This is equation is made possible by the observation that every observable event in the Universe involved at least one quantum of action. No smaller events are observed. Their discreteness renders the events of the Universe countable and so we assume that they can be placed into correspondence with some set of natural numbers.

So let the alphabet of discrete events in the life of the Universe has ℵ₀ elements. The physical observation of discrete (quantum) events (particles) in the Universe is supported by the mathematical theory of communication. The role of error correcting codes in communication theory is to make the distance between valid codewords so great that there is a suitable infinitesimal chance of confusion. If the role of the physical events in the world is communication, we would expect to find a fundamental alphabet of discrete events.

In the General Scholium of the Principia, Newton gave the role of designing and sustaining the physical Universe he had revealed to God, conceived in the classical Christian model. The quantum

[page 169]

mechanical version of God is the wave function of the Universe, an abstract piece of mathematical machinery that gives us a rather miraculously useful description of what selects the events we see from the ones we don't.

We get from the CU to quantum mechanics via the idea of function space realized as Hilbert space.

The Hamiltonian for a permutation, ie order 1 to order w. Hamiltonian matrix gives us all possible transitions. [matrix representation of the permutation or symmetric group Higman]

Thursday 30 June 2005

A mind is a superposition of all the things that it could say. So an atom is the superposition of an infinity of states which are revealed by the infinity of different photon frequencies that it can emit and absorb. Minds form the nodes of our network, and these nodes communicate by exchanging physical states, like this writing. The physical systems know nothing of the 'meaning' of the information they carry. The meaning is a property of the minds using certain algorithms to encode and decode the messages they exchange. A related set of communication algorithms may be understood as a language. The languages we see around us include the deterministic languages of conventional computers (ie assemblers, C, Perl etc) a the way to the rather indeterminate languages of music, love and so on.

Asking questions is a way of perturbing fixed energy states in order to increase the probability of transitions between them. Feynman ammonia maser. Feynman

[page 170]

Intuitive quantum mechanics - not Newtonian biffo, but the subtle interaction of complex processes.

Friday 1 July 2005

Saturday 2 July 2005

Related sites

Concordat Watch

Revealing Vatican attempts to propagate its religion by international treaty

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

Arsan, Emanuelle, and Lowell Blair (translator), Emanuelle, Grove Press 1994 'This now classic book of erotica is, alongside Story of O, the most famous French underground novel of the late twentieth century and a work of seductive literary merit. Written by the wife of a diplomat in the French Foreign Service, it takes the form of an autobiographical novel, which it may or may not be.'
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Berndt, Ronald M, Love Songs of Arnhem Land, 1978 Jacket: Love Songs of Arnhem Land is a contribution towards an increasing interest within and outside Australia in understanding Australian Aboriginal Culture. . . . The song-poetry itself is hauntingly beautiful. Its traditional imagery creates a special and unique atmosphere. Men and women are agents in a divine plan in which they play a crucial role, working in harmony with the forces of nature symbolized by the mythic beings. . . . '
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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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Higman, Bryan, Applied Group-Theoretic and Matrix Methods, Dover Publications Jacket: '... This work, a comprehensive, thoroughly reliable exposition of the basic ideas of group theory (realized through matrices) and its applications to various areas of physics and chemistry, systematically covers this important ground for the first time. ... Although [it] deals basiclaly with advanced level material, the unusually clear exposition provides much valuable insight and fruitful suggestion for student and specialist alike. Chemists, physicists, mathematicians, and others who would like an idea of the applications and methods of group and matrix theory in the physical sciences will profit greatly from this book. ...'back

