VII Notes
2010
Notes
[Sunday 17 October 2010 - Saturday 23 October 2010]
[Notebook: DB 70 Mathematical Theology]
[page 114]
Sunday 17 October 2010
A symbol has a lifetime and the longer it lives (the greater its space-time volume) the more precisely it is defined.
Pétrement page 230: Weil: '"To my mind it is not events which make the revision of Marxism a necessity; it is Marx's doctrine, which because of the gaps and inconsistencies it contains, is and has always been far inferior to the role people
wanted to make it play. Which does not mean that then or since has anything better been thought of."' Pétrement
page 239: 'Simone and Mme Weil spent ten days at Solesmes, from Palm Sunday to the Tuesday of Easter week. Mme Weil did not attend all the services but Simone did. Some people were amazed; they said to Mme Weil, "She is not a Catholic and yet she goes to all the services more faithfully than anyone else."'
'Later she wrote to Father Perrin: "I was suffering from splitting headaches; each second hurt me like a blow; by an extreme effort of concentration I was able to rise above this wretched flesh, to leave it to suffer by itself, heaped up in a corner and to find pure and perfect joy in the unimaginable beauty of the chanting and the words. This experience enabled me by analogy to get a better understanding of the possibility of divine love in the midst of affliction. It goes without saying that in the course of the services the thought of the Passion of Christ entered into my being once and for all."'
page 322: Weil: '"My own feeling was that once a certain class of people has ben placed by the temporal and spiritual authorities outside the ranks pf those whose life has value, then nothing comes more naturally to men than to kill. . . ."'
We might say that in general quantum mechanics predicts the probability of connection between two states.
Pétrement page 337: André Weil - Bourbaki Nicholas Bourbaki - Wikipedia
Monday 18 October 2010
[page 116]
The basic approach to conflict resolution, that is the removal of contradiction, is the increase of the resource at the centre of the conflict, as predicted by Cantor'd theorem and touched upon rather dimly in the theory of peace. [A theory of peace] We increase resources basically by ordering as suggested by our ability to express and manipulate much greater numbers by position significant representation rather than simply by one to one correspondences as we find, for instance, by representing the count of one's sheep by the number of stones in a bag or repeated identical symbols on paper.In argument this approach is represented by the dictum oportet distinguere, that is we must ultimately produce a phase space of the same entropy ss the system to be represented if we are to produce a map that truly corresponds to reality.
SHAME <--> CONTROL
SHAMELESS <--> FREE
Tuesday 19 October 2010
Wednesday 20 October 2010
Pétrement page 344: '[Simone] told [David Garnett] that after reading The Seven Pillars of Wisdom she had immediately recognized that Lawrence is the only famous man, not only in our times but so far as she knew, of all times, whom she could wholeheartedly love and admire.'
Moses Mendelson Moses Mendelssohn - Wikipedia
Thursday 21 October 2010
Friday 22 October 2010
[page 117]
ENERGY = FREQUENCY = 'rate of rotation' = dφ / dt
ACTION = ∫ E dt = total number of turns = φ.
Energy is conserved. Action is conserved. Momentum is conserved. [Assume the foundation of these conservation is conservation of action which appers in the time domain as conservation of energy and in the space domain as conservation of momentum]
We interpret energy as processing rate and action as total quantity of process, turns of Feynman's little arrow. Feynman [action is an 'affine parameter'?]
Feynman applied this idea in the path integral to compute the probability of getting from |a> to |b>. How do we get from path integral to Feynman diagram? Veltman Veltman
Heinrich Zille Heinrich Zille - Wikipedia
Käthe Kollwitz Käthe Kollwitz - Wikipedia
NETWORKS are naturally PERTURBATIVE - each message I receive perturbs me more or less, as I stand at my point in the universal network.
Saturday 23 October 2010
Mathematics of quantum mechanics has no intrinsic meaning, but physics gives meaning to this formalism, first via the relationship between action, energy and frequency.
All capital investment is an act of faith, or is it hope - will it repay itself or is the investment going to be lost. This work is in a sense an investment of my life's energy (apart from all the other things I do) which I hope will in the long run . . . yield a manyfold payoff.
So we can say the mathematics of quantum mechanics has
[page 118]
a life of its own independent of physics, even though it might have been inspired by physics. Dirac, von Neumann, Nicholas Bourbaki - Wikipedia Tymoczko
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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!)
Cantor, Georg, Contributions to the FoundinCantorg of the Theory of Transfinite Numbers (Translated, with Introduction and Notes by Philip E B Jourdain), Dover 1955 Jacket: 'One of the greatest mathematical classics of all time, this work established a new field of mathematics which was to be of incalculable importance in topology, number theory, analysis, theory of functions, etc, as well as the entire field of modern logic.'
Amazon
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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).
Amazon
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Dirac, P A M, The Principles of Quantum Mechanics (4th ed), Oxford UP/Clarendon 1983 Jacket: '[this] is the standard work in the fundamental principles of quantum mechaincs, indispensible both to the advanced student and the mature research worker, who will always find it a fresh source of knowledge and stimulation.' (Nature)
Amazon
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Feynman, Richard, QED: The Strange Story of Light and Matter, Princeton UP 1988 Jacket: 'Quantum electrodynamics - or QED for short - is the 'strange theory' that explains how light and electrons interact. Thanks to Richard Feynmann and his colleagues, it is also one of the rare parts of physics that is known for sure, a theory that has stood the test of time. ... In this beautifully lucid set of lectures he provides a definitive introduction to QED.'
