"natural theology > notes > 2013 > Sunday 27 January 2013"

vol VII: Notes

2013

Notes

[Sunday 27 January 2013 - Saturday 19 January 2013]

[Notebook: DB 74 CREATION]

[page 80]

Sunday 27 January 2013

My communication with Aristotle is made possible by the asynchronous nature of fixed points. This communication works in only one direction (A to me).

We combine an insight by Aristotle with a theorem by Brouwer.

Monday 28 January 2013

Why is quantum mechanics linear and gravitation non-linear? How does energy couple to energy, money couple to money? [It seems that gravitation is more complex than quantum mechanics, and so must be built on quantum mechanics]

Complex exponentials vs real exponentials?

Tuesday 29 January 2013

The space of Gödel numbers is exponentially larger than (transfinite with respect to) the space numbers and may be seen as the conscious space relative to the space of which it is conscious, having sufficient variety to control the subject space. [the distinction between discrete and continuous is a matter of cybernetics]

[page 81]

Cantor changed the search for understanding of the continuum from geometrical infinitesimals to arithmetical infinities, a change of emphasis that gave us an arithmetic way to understand Dirac's delta.

Perhaps many deficiencies in my sexual relationships an be attributed to a greatly controlled relationship with girls in my years of puberty. I attended all boys catholic colleges from grade five on, and I remember my terror when friends introduced me to a beautiful potential partner [for the prefects ball]. I shied off and attended the prefects ball unaccompanied, a significant faux pas in many dimensions. From there I entered the monastery having had no girlfriend beyond a crush on a young woman who used to come to the same Catholic Church. It may have encouraged me to go to mass every morning in the hope of seeing her. Ultimately my sexuality saved me from the Monastery because I fell in love with some of the brethren and we were is such close proximity to our teachers and mentors that there is little chance of not being discovered. I was fairly pen, inviting my loves to take science lessons or some other approved pursuit in order to spend time together. In addition an overt reason for dismissing me, I was objecting to some of the philosophical and theological doctrines that I was required to learn, I felt that my grounds were good and that my questions were not so much designed to create difficulties for my teachers as a genuine need to know.

Most of my sensual experiences has come from wrestling other boys, since fighting seems to be something of a universal cover for sensuality in those societies that proscribe sensual contact.

[page 82]

We might say that all the action in physics, mathematics and logic takes place between sets of countable and uncountable cardinality. Symmetry with repsect to cardibnality means that this duality is repeated at all cardinal levels, aleph(n) being in effect countable and aleph(n+1) uncountable with the variety necessary to conrol the elements of aleph(n) so that they are orthogonal.

CYBERNETICS - ORTHOGONALITY

Wednesday 30 January 2013

Thursday 31 January 2013

I ended my monastic career with heterosexual motivation and no sexual desire toward children that seems to have affected many celibate clergy, a fortunate outcome. The whole experience did leave me with a clear understanding of the political motivations of the Church in requiring its servants to become drones by vowing themselves to poverty, chastity and obedience and the conviction that in a reasonable religion workers should not be subject to any such restrictions but enjoy full human rights to reproduce, earn a living an make their own decisions.

Hoping to complete Unreasonable Effectiveness soon.

Friday 1 February 2013

Each layer is a 'carrier wave' for the layer above it, and the carrier is modulated by the higher (signalling) layer. We tend to think of waves and modulation as continuous functions, but they are really a statityical envelope in which we see a lot of discrete actions

[page 83]

occurring with different frequencies in random (continuous) or coupled (discrete) relationships to one another. When we listen to a digital computer we observe many different frequencies, just as we observe when we listen to an atom (using a spectrometer). Spectrometer - Wikipedia

The difference between continuous and discrete is obvious when we look at the world. Some things, like fog, have no discernible structure, others, like landscapes, are structured in endless detail.

There appears to be a tendency for physical theories to become more complex the further they reach back in time. This is counterintuitive, since a complexifying Universe looks simple as we go back in time toward the beginning of time, the initial singularity. So perhps modern theorists are looking the wrong way and physics should be getting simpler as we go back. The transfinite computer network modified by Landauer's hypothesis shows how to do it.

Since sets are [per se] symmetrical with respect to complexity, there is no was one can determine the 'cardinal of the continuum' with set theory alone, and we can think of a continuum as simply something unresolved which may then be resolved into two, 3, 4, . . . points, that is non overlapping or orthogonal points/states.

All processes are periodic [except perhaps the life of the Universe as a whole], even if the steps do not follow one another deterministically (and here memory steps in to create order because now things an wait for one another rather than have to be carefully synchronized).