Kanigel, Robert, The Man Who Knew Infinity: A life of the genius Ramanujan, Washington Square Press 2016 'In 1913, a young unschooled Indian clerk wrote a letter to G H Hardy, begging the preeminent English mathematician's opinion on several ideas he had about numbers. Realizing the letter was the work of a genius, Hardy arranged for Srinivasa Ramanujan to come to England. Thus began one of the most improbable and productive collaborations ever chronicled. With a passion for rich and evocative detail, Robert Kanigel takes us from the temples and slums of Madras to the courts and chapels of Cambridge University, where the devout Hindu Ramanujan, "the Prince of Intuition," tested his brilliant theories alongside the sophisticated and eccentric Hardy, "the Apostle of Proof." In time, Ramanujan's creative intensity took its toll: he died at the age of thirty-two and left behind a magical and inspired legacy that is still being plumbed for its secrets today.
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Mayer, Jane, Dark Money, Doubleday 2016 ' . . . Jane MAyer shows in this powerful, meticulously reported history, a network of exceedIngly wealthy people with extreme libertarian views bankrolled a systematic, step-by-step plan to fundamentally alter the American political system.'
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Miles, Jack, God: A Biography, Vintage Books 1996 Jacket: 'Jack Miles's remarkable work examines the hero of the Old Testament . . . from his first appearance as Creator to his last as Ancient of Days. . . . We see God torn by conflicting urges. To his own sorrow, he is by turns destructive and creative, vain and modest, subtle and naive, ruthless and tender, lawful and lawless, powerful yet powerless, omniscient and blind.'
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Misner, Charles W, and Kip S Thorne, John Archibald Wheeler, Gravitation, Freeman 1973 Jacket: 'Einstein's description of gravitation as curvature of spacetime led directly to that greatest of all predictions of his theory, that the universe itself is dynamic. Physics still has far to go to come to terms with this amazing fact and what it means for man and his relation to the universe. John Archibald Wheeler. . . . this is a book on Einstein's theory of gravity. . . . '
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Popper, Karl Raimund, The Open Society and its Enemies (volume 2) : The High Tide of Prophecy, Hegel, Marx and the Aftermath, Routledge 1966 Jacket: '... "a work of first-class importance which ought to be widely read for its masterly criticism of the enemies of democracy, ancient and modern. His attack on Plato, while unorthodox, is in my opinion thoroughly justified. His analysis of Hegel is deadly. Marx is dissected with equal acumen, and given his due share of responsibility for modern misfortunes. The book is a vigorous and profound defence of democracy, timely, very interesting andf very well written".' Bertrand Russell
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Riefenstahl, Leni, People of Kau, Harpercollins 1976 'This is a photographic monograph on the life of the people of Kau. Leni Riefenstahl spent 16 weeks with the Nuba of Kau in 1975. These people, known as the " South East Nuba" , live only 100 miles away from the Mesakin Nuba. Yet, they speak another language, follow different customs, and are very different in character and temperament. The knife-fights, dances of love and elaborately painted faces and bodies are photographed in the book.'
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Tanenbaum, Andrew S, Computer Networks, Prentice Hall International 1996 Preface: 'The key to designing a computer network was first enunciated by Julius Caesar: Divide and Conquer. The idea is to design a network as a sequence of layers, or abstract machines, each one based upon the previous one. . . . This book uses a model in which networks are divided into seven layers. The structure of the book follows the structure of the model to a considerable extent.'
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Wilson, Colin, The Outsider, Tarcher 1987 'The seminal work on alienation, creativity, and the modern mind-set. "An exhaustive, luminously intelligent study. . . a real contribution to our understanding of our deepest predicament."—Philip Toynbee.'
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Papers

Landauer, Rolf, "Information is a physical entity", Physica A, 263, 1, 1 February 1999, page 63-7. 'This paper, associated with a broader conference talk on the fundamental physical limits of information handling, emphasizes the aspects still least appreciated. Information is not an abstract entity but exists only through a physical representation, thus tying it to all the restrictions and possibilities of our real physical universe. The mathematician's vision of an unlimited sequence of totally reliable operations is unlikely to be implementable in this real universe. Speculative remarks about the possible impact of that, on the ultimate nature of the laws of physics are included.'. back

Links

Brendan Byrne, 'War on business' rhetoric echoes '07 union bashing, 'The contentious Dyson Royal Commission, while turning up significant examples of corruption within the union movement, also singularly failed to apply the lesson of history provided by the Costigan Royal Commission: that corruption within the union movement does not operate in a vacuum, and occurs both in parallel with, and as a reflection of, corruption within the business community. Unlike the Costigan Commission, however, the Dyson Commission didn't turned up any 'bottom of the harbour' scandals with which to vex the business world — precisely because its terms of reference didn't allow it to go there.' back