Amazon
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Mead, Margaret, Blackberry Winter, Peter Smith Publishers 1989 Amazon: Editorial Review 'During her lifetime, Margaret Mead (1901-78) was the world's most famous anthropologist. In this insightful memoir, she recalls her childhood, her place in her family, and how the lessons learned and ideals instilled then shaped her life. ... In Blackberry Winter, she reflects on her life and work, through three marriages and ground-breaking fieldwork in eight cultures. But perhaps her most fascinating revelations are the "gathered threads" of her own experience of childhood, motherhood, and grandparenthood. From her observations of sex roles, childhood, and parenting styles in other cultures, her appreciation of her own upbringing, and her shift to single, working motherhood after the break-up of her third marriage, she anticipated and pioneered a new model for family life. ... ' Lynne Auld
Amazon
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| Pétrement, Simone, and Raymond Rosenthal (translator), Simone Weil: A Life, Schocken
1988 Jacket: 'A French Jew who broke with Judaism and wavered on the edge of Roman Catholicism, the daughter of a respected physician, the sister of one of the century's greatest mathematicians, Simone Weil devoted her life to the search for truth and God amid the poverty and misery of the poor.
Since her death in 1943 at the age of thirty-four, Simone Weil has become a person of legend. T S Eliot, Dwight Macdonald, Leslie Fiedler and Robert Coles spoke of her as the saint of the twentieth century who lived the contradictions of our era more intensely and continuously than anyone else.'
Amazon
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Reid, Constance, Hilbert-Courant, Springer Verlag 1986 Jacket: '[Hilbert] is woven out of three distinct themes. It presents a sensitive portrait of a great human being. It describes accurately and intelligibly on a non-technical level the world of mathematical ideas in which Hilbert created his masterpieces. And it illuminates the background of German social history against which the drama of Hilbert's life was played. ... Beyond this, it is a poem in praise of mathematics.' Science
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Tymoczko, Thomas, New Directions in the Philosophy of Mathematics: An Anthology, Princeton University Press 1998 Jacket: 'The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. ... By bringing together essays of leading philosophers, mathematicians, logicians and computer scientists, TT reveals an evolving effort to account for the nature of mathematics in relation to other human activities.'
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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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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.'
Amazon
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Papers
| Babaev, Egor, Asle Sudbo, N W Ashcroft, "A superconductor superfluid phase transition in liquid metallic hydrogen", Nature, 431, 7009, 7 October 2004, page 666-668. Abstract: 'Although hydrogen is the lightest of atoms, it does not form the simplest of solids or liquids. Quantum effects in these phases are considerable (a consequence of the light proton mass) and they have a demonstrable and often puzzling influence on many physical proerties, including spatial order. ...'. back |
Links
| Heinrich Zille - Wikipedia Heinrich Zille - Wikipedia, the free encyclopedia 'Rudolf Heinrich Zille (January 10, 1858 - August 9, 1929), German illustrator and photographer, was born in Radeburg near Dresden, as the son of watchmaker Johann Traugott Zill (Zille since 1854) and Ernestine Louise (born Heinitz). In 1867, his family moved to Berlin, where he finished school in 1872 and started an apprenticeship as a lithographer.' back |
| Käthe Kollwitz - Wikipedia Käthe Kollwitz - Wikipedia, the free encyclopedia 'Käthe Schmidt Kollwitz (July 8, 1867 – April 22, 1945) was a German painter, printmaker, and sculptor whose work offered an eloquent and often searing account of the human condition in the first half of the 20th century. Her empathy for the less fortunate, expressed most famously through the graphic means of drawing, etching, lithography, and woodcut, embraced the victims of poverty, hunger, and war. Initially her work was grounded in Naturalism, and later took on Expressionistic qualities back |
| Moses Mendelssohn - Wikipedia Moses Mendelssohn - Wikipedia, the free encyclopedia 'Moses Mendelssohn (6 September 1729 – 4 January 1786) was a German Jewish philosopher to whose ideas the renaissance of European Jews, Haskalah (the Jewish Enlightenment) is indebted. He has been referred to as the father of Reform Judaism.
Born to a poor Jewish family in Dessau and originally destined for a rabbinical career, Mendelssohn educated himself in German thought and literature and from his writings on philosophy and religion came to be regarded as a leading cultural figure of his time by both Germans and Jews. He also established himself as an important figure in the Berlin textile industry, which was the foundation of his family's wealth.
Moses Mendelssohn's descendants include the composers Fanny and Felix Mendelssohn and the founders of the Mendelssohn & Co. banking house.' back |
| Nicholas Bourbaki - Wikipedia Nicholas Bourbaki - Wikipedia, the free encyclopedia 'Nicolas Bourbaki is the collective pseudonym under which a group of (mainly French) 20th-century mathematicians wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. With the goal of founding all of mathematics on set theory, the group strove for rigour and generality. Their work led to the discovery of several concepts and terminologies still discussed.' back |
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