Notes

[Notebook Turkey, DB 55]

[Sunday 27 January 2002 - Saturday 2 February 2002]

[page 33]

Sunday 27 January 2002

Monday 28 January 2002

The Tao of physics seems to spend most of its time tilting at paper tigers constructed by asserted misunderstandings of history. Capra. It seems that human intellectual development, properly understood, follows a pretty straight course. Most of the claims and counterclaims made by schools of thought are just eddies in the flow. There seems to have been enough coupling between east and west (and north and south, etc etc) (at least at the level of those wealthy enough to read, travel, etc) to keep the ideas of the world more or less in synch.

Capra asserts that he and his kind are the vanguard of a new style of thought which is in fact thousands of years old. We call it rationalism, or idealism, trying to discern the structure of the world by reflecting on the structure of mind and knowledge. In the tradition I am following, Lonergan is one of the most recent examples of this, but his work is less enlightening than the mathematical modelling approach to knowledge which we are trying to capture with the transfinite network. It is becoming clearer that the next developments on my path will come from a closer study of

[page 34]

structures in Hilbert space. Here, by studying the structure and composition of transfinite Hilbert spaces we hope to arrive at a comprehensive metaphysics, that is a general heuristic structure for the whole Universe, ie a model of god which, by determination of the actual structures that are realized, gives us a model of this world, at the same time as showing us the possibilities that might exist in other worlds. Lonergan, Hilbert space - Wikipedia

The relationship between non-relativistic QM and spacetime, which remains problematic in quantum field theory, may yield to this approach, showing that General Relativity exists at the complex, rather than at the simple end of the spectrum, ie while QM is countable, GR exists at the highest level of uncountability.

ie can we construct QM on the basis of 'wavefunctions' whose domain and range are natural (rational) numbers, ie complex operators based on x + iy where x and y are rational rather than real?

The current argument fir the divinity of the Universe is based on cardinal numbers. The quantum field theory version must be based on ordinal numbers. Here Hilbert space comes into play in its ordinal rather than its cardinal structure. We are in the dark again.

Tuesday 29 January 2002

A hopeless feeling arises when one sees how fluffy the professionals seem to be. One gets the feeling of drug fucked Californian dreaming where one would like to see a more definite program of human development for peace and prosperity.

Particularly upsetting is the claim for the absolute truth of mysticism, which lies at the root of the religious claim to the lives of its followers, rather than recognition that all human mental systems are merely adaptations to the environment, into which we are born, and something that must change if the environment (society) is to change as parts must change to adapt to changing wholes (and vice versa).

[page 35]

Perhaps what upsets me most about Capra is the weakness with which the case for holism is made, without recognizing the importance of superposition and entanglement (perhaps justifiably since quantum information theory did not take off till Deutsch 1984). Deutsch. These matters are still ignored in the afterword to the fourth edition, which is less excusable. This is the clue which we must follow up, and perhaps look for the link to special and general relativity in entanglement.

When I get home I must go back to the theory of functions and Hilbert spaces while edging forward into the darkness that surrounds me. The challenge is not to pick holes in Capra but to do better, which means a continual shuffling of my feelings for the whole in order to find the parts than consistently go together to create it. The simplest Hilbert space is the complex plane, and the constitution of the whole comprises a union of an infinity of examples of this plane.

Wednesday 30 January 2002

Thursday 31 January 2002

Rights without power are meaningless.

Cyberalms.org: will it work? The first step is to establish the facility for entropy increase, and then see if it increases. How does the cyberalms.org facility relate to Caratheodory's theorem?

Friday 1 February 2002

Saturday 2 February 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!)

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   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   Amazon   back

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  Amazon   back

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.  Amazon   back

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   Amazon   back

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.  Amazon   back

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.'  Amazon   back

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. ...'  Amazon   back

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