Emmylou Harris, Dolly Parton, Linda Ronstadt, Neil Young, Across the Border, 'A beautiful Bruce Springsteen song, done wonderfully by Linda, Emmylou, and Neil. Neil's harmonica work is killer. The guitar work is very nice, too. I think it's Bernie Leadon, formerly of the Eagles and other groups, but I'm not positive. From the "Western Wall: Tucson Sessions" album (vastly underrated, by the way.) back

Henry Ford - Wikipedia, Henry Ford - Wikipedia, the free encyclopedia, 'Henry Ford (July 30, 1863 – April 7, 1947) was an American industrialist, the founder of the Ford Motor Company, and sponsor of the development of the assembly line technique of mass production. His introduction of the Model T automobile revolutionized transportation and American industry. As owner of the Ford Motor Company, he became one of the richest and best-known people in the world. He is credited with "Fordism": mass production of inexpensive goods coupled with high wages for workers. Ford had a global vision, with consumerism as the key to peace.' back

Observable - Wikipedia, Observable - Wikipedia, the free encyclopedia, 'In physics, particularly in quantum physics, a system observable is a measurable operator, or gauge, where the property of the system state can be determined by some sequence of physical operations. For example, these operations might involve submitting the system to various electromagnetic fields and eventually reading a value. In systems governed by classical mechanics, any experimentally observable value can be shown to be given by a real-valued function on the set of all possible system states.' back

Peter Reith, Why is Abbott so spooked by the WorkChoices bogeyman, 'It was good that Abbott publicly called for the business community to make the case for reform. I hope he means it. Since that call, the voices from business have been growing louder. Prime Minister Julia Gillard's retrograde changes to workplace relations law are slowly burning our economy and in time the voices of embattled business will be heard across the country.' back

Rolf Landauer , Information is a Physical Entity, 'Abstract: This paper, associated with a broader conference talk on the fundamental physical limits of information handling, emphasizes the aspects still least appreciated. Information is not an abstract entity but exists only through a physical representation, thus tying it to all the restrictions and possibilities of our real physical universe. The mathematician's vision of an unlimited sequence of totally reliable operations is unlikely to be implementable in this real universe. Speculative remarks about the possible impact of that on the ultimate nature of the laws of physics are included.' back

Self-adjoint operator, Self-adjoint operator, ' In mathematics, a self-adjoint operator on a complex vector space V with inner product ⟨ ⋅ , ⋅ ⟩ . . . is a linear map A (from V to itself) that is its own adjoint: ⟨ A v , w ⟩ = ⟨ v , A w ⟩ . . . If V is finite-dimensional with a given orthonormal basis, this is equivalent to the condition that the matrix of A is Hermitian, i.e., equal to its conjugate transpose A*. By the finite-dimensional spectral theorem, V has an orthonormal basis such that the matrix of A relative to this basis is a diagonal matrix with entries in the real numbers. In this article, we consider generalizations of this concept to operators on Hilbert spaces of arbitrary dimension.' back

Stephen King, For the English, Brexit will mean economic pain, 'So expect a rocky economic road ahead for England. To paraphrase Winston Churchill, the trouble with committing economic suicide is that you live to regret it.' back

Thomas Instituut te Utrecht (Tilberg University), About the Institute, 'The Thomas Instituut te Utrecht (Tilburg University) is a co-operative group of theologians, philosophers and historians from several universities and institutes in the Netherlands, specialised in the study of the work of Saint Thomas Aquinas (1225-1274). The institute was founded more than twenty years ago (see the History of the institute) and has been an official research institute of the former Catholic Theological University at Utrecht since 1996. In 2000 it became an interuniversity institute in combination with the Tilburg Faculty of Theology. Since 2007 the Thomas Instituut te Utrecht is located at the Tilburg School of Theology, which is a faculty of Tilburg University.' back

USSG - Indiana University, ISO/OSI Network Model, 'The standard model for networking protocols and distributed applications is the International Standard Organization's Open System Interconnect (ISO/OSI) model. It defines seven network layers: Layer 1 - Physical ... Layer 2 - Data Link ... Layer 3 - Network ...Layer 4 - Transport ... :ayer 5 - Session ... Layer 6 - Presentation ... Layer 7 - Application back