[page 84]

So we look for logical processes whose statistical envelope is described by quantum theory.

The two slit experiment shows how spacing modulates timing; but maybe in reality timing is everything as it is in quantum mechanics, the one dimensional field theory.

The better you debug things the more stable they are holds for milk and software, food preservation and deterministic process.

Saturday 2 February 2013

End of story. I look at my thousands of books and feel that they have nothing more to tech me. After nearly seventy years of absorbing the thoughts of others I am on my own, but have I got anything to say? It is to some extent a tangled bank in my mind with a few overriding themes, divine simplicity, divine complexity, love, fate, the human condition. Now, after putting off the moment for so long, I feel that I can write something to justify my existence, that is to contribute substantially to my understanding of myself as a element of a divine creative Universe, By creatively misunderstanding everything I have read, I hope to create something new and valuable, an understanding of the complexification of pure action that began with the Christian doctrine of the Trinity. If experience is any guide, as soon as I begin

[page 85]

writing new difficulties will crop ut, but it seems to me now that my story has enough momentum to carry through these to a new point of view of hte Universe.

Momentum measures structure, big integrated structure = big momentum. Since motin is relative, momentum is in a sense independent of motion and equivalent to mass, which is in tern a measure dynamism, the energy or rate of action. Momentum is a spatial version of the rate of action, energy a temporal version, and energy and momentum transform as time and space.

Tranquillity - residing in one's own fixed point, home, my castle.

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Ashby, W Ross, An Introduction to Cybernetics, Methuen 1964 'This book is intended to provide [an introduction to cybernetics]. It starts from common-place and well understood concepts, and proceeds step by step to show how these concepts can be made exact, and how they can be developed until they lead into such subjects as feedback, stability, regulation, ultrastability, information, coding, noise and other cybernetic topics'
Amazon back

Bell, John S, Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press 1987 Jacket: JB ... is particularly famous for his discovery of a crucial difference between the predictions of conventional quantum mechanics and the implications of local causality ... This work has played a major role in the development of our current understanding of the profound nature of quantum concepts and of the fundamental limitations they impose on the applicability of classical ideas of space, time and locality.
Amazon back

Capra, Fritjof, The Tao of Physics: An exploration of the parallels between modern physics and Eastern mysticism, Shambala 1991 Amazon.com: 'First published in 1975, The Tao of Physics ... still stands up to scrutiny, explicating not only Eastern philosophies but also how modern physics forces us into conceptions that have remarkable parallels. Covering over 3,000 years of widely divergent traditions across Asia, Capra can't help but blur lines in his generalizations. But the big picture is enough to see the value in them of experiential knowledge, the limits of objectivity, the absence of foundational matter, the interrelation of all things and events, and the fact that process is primary, not things. Capra finds the same notions in modern physics. ...' Brian Bruya
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Christie, Agatha, Murder at the Vicarage, Dodd Mead 1986 Amnazon customer review: 'Murder at the Vicarage, first published in 1930, is the book that first introduced the world to Miss Jane Marple and the cozy English village of St. Mary Mead. Every mystery fan in the world is or should be familiar with Christie's classic character of Miss Marple. This book presents her at her best and is required reading for any mystery fan. The writing is sharp, the plotting crisp and clever, there are many red herrings and the solution is very satisfying. This is Christie at her very best. Highly recommended.' Lisa Bahrami
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Feynman, Richard P, and Albert P Hibbs, Quantum Mechanics and Path Integrals, McGraw Hill 1965 Preface: 'The fundamental physical and mathematical concepts which underlie the path integral approach were first developed by R P Feynman in the course of his graduate studies at Princeton, ... . These early inquiries were involved with the problem of the infinte self-energy of the electron. In working on that problem, a "least action" principle was discovered [which] could deal succesfully with the infinity arising in the application of classical electrodynamics.' As described in this book. Feynam, inspired by Dirac, went on the develop this insight into a fruitful source of solutions to many quantum mechanical problems.
Amazon back

Hallett, Michael, Cantorian set theory and limitation of size, Oxford UP 1984 Jacket: 'This book will be of use to a wide audience, from beginning students of set theory (who can gain from it a sense of how the subject reached its present form), to mathematical set theorists (who will find an expert guide to the early literature), and for anyone concerned with the philosophy of mathematics (who will be interested by the extensive and perceptive discussion of the set concept).' Daniel Isaacson.
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Kreyszig, Erwin, Introductory Functional Analysis with Applications, John Wiley and Sons 1989 Amazon: 'Kreyszig's "Introductory Functional Analysis with Applications", provides a great introduction to topics in real and functional analysis. This book is part of the Wiley Classics Library and is extremely well written, with plenty of examples to illustrate important concepts. It can provide you with a solid base in these subjects, before one takes on the likes of Rudin and Royden. I had purchased a copy of this book, when I was taking a graduate course on real analysis and can only strongly recommend it to anyone else.' Krishnan S. Kartik
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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'
Amazon back

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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Schiff, Leonard I, Quantum Mechanics, McGraw-Hill 1968 Preface: 'This volme has a threefold purpose: to explain the physical concepts of quantum mechanics, to describe the mathematical formalism, and to provide illustrative examples of both the ideas and the methods.'
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Veltman, Martinus, Diagrammatica: The Path to the Feynman Rules, Cambridge University Press 1994 Jacket: 'This book provides an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics. The aim is to make clear what the physical foundations of present-day field theory are, to clarify the physical content of Feynman rules, and to outline their domain of applicability. ... The book includes valuable appendices that review some essential mathematics, including complex spaces, matrices, the CBH equation, traces and dimensional regularization. ...'
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Papers

d'Espagnat, Bernard, "Quantum theory and reality", Scientific American, 241, 5, November 1979, page 128-140. 'Most particles or aggregates of particles that are ordinarily regarded as separate objects have interacted at some time in the past with other objects. The violation of separability seems to imply that in some sense all these objects constitute an indivisible whole. Perhaps in such a world the concept of an independently existing reality can reatain some meaning, but it will be an altered meaning and one remove from everyday experience.' (page 140). back

Deutsch, David, "Quantum theory, the Church-Turing principle and the universal quantum computer", Proceedings of the Royal Society of London, , A 400, 1985, page 97-117. 'It is argued that underlying the Church-Turing hypothesis there is an implicit physical assertion. Here this assertion is presented explicitly as a physical principle: 'every finitely realizible physical system can be perfectly simulated by a universal model computing machine operating by finite means'.'. back

Gruber, Nicolas, James N Galloway, "An earth-system perspective of the global nitrogen cycle", Nature, 451, 7176, 17 Janurary 2008, page 293 - 296. 'With humans having an increasing impact on the planet, the interactions between the nitrogen cycle, the carbon cycle and climate are expected to become an increasingly important determinant of the Earth system.'. back

Heimann, Martin, Markus Reichstein, "Terrestrial ecosystem carbon dynamics and climate feedbacks", Nature, 451, 7176, 17 Janurary 2008, page 289-292. 'Recent evidence suggests that, on a global scale, terrestrial ecosystems will provide a positive feedback in a warming world, albeit of uncertain magnitude.'. back

Kump, Lee R, "The rise of atmospheric oxygen", Nature, 451, 7176, 17 Janurary 2008, page 277-278. 'Clues from ancient rocks are helping to produce a coherent picture of how Earth's atmosphere changed from one that was almost devoid of oxygen to one that is one-fifth oxygen.'. back

Pan, Jian-Wei, et al, "Experimental test of quantum nonlocality in three-photon Greenberger_horne-Zeilinger entanglement", Nature, 403, 6769, 3 February 2000, page 515-519. 'The results of three specific experiments, involving measurements of polarisation correlations between three photons lead to predictions for a fourth experiment; quantum physical predictions are mutually contradictory with expectations based on local realism. We find the results of the fourth experiment to be in agreement with the quantum prediction and in striking conflict with local realism'. back

Links

Bra-Ket notation - Wikipedia Bra-Ket notation - Wikipedia, the free encyclopedia 'Bra-ket notation is the standard notation for describing quantum states in the theory of quantum mechanics. It can also be used to denote abstract vectors and linear functionals in pure mathematics. It is so called because the inner product (or dot product) of two states is denoted by a bracket, , consisting of a left part, , called the ket. The notation was invented by Paul Dirac, and is also known as Dirac notation.' back

Hilbert space - Wikipedia Hilbert space - Wikipedia, the free encyclopedia 'The mathematical concept of a Hilbert space (named after the German mathematician David Hilbert) generalizes the notion of Euclidean space in a way that extends methods of vector algebra from the two-dimensional plane and three-dimensional space to infinite-dimensional spaces. In more formal terms, a Hilbert space is an inner product space — an abstract vector space in which distances and angles can be measured — which is "complete", meaning that if a sequence of vectors approaches a limit, then that limit is guaranteed to be in the space as well.' back

Spectrometer - Wikipedia Spectrometer - Wikipedia, the free encyclopedia 'A spectrometer (spectrophotometer, spectrograph or spectroscope) is an instrument used to measure properties of light over a specific portion of the electromagnetic spectrum, typically used in spectroscopic analysis to identify materials.